BACK TO BENTHAMEXPLORATIONS OF EXPERIENCED UTILITY

DANIEL KAHNEMAN

PETER P WAKKER

RAKESH SARIN

Two core meanings of ldquoutilityrdquo are distinguished ldquoDecision utilityrdquo is theweight of an outcome in a decision ldquoExperienced utilityrdquo is hedonic quality as inBenthamrsquos usage Experienced utility can be reported in real time (instant utility)or in retrospective evaluations of past episodes (remembered utility) Psychologi-cal research has documented systematic errors in retrospective evaluationswhich can induce a preference for dominated options We propose a formal norma-tive theory of the total experienced utility of temporally extended outcomes Mea-suring the experienced utility of outcomes permits tests of utility maximizationand opens other lines of empirical research

INTRODUCTION

The concept of utility has carried two quite different mean-ings in its long history As Bentham [1789] used it utility refersto pleasure and pain the ldquosovereign mastersrdquo that ldquopoint outwhat we ought to do as well as determine what we shall dordquo Thisusage was retained in the economic writings of the nineteenthcentury but it was gradually replaced by a different interpreta-tion [Stigler 1950] In current economics and in decision theorythe utility of outcomes and attributes refers to their weight indecisions utility is inferred from observed choices and is in turnused to explain these choices To distinguish the two notions weshall refer to Benthamrsquos concept as experienced utility and to themodern usage as decision utility With few exceptions1 experi-enced utility is essentially ignored in modern economic discourseThe rejection of experienced utility is justied by two standardarguments (i) subjective hedonic experience cannot be observedor measured (ii) choices provide all necessary information aboutthe utility of outcomes because rational agents who wish to do sowill optimize their hedonic experience Contrary to this position

This work is dedicated to the memory of Amos Tversky We are grateful tomany friends and colleagues who commented on earlier versions Special thanksare due to Peter Diamond and David Laibson The usual caveats apply

1 For some recent attempts to use subjective measures in economic analy-ses see Clark and Oswald [1994] Kapteyn [1994] Tinbergen [1991] and vanPraag [1991]

q 1997 by the President and Fellows of Harvard College and the Massachusetts Instituteof TechnologyThe Quarterly Journal of Economics May 1997

we will argue that experienced utility is both measurable and em-pirically distinct from decision utility

The following example illustrates the distinction between thetwo concepts of utility2 A patient suffering from unusually pro-found amnesia has two toasters in his kitchen The toaster on theright functions normally The toaster on the left delivers an elec-tric shock when the toast is removed The patientrsquos gasp andquick retraction of his hand indicate that the shock is painfulBecause the patient does not remember the experience howeverhe does not anticipate the shock the next morning and is conse-quently indifferent between the toasters The patientrsquos decisionutility for using the two toasters is equal but his experiencedutilities are quite different The patientrsquos choices of the left-handtoaster will not maximize utility in Benthamrsquos sense As we willshow later discrepancies between decision utility and experi-enced utility are not restricted to such pathological cases Sys-tematic errors in the evaluation of past events and decisions thatdo not maximize future experienced utility can be observed indecision makers whose cognitive functions are normal These ob-servations raise doubts about a methodology in which observedchoices provide the only measure of the utility of outcomes

Pleasure and displeasure are attributes of each moment ofexperience but the outcomes that people value are normally ex-tended over time The basic building block of experienced utilityin our analysis is instant utility a measure of hedonic and af-fective experience which can be derived from immediate reportsof current subjective experience or from physiological indices In-stant utility corresponds to the dimension of ldquointensityrdquo in thewritings of Bentham Jevons and Edgeworth The focus of ouranalysis is the evaluation of temporally extended outcomes(TEOs) such as a single medical procedure or the concatenationof a Kenya safari and subsequent episodes of slide-showing andstorytelling Two measures of the experienced utility of tempo-rally extended outcomes will be considered Remembered utilityis a measure on past TEOs which is inferred from a subjectrsquosretrospective reports of the total pleasure or displeasure associ-ated with past outcomes Total utility is a normative concept It isa measure on possible TEOs which is constructed from temporalproles of instant utility according to a set of normative rulesDecision utility is a measure on TEOs which is inferred fromchoices either by direct comparisons of similar objects or by indi-

2 This example was suggested by Paul Romer

QUARTERLY JOURNAL OF ECONOMICS376

rect methods such as elicited willingness to pay Finally we willdiscuss predicted utility which refers to beliefs about the experi-enced utility of outcomes The relations among the various utilityconcepts dene a complex agenda for research Figure I lists someof the questions that arise Several of these questions will be ad-dressed here

Section I discusses the adaptive signicance and the mea-surement of instant and remembered utility Section II describesstudies in which participants provided a continuous record of in-stant utility during an episode (eg a short lm or a medicalprocedure) and later reported a global evaluation of the episode(remembered utility) or made choices about which of several epi-sodes to repeat (decision utility) These studies are concernedwith the determinants of remembered utility (question 4 in Fig-ure I) and with the role of remembered utility in choice (8) Theduration of episodes played very little role in subjectsrsquo retrospec-tive evaluations in these experiments contrary to an obviousnormative rule (5) Subjects also made choices that exposedthem to avoidable pain or discomfort in violation of dominanceTheir decisions did not maximize experienced utility (9) al-though they may have maximized remembered utility (10)

Section III and the Appendix present a normative theory oftotal utility which yields rules for the evaluation of temporallyextended outcomes on the basis of a temporal prole of instantutility (3) The theory assumes time-neutral weighting of in-stants (no time preference) and derives temporal integration asthe principle of global evaluation Section IV elaborates on theconsequences of accepting experienced utility as a measure of thequality of outcomes distinct from decision utility The sectionalso includes a brief review of some results concerning the accu-racy of predicted utility (6) Section V concludes Proofs are pre-sented in the Appendix

An important reservation should be stated early Our norma-tive treatment of the utility of temporally extended outcomesadopts a hedonic interpretation of utility but no endorsement ofBenthamrsquos view of pleasure and pain as sovereign masters of hu-man action is intended Our analysis applies to situations inwhich a separate value judgment designates experienced utilityas a relevant criterion for evaluating outcomes3 This set does notinclude all human outcomes but it is certainly not empty

3 For more comprehensive conceptions of the quality of life see Dasgupta[1993] Nussbaum and Sen [1993] and Sen [1991]

BACK TO BENTHAM 377

FIGURE IResearch Designs for the Study of Experienced Utility

QUARTERLY JOURNAL OF ECONOMICS378

I THE FUNCTIONS OF EXPERIENCED UTILITY

We have distinguished two descriptive notions of experiencedutility instant utility is the pleasure or distress of the momentremembered utility is the retrospective evaluation of a tempo-rally extended outcome This section presents a brief introductionto the biology and psychology of these forms of utility and to someissues of measurement

The adaptive functions of pleasure and pain can be deducedfrom the conditions under which these experiences are biologi-cally programmed to occur Pleasure is evidently a ldquogordquo signalwhich guides the organism to continue important activities suchas foreplay or consuming sweet energy-rich food Pain is a ldquostoprdquosignal which interrupts activities that are causing harm such asplacing weight on a wounded foot The common characteristic ofthe basic forms of pleasure and distress is that they regulate theresponse to the current situation

To achieve its function in the control of immediate consump-tion or escape hedonic value must accurately reect the needs ofthe moment The palatability of salt for example increases inconditions of sodium depletion On a different time scale the he-donic value of food changes substantially during a single feedingepisode and normally drops to zero or becomes negative whenfeeding continues beyond satiation [Cabanac 1971] Of coursenot all human pleasures and pains are biologically programmedin detail Prior consumption experiences and various cultural andsocial inuences can alter the hedonic value of stimuli as whenpeople learn to like coffee or chili peppers develop a dislike forrich desserts or acquire a passion for opera Furthermore posi-tive or negative instant utility can be evoked by social stimulisuch as smiles or frowns and by purely internal events such asmemories of embarrassment or amusing thoughts [Schelling1984] In spite of the immense diversity in the occasions thatevoke pleasure (or displeasure) in the human adult the hedonicattribute that they share is salient and readily recognized

The view that hedonic states cannot be measured becausethey are private events is widely held but incorrect The measure-ment of subjective experiences and the determination of the func-tions that relate subjective variables to features of present andpast stimuli are topics in the well-established eld of psycho-physical research [Stevens 1975 Wegener 1982] The loudness ofa noise and the felt temperature of a limb are no less subjective

BACK TO BENTHAM 379

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

we will argue that experienced utility is both measurable and em-pirically distinct from decision utility

The following example illustrates the distinction between thetwo concepts of utility2 A patient suffering from unusually pro-found amnesia has two toasters in his kitchen The toaster on theright functions normally The toaster on the left delivers an elec-tric shock when the toast is removed The patientrsquos gasp andquick retraction of his hand indicate that the shock is painfulBecause the patient does not remember the experience howeverhe does not anticipate the shock the next morning and is conse-quently indifferent between the toasters The patientrsquos decisionutility for using the two toasters is equal but his experiencedutilities are quite different The patientrsquos choices of the left-handtoaster will not maximize utility in Benthamrsquos sense As we willshow later discrepancies between decision utility and experi-enced utility are not restricted to such pathological cases Sys-tematic errors in the evaluation of past events and decisions thatdo not maximize future experienced utility can be observed indecision makers whose cognitive functions are normal These ob-servations raise doubts about a methodology in which observedchoices provide the only measure of the utility of outcomes

Pleasure and displeasure are attributes of each moment ofexperience but the outcomes that people value are normally ex-tended over time The basic building block of experienced utilityin our analysis is instant utility a measure of hedonic and af-fective experience which can be derived from immediate reportsof current subjective experience or from physiological indices In-stant utility corresponds to the dimension of ldquointensityrdquo in thewritings of Bentham Jevons and Edgeworth The focus of ouranalysis is the evaluation of temporally extended outcomes(TEOs) such as a single medical procedure or the concatenationof a Kenya safari and subsequent episodes of slide-showing andstorytelling Two measures of the experienced utility of tempo-rally extended outcomes will be considered Remembered utilityis a measure on past TEOs which is inferred from a subjectrsquosretrospective reports of the total pleasure or displeasure associ-ated with past outcomes Total utility is a normative concept It isa measure on possible TEOs which is constructed from temporalproles of instant utility according to a set of normative rulesDecision utility is a measure on TEOs which is inferred fromchoices either by direct comparisons of similar objects or by indi-

2 This example was suggested by Paul Romer

QUARTERLY JOURNAL OF ECONOMICS376

rect methods such as elicited willingness to pay Finally we willdiscuss predicted utility which refers to beliefs about the experi-enced utility of outcomes The relations among the various utilityconcepts dene a complex agenda for research Figure I lists someof the questions that arise Several of these questions will be ad-dressed here

Section I discusses the adaptive signicance and the mea-surement of instant and remembered utility Section II describesstudies in which participants provided a continuous record of in-stant utility during an episode (eg a short lm or a medicalprocedure) and later reported a global evaluation of the episode(remembered utility) or made choices about which of several epi-sodes to repeat (decision utility) These studies are concernedwith the determinants of remembered utility (question 4 in Fig-ure I) and with the role of remembered utility in choice (8) Theduration of episodes played very little role in subjectsrsquo retrospec-tive evaluations in these experiments contrary to an obviousnormative rule (5) Subjects also made choices that exposedthem to avoidable pain or discomfort in violation of dominanceTheir decisions did not maximize experienced utility (9) al-though they may have maximized remembered utility (10)

Section III and the Appendix present a normative theory oftotal utility which yields rules for the evaluation of temporallyextended outcomes on the basis of a temporal prole of instantutility (3) The theory assumes time-neutral weighting of in-stants (no time preference) and derives temporal integration asthe principle of global evaluation Section IV elaborates on theconsequences of accepting experienced utility as a measure of thequality of outcomes distinct from decision utility The sectionalso includes a brief review of some results concerning the accu-racy of predicted utility (6) Section V concludes Proofs are pre-sented in the Appendix

An important reservation should be stated early Our norma-tive treatment of the utility of temporally extended outcomesadopts a hedonic interpretation of utility but no endorsement ofBenthamrsquos view of pleasure and pain as sovereign masters of hu-man action is intended Our analysis applies to situations inwhich a separate value judgment designates experienced utilityas a relevant criterion for evaluating outcomes3 This set does notinclude all human outcomes but it is certainly not empty

3 For more comprehensive conceptions of the quality of life see Dasgupta[1993] Nussbaum and Sen [1993] and Sen [1991]

BACK TO BENTHAM 377

FIGURE IResearch Designs for the Study of Experienced Utility

QUARTERLY JOURNAL OF ECONOMICS378

I THE FUNCTIONS OF EXPERIENCED UTILITY

We have distinguished two descriptive notions of experiencedutility instant utility is the pleasure or distress of the momentremembered utility is the retrospective evaluation of a tempo-rally extended outcome This section presents a brief introductionto the biology and psychology of these forms of utility and to someissues of measurement

The adaptive functions of pleasure and pain can be deducedfrom the conditions under which these experiences are biologi-cally programmed to occur Pleasure is evidently a ldquogordquo signalwhich guides the organism to continue important activities suchas foreplay or consuming sweet energy-rich food Pain is a ldquostoprdquosignal which interrupts activities that are causing harm such asplacing weight on a wounded foot The common characteristic ofthe basic forms of pleasure and distress is that they regulate theresponse to the current situation

To achieve its function in the control of immediate consump-tion or escape hedonic value must accurately reect the needs ofthe moment The palatability of salt for example increases inconditions of sodium depletion On a different time scale the he-donic value of food changes substantially during a single feedingepisode and normally drops to zero or becomes negative whenfeeding continues beyond satiation [Cabanac 1971] Of coursenot all human pleasures and pains are biologically programmedin detail Prior consumption experiences and various cultural andsocial inuences can alter the hedonic value of stimuli as whenpeople learn to like coffee or chili peppers develop a dislike forrich desserts or acquire a passion for opera Furthermore posi-tive or negative instant utility can be evoked by social stimulisuch as smiles or frowns and by purely internal events such asmemories of embarrassment or amusing thoughts [Schelling1984] In spite of the immense diversity in the occasions thatevoke pleasure (or displeasure) in the human adult the hedonicattribute that they share is salient and readily recognized

The view that hedonic states cannot be measured becausethey are private events is widely held but incorrect The measure-ment of subjective experiences and the determination of the func-tions that relate subjective variables to features of present andpast stimuli are topics in the well-established eld of psycho-physical research [Stevens 1975 Wegener 1982] The loudness ofa noise and the felt temperature of a limb are no less subjective

BACK TO BENTHAM 379

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

rect methods such as elicited willingness to pay Finally we willdiscuss predicted utility which refers to beliefs about the experi-enced utility of outcomes The relations among the various utilityconcepts dene a complex agenda for research Figure I lists someof the questions that arise Several of these questions will be ad-dressed here

Section I discusses the adaptive signicance and the mea-surement of instant and remembered utility Section II describesstudies in which participants provided a continuous record of in-stant utility during an episode (eg a short lm or a medicalprocedure) and later reported a global evaluation of the episode(remembered utility) or made choices about which of several epi-sodes to repeat (decision utility) These studies are concernedwith the determinants of remembered utility (question 4 in Fig-ure I) and with the role of remembered utility in choice (8) Theduration of episodes played very little role in subjectsrsquo retrospec-tive evaluations in these experiments contrary to an obviousnormative rule (5) Subjects also made choices that exposedthem to avoidable pain or discomfort in violation of dominanceTheir decisions did not maximize experienced utility (9) al-though they may have maximized remembered utility (10)

Section III and the Appendix present a normative theory oftotal utility which yields rules for the evaluation of temporallyextended outcomes on the basis of a temporal prole of instantutility (3) The theory assumes time-neutral weighting of in-stants (no time preference) and derives temporal integration asthe principle of global evaluation Section IV elaborates on theconsequences of accepting experienced utility as a measure of thequality of outcomes distinct from decision utility The sectionalso includes a brief review of some results concerning the accu-racy of predicted utility (6) Section V concludes Proofs are pre-sented in the Appendix

An important reservation should be stated early Our norma-tive treatment of the utility of temporally extended outcomesadopts a hedonic interpretation of utility but no endorsement ofBenthamrsquos view of pleasure and pain as sovereign masters of hu-man action is intended Our analysis applies to situations inwhich a separate value judgment designates experienced utilityas a relevant criterion for evaluating outcomes3 This set does notinclude all human outcomes but it is certainly not empty

3 For more comprehensive conceptions of the quality of life see Dasgupta[1993] Nussbaum and Sen [1993] and Sen [1991]

BACK TO BENTHAM 377

FIGURE IResearch Designs for the Study of Experienced Utility

QUARTERLY JOURNAL OF ECONOMICS378

I THE FUNCTIONS OF EXPERIENCED UTILITY

We have distinguished two descriptive notions of experiencedutility instant utility is the pleasure or distress of the momentremembered utility is the retrospective evaluation of a tempo-rally extended outcome This section presents a brief introductionto the biology and psychology of these forms of utility and to someissues of measurement

The adaptive functions of pleasure and pain can be deducedfrom the conditions under which these experiences are biologi-cally programmed to occur Pleasure is evidently a ldquogordquo signalwhich guides the organism to continue important activities suchas foreplay or consuming sweet energy-rich food Pain is a ldquostoprdquosignal which interrupts activities that are causing harm such asplacing weight on a wounded foot The common characteristic ofthe basic forms of pleasure and distress is that they regulate theresponse to the current situation

To achieve its function in the control of immediate consump-tion or escape hedonic value must accurately reect the needs ofthe moment The palatability of salt for example increases inconditions of sodium depletion On a different time scale the he-donic value of food changes substantially during a single feedingepisode and normally drops to zero or becomes negative whenfeeding continues beyond satiation [Cabanac 1971] Of coursenot all human pleasures and pains are biologically programmedin detail Prior consumption experiences and various cultural andsocial inuences can alter the hedonic value of stimuli as whenpeople learn to like coffee or chili peppers develop a dislike forrich desserts or acquire a passion for opera Furthermore posi-tive or negative instant utility can be evoked by social stimulisuch as smiles or frowns and by purely internal events such asmemories of embarrassment or amusing thoughts [Schelling1984] In spite of the immense diversity in the occasions thatevoke pleasure (or displeasure) in the human adult the hedonicattribute that they share is salient and readily recognized

The view that hedonic states cannot be measured becausethey are private events is widely held but incorrect The measure-ment of subjective experiences and the determination of the func-tions that relate subjective variables to features of present andpast stimuli are topics in the well-established eld of psycho-physical research [Stevens 1975 Wegener 1982] The loudness ofa noise and the felt temperature of a limb are no less subjective

BACK TO BENTHAM 379

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

FIGURE IResearch Designs for the Study of Experienced Utility

QUARTERLY JOURNAL OF ECONOMICS378

I THE FUNCTIONS OF EXPERIENCED UTILITY

We have distinguished two descriptive notions of experiencedutility instant utility is the pleasure or distress of the momentremembered utility is the retrospective evaluation of a tempo-rally extended outcome This section presents a brief introductionto the biology and psychology of these forms of utility and to someissues of measurement

The adaptive functions of pleasure and pain can be deducedfrom the conditions under which these experiences are biologi-cally programmed to occur Pleasure is evidently a ldquogordquo signalwhich guides the organism to continue important activities suchas foreplay or consuming sweet energy-rich food Pain is a ldquostoprdquosignal which interrupts activities that are causing harm such asplacing weight on a wounded foot The common characteristic ofthe basic forms of pleasure and distress is that they regulate theresponse to the current situation

To achieve its function in the control of immediate consump-tion or escape hedonic value must accurately reect the needs ofthe moment The palatability of salt for example increases inconditions of sodium depletion On a different time scale the he-donic value of food changes substantially during a single feedingepisode and normally drops to zero or becomes negative whenfeeding continues beyond satiation [Cabanac 1971] Of coursenot all human pleasures and pains are biologically programmedin detail Prior consumption experiences and various cultural andsocial inuences can alter the hedonic value of stimuli as whenpeople learn to like coffee or chili peppers develop a dislike forrich desserts or acquire a passion for opera Furthermore posi-tive or negative instant utility can be evoked by social stimulisuch as smiles or frowns and by purely internal events such asmemories of embarrassment or amusing thoughts [Schelling1984] In spite of the immense diversity in the occasions thatevoke pleasure (or displeasure) in the human adult the hedonicattribute that they share is salient and readily recognized

The view that hedonic states cannot be measured becausethey are private events is widely held but incorrect The measure-ment of subjective experiences and the determination of the func-tions that relate subjective variables to features of present andpast stimuli are topics in the well-established eld of psycho-physical research [Stevens 1975 Wegener 1982] The loudness ofa noise and the felt temperature of a limb are no less subjective

BACK TO BENTHAM 379

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

I THE FUNCTIONS OF EXPERIENCED UTILITY

We have distinguished two descriptive notions of experiencedutility instant utility is the pleasure or distress of the momentremembered utility is the retrospective evaluation of a tempo-rally extended outcome This section presents a brief introductionto the biology and psychology of these forms of utility and to someissues of measurement

The adaptive functions of pleasure and pain can be deducedfrom the conditions under which these experiences are biologi-cally programmed to occur Pleasure is evidently a ldquogordquo signalwhich guides the organism to continue important activities suchas foreplay or consuming sweet energy-rich food Pain is a ldquostoprdquosignal which interrupts activities that are causing harm such asplacing weight on a wounded foot The common characteristic ofthe basic forms of pleasure and distress is that they regulate theresponse to the current situation

To achieve its function in the control of immediate consump-tion or escape hedonic value must accurately reect the needs ofthe moment The palatability of salt for example increases inconditions of sodium depletion On a different time scale the he-donic value of food changes substantially during a single feedingepisode and normally drops to zero or becomes negative whenfeeding continues beyond satiation [Cabanac 1971] Of coursenot all human pleasures and pains are biologically programmedin detail Prior consumption experiences and various cultural andsocial inuences can alter the hedonic value of stimuli as whenpeople learn to like coffee or chili peppers develop a dislike forrich desserts or acquire a passion for opera Furthermore posi-tive or negative instant utility can be evoked by social stimulisuch as smiles or frowns and by purely internal events such asmemories of embarrassment or amusing thoughts [Schelling1984] In spite of the immense diversity in the occasions thatevoke pleasure (or displeasure) in the human adult the hedonicattribute that they share is salient and readily recognized

The view that hedonic states cannot be measured becausethey are private events is widely held but incorrect The measure-ment of subjective experiences and the determination of the func-tions that relate subjective variables to features of present andpast stimuli are topics in the well-established eld of psycho-physical research [Stevens 1975 Wegener 1982] The loudness ofa noise and the felt temperature of a limb are no less subjective

BACK TO BENTHAM 379

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

than pleasure and pain The main argument for consideringthese experiences measurable is that the functions that relatesubjective intensity to physical variables are qualitatively similarfor different people For example reported subjective intensity isoften a power function of physical magnitude with an exponentthat varies for different sensory dimensions Pleasure and dis-tress have the same status the psychophysical functions thatgovern the pleasure of drinking sugar solutions and the pain ofelectric shock are orderly and interpersonally similar [Stevens1975] Verbal or numerical reports of hedonic value can be sup-plemented by physiological indicators of emotional quality andintensity including objective measurements of subtle facial ex-pressions [Frank 1988] Although the correlations among thesemeasures are imperfect the variance they share can serve to op-erationalize the concept of instant experienced utility

As an object of measurement experienced utility has muchin common with subjective temperature Like hot and cold theexperiences of pleasure and distress differ in quality A scale thatranges from extreme pleasure to extreme distress (or from veryhot to very cold) effectively comprises separate scales for two dis-tinct attributes The two scales are joined by a distinctive neutralpoint ldquoneither hot nor coldrdquo ldquoneither pleasant nor unpleasantrdquoThe stimulus that gives rise to a neutral experience may be dif-ferent in different contexts but the neutral experience itself isconstant A standard demonstration involves two pails of warmwater one warmer than the other A subject who immerses onehand in each of these pails will eventually report that both handsfeel alike neither hot nor cold The neutral value provides a natu-ral zero point for bipolar dimensions Because of its distinc-tiveness the neutral value can be used with some condenceto match thermal (or hedonic) experiences across time for agiven individual and even to support interpersonal comparisons[Kahneman and Varey 1991]

Remembered utilities also have an adaptive function theydetermine whether a situation experienced in the past shouldnow be approached or avoided Unlike pain and pleasure whichcontrol behavior in the current situation learned attractions andaversions adjust current behavior to the remembered evaluationsof events in the past Remembered utilities can be measured inhumans by reported evaluations of past experiences or byphysiological indications of the emotion aroused by reminders of

QUARTERLY JOURNAL OF ECONOMICS380

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

the event Remembered utilities can also be inferred from the ap-proach or avoidance tendencies that they induce

Like the hedonic system the system that governs the re-membered evaluation of past experiences has been under evolu-tionary pressure However the effect of natural selection is toincrease overall tness not necessarily to produce organismsthat maximize pleasure and minimize pain over time For ex-ample the fear displayed by rats that have been repeatedly ex-posed to an electric shock is affected by the intensity of the shockbut not by its duration [Mowrer and Solomon 1954] The nextsection reports similar observations of duration neglect in humansubjects These ndings suggest that the system that forms andstores evaluations of situations is not designed to optimize expe-rienced utility

II THE EXPERIENCED UTILITY AND DECISION UTILITY OF EPISODES

The present section summarizes the results of a series ofstudies of remembered utility which investigated two questions(i) what attributes of the temporal prole of instant utility deter-mine the remembered utility of an episode (ii) are biases in re-membered utility reected in subsequent choices A central issuein these studies was the role of duration as a determinant ofthe utility of episodes The results support two generalizations(1) Peak-End evaluation the remembered utility of pleasant orunpleasant episodes is accurately predicted by averaging thePeak (most intense value) of instant utility (or disutility) re-corded during an episode and the instant utility recorded nearthe end of the experience (2) Decisions by remembered utilitywhen given the choice of which of several episodes to repeat indi-viduals generally choose the episode that has the highest remem-bered utility Two consequences of Peak-End evaluation havebeen conrmed both in measures of remembered utility and inchoices (1) Duration neglect the duration of experiences haslittle or no independent effect on their remembered utility (2)Violations of temporal monotonicity the remembered disutility ofan aversive episode can be reduced by adding an extra period ofdiscomfort that reduces the Peak-End average

Several experimental designs were employed in this re-search The participants in the experiments generally providedcontinuous or intermittent measures of instant utility which per-

BACK TO BENTHAM 381

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

mitted a computation of the Peak-End average The duration ofthe episodes was allowed to vary naturally in some studies andwas varied experimentally in others Diverse measures of remem-bered utility were used including ratings of overall aversivenessand comparative evaluations Choices were recorded in some ofthe experiments

Participants in experiments reported by Fredrickson andKahneman [1993] were exposed to sixteen short plotless lmclips Half of these lms were pleasant (eg views of a coral reef)half were aversive (eg an amputation) There were two versionsof each lm a short version (approximately 45 seconds) and alonger version (approximately 120 seconds) with no notablevariation of content or affective value Each subject saw the shortversions of half the lms and the long versions of the others Thesubjects used a sliding knob that controlled an array of coloredlights to provide a continuous measure of the instant utility (ordisutility) they experienced during the presentation of each lm[Gottman and Levenson 1985]

Several measures of remembered utility were used Partici-pants in one study answered the question ldquoOverall how muchpleasure [displeasure or discomfort] did you experience duringthe lmrdquo Because this instruction could perhaps be interpretedas referring to the most extreme affect experienced during theepisode another measure was used in a subsequent study Par-ticipants were told that the researchers sought their advice tocompile videotapes that subjects would view in future experi-ments The task was to rank the lms according to the contribu-tion each made to the overall affective experience of viewing thevideotape Pleasant and unpleasant clips were ranked separatelyThe ranking of the aversive clips was explained as follows ldquoTheunpleasant videotape will consist of several of the unrelated un-pleasant clips that you just saw Of course people who will seethis unpleasant videotape will experience some unpleasant-ness Your task is to help us select the unpleasant clips weshould include in order to MINIMIZE the overall experience ofunpleasantness for most peoplerdquo

The results of both experiments generally supported thehypotheses of Peak-End evaluation and duration neglect In awithin-subject regression analysis of the rst experiment themean correlations between the Peak-End average of the real-timemeasure and ratings of remembered utility were 77 for pleasantlms and 69 for aversive lms When the Peak-End measure was

QUARTERLY JOURNAL OF ECONOMICS382

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

statistically controlled the mean correlations between the re-membered utility of lms clips and their duration were 06 and2 02 respectively4 Very similar results were obtained with theranking measure used in the second experiment The subjectsrsquorankings of the lm clips they wished to include in a videotapewere entirely unaffected by duration

Duration neglect and Peak-End evaluation were conrmedin a more realistic setting using a between-subjects design [Re-delmeier and Kahneman 1996a] The participants were patientsundergoing a colonoscopy in a Toronto hospital The patients re-ported their level of discomfort every 60 seconds throughout theprocedure (see Figure II) Later the patients reported the remem-bered disutility of the procedure using several different scalesThe patients rated the ldquototal amount of pain experiencedrdquo on a10-point scale They also ranked a list of unpleasant experienceswhich included ldquothe colonoscopy you have just hadrdquo along withother incidents such as stubbing a toe and ldquoan average visit tothe dentistrdquo The patients were also required to indicate a prefer-ence between a repeat colonoscopy and a barium enema Peak-End evaluation and duration neglect were observed for all thesemeasures For example the correlation of the Peak-End averagewith the global rating of the procedure was 67 Although therewas substantial variability in the duration of the colonoscopiesthat different patients experienced (the mean duration was 23minutes with a standard deviation of 13 minutes) the correla-tion between duration and the global evaluation of the procedurewas only 03 Figure II shows illustrative data for two patientsAlthough most observers judge that Patient B had a worse expe-rience the Peak-End rule correctly predicts a worse retrospectiveevaluation by Patient A whose End rating was much higher

A notable feature of this study is that robust results wereobtained in a design which effectively assumes the interpersonalcomparability of measures of experienced utility Several ndingssupport the conclusion that people share a common scale for bothinstant and remembered utility First the requirement to provideratings of discomfort during the procedure was eliminated for agroup of 53 patients an observer who attended the examination

4 The rst-order correlation between disutility and duration was signicantfor the aversive clips but this correlation was produced by a general tendency forthe ratings of instant discomfort to increase during the exposure of these clips Apattern of escalating discomfort is common in aversive situations where it in-duces a positive correlation between duration and the Peak-End measure

BACK TO BENTHAM 383

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

estimated the patientrsquos discomfort every 60 seconds The Peak-End average of the observer rsquos estimates predicted the retrospec-tive evaluations subsequently elicited from patients (r 5 71)Second the physicians who administered the procedure also pro-vided several ratings of each patientrsquos overall discomfort The cor-relation between the ratings of patients and physicians was 67The physicians evidently applied the same model of evaluation(Peak-End rule and duration neglect) as did the patients One ofthe questions put to the physicians was whether more anestheticshould have been used The correlation between answers to thisquestion and the duration of the procedure was 05

The psychological interpretation of this pattern of ndingsis straightforward The subjects and observers in these studiesapparently constructed a representative moment of each episodethey had experienced (or observed) and used this representativemoment as a proxy to evaluate the utility of the entire episode

FIGURE IIPain Intensity Reported by Two Colonoscopy Patients (from Redelmeier and

Kahneman [1996])

QUARTERLY JOURNAL OF ECONOMICS384

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

The representative moment is better described as a collage thanas a precise memory of a particular instant of the experience itis affected by several singular instants including the peak andthe end of the episode The duration of the episode is not includedin this basic representation even when it is accurately known[Fredrickson and Kahneman 1993 Kahneman FredricksonSchreiber and Redelmeier 1993 Varey and Kahneman 1992]The Peak-End representation controls an emotional responsewhich is reected in the global evaluations of the episode andwhich we label remembered utility As was previously observedin the fear response of lower animals [Mowrer and Salomon1954] this emotional response is essentially independent of dura-tion When their attention is directed to it of course human sub-jects universally agree that duration is a relevant attribute ofpleasant or aversive episodes

The Peak-End rule entails violations of temporal monoton-icity adding an extra period of discomfort to an aversive episodewill improve the remembered utility of the episode if the addedperiod ends on a less unpleasant note Redelmeier and Kahne-man [1996b] tested this prediction in a clinical setting with alarge population (N 5 682) of patients undergoing a colonoscopyHalf the patients were randomly assigned to a condition in whichthe procedure was extended by leaving the colonoscope in placefor about a minute after the completion of the clinical examina-tion The patients were not informed of the experimental treat-ment The experience during the added period was mildlyuncomfortable (certainly less preferred than the alternative of re-moving the instrument) but for many patients less painful thanthe preceding moments As predicted by the Peak-End rule theprolongation of the colonoscopy yielded a highly signicant im-provement in the global evaluations of the procedure The pur-pose of the experiment was to test the hypothesis that anintervention that reduces the remembered disutility of the proce-dure could increase patientsrsquo willingness to undergo further co-lonoscopies if needed

We next consider whether the biases of remembered utilitytransfer to decision utility As we saw earlier the description ofbehavior as governed by pleasure and pain is only applicable toconsumption and escape In many other situations the sovereignmasters that determine what people do are not pleasure andpain but memories of pleasure and pain Indeed the only utilitythat people (and other organisms) can learn from personal experi-

BACK TO BENTHAM 385

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

ence to maximize is the utility that they remember If a retrospec-tive evaluation distorts the hedonic quality of an experiencesubsequent preferences will be governed by the biased evalua-tion not by the original experience This reasoning implies thatthe violations of temporal monotonicity observed in ratings of re-membered utility should also be observed in actual choices Sev-eral experiments have tested this prediction

Participants in an experiment reported by Kahneman et al[1993] were advised that they would undergo painful experiencesand as part of the informed consent procedure were asked to im-merse a hand to the wrist in very cold water for ten secondsThey were told to expect three trials of this kind but only twowere actually conducted In the Short trial the subject kept onehand in water at 14degC for 60 seconds after which he was allowedto remove the hand from the water and to dry it with a warmtowel In the Long trial the immersion lasted a total of 90 sec-onds Water temperature was kept at 14deg for the rst 60 secondsat which point (unbeknownst to the subject) the experimentercaused the temperature of the water to rise gradually from 14deg to15deg over the next 30 seconds Different hands were used for theShort and for the Long trials Half the subjects experienced theShort trial before the Long one the sequence was reversed forthe other subjects The trials were separated by seven minutesduring which the subject performed an unrelated task which wasresumed after the second trial Seven minutes later the subjectwas called in for a third trial informed that one of the two previ-ous procedures would be repeated exactly given a choice ofwhether the rst or the second trial should be repeated andasked to answer several questions about the rst two trials

Several experiments were conducted in this general designwith minor variations of procedure The 32 participants in themain experiment used a ldquodiscomfort meterrdquo to provide a continu-ous indication of the pain they experienced on a scale rangingfrom 0 (no pain at all) to 14 (intolerable pain) The real-time re-cords permitted a classication of subjects into two groups Mostsubjects indicated a decline of two or more points on the painscale during the last 30 seconds of the experiment the mean levelof pain that these subjects recorded was 85 at 60 seconds and 44at 90 seconds For these subjects the Peak-End average waslower on the Long than on the Short trial As expected a largemajority of them (17 of 21) preferred to repeat the Long trial Theother eleven subjects did not indicate a signicant decrease of

QUARTERLY JOURNAL OF ECONOMICS386

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

pain as the temperature of the water was raised For these sub-jects the Peak-End average was very similar on the Short and onthe Long trial Only ve of the eleven subjects preferred the Longtrial The difference between the preferences of the two groupswas statistically signicant as was the overall preference for theLong trial (69 percent for the 32 subjects) To check the ro-bustness of the results the experiment was replicated with 37new subjects without the requirement to report pain in real timeThe results conrmed the original ndings 65 percent of the newsubjects preferred to repeat the Long rather than the Short trial

Subjects did not spend much time in analytic comparisonsbefore choosing which trial to repeat they simply determinedwhich of the two memories they disliked less Postexperimentalinterviews and other observations provided no support for morespeculative accounts First the interviews conrmed that theLong trial was not chosen out of a wish to endure more painIndeed all subjects quickly removed their hand from the wateras soon as they were allowed to do so Second the subjects neverdescribed the last segment of the Long trial as a pleasurable ex-perience Third they did not prefer the Long trial because ityielded a more pleasant postimmersion experience On the con-trary pleasurable relief was more intense after the Short trial

The neglect of duration in this experiment represents neithera failure of duration memory (most subjects could correctly an-swer a question about the durations of the two trials) nor a delib-erate strategy We have observed in unpublished experimentsthat subjects who are are asked to choose between hypotheticalproles of a Long and Short trial almost invariably obey domi-nance although most subjects follow the Peak-End rule and im-plicitly violate dominance when judging a series of hypotheticalproles one by one [Varey and Kahneman 1992] In the cold-water experiment the choice is made by comparing rememberedutilities without performing the explicit comparison that couldreveal the Long trial to be a dominated option

The violations of dominance observed in the cold-water ex-periment have been replicated with loud sounds as aversive stim-uli [Schreiber and Kahneman 1996] Subjects heard pairs ofsounds in immediate succession then indicated which of the twosounds they would rather hear repeated in a subsequent phaseof the experiment Some of the stimuli were constructed alongthe lines of the cold-water experiment For example one of thepairs of stimuli that the subjects heard was (i) ten seconds of an

BACK TO BENTHAM 387

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

unpleasant sound at 78 db and (ii) the same sound followed byfour additional seconds at a lower intensity (66db) There was asignicant preference for repeating the Long sounds in suchpairs The pattern did not change in the course of a series of tendecisions including ve which pitted a Long sound against aShort one

The experiments reviewed in this section all involved shortepisodes in which the subjects were passive The episodes werealso hedonically homogeneous none combined pleasant and un-pleasant moments Although the exact pattern of ndings may bespecic to this particular class of situations the results supporttwo general observations The rst observation is methodologicalsome peculiarities of preferences are unlikely to be understoodor even detected without rst understanding experienced and re-membered utility The second observation is that the statementthat decisions maximize utility is not a tautology it can beproved false

III NORMATIVE ANALYSIS

The subjects in the experiments described in the precedingsection violated a compelling principle of temporal monotonicityWe therefore claimed to have observed preferences that do notmaximize experienced utility but we did not specify preciselywhat maximization means in the context of temporally extendedoutcomes We turn to this task now

The measured primitive of experienced utility is instant util-ity the hedonic value of a moment of experience as immediatelyreported or recorded Signicant outcomes last more than an in-stant however and the total utility of such outcomes must there-fore be derived from a temporal prole of instant utility Thetheory presented in this section species the conditions underwhich the total utility of an extended outcome is the temporalintegral of some transformation of instant utility This normativeanalysis serves two goals On the one hand it identies axiomsof total utility that yield a rule of temporal integration and allowsan evaluation of the intuitive appeal of these axioms On theother hand the analysis constrains the measure of instant utilitywhich must provide all the information required for an adequateassessment of total utility

The normative treatment of total utility can be interpretedin at least two ways The most straightforward interpretation is

QUARTERLY JOURNAL OF ECONOMICS388

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

that retrospective evaluation of outcomes is a cognitive activityin which people routinely engage much as they engage in gram-matical speech or in deductive reasoning Normative standardsapply to each of these activities Rules and errors can be identi-ed for grammar for deduction and also for retrospective evalua-tion Economists who associate normative analysis exclusivelywith decisions may prefer another interpretation in which totalexperienced utility is the objective function that a benevolent so-cial planner would wish to maximize

Temporal integration is an obvious candidate for a normativeprinciple of total utility A sketch of the idea can be found in Edge-worth [1881 p 101] ldquo let there be granted to the science ofpleasure what is granted to the science of energy to imaginean ideally perfect instrument a psychophysical machine con-tinually registering the height of pleasure experienced by anindividual The continually indicated height is registered byphotographic or other frictionless apparatus upon a uniformlymoving vertical plane Then the quantity of happiness betweentwo epochs is represented by the area contained between thezero-line perpendiculars thereto at the points corresponding tothe epochs and the curve traced by the indexrdquo

The analysis that follows assumes ordinal measurement ofboth instant utility and total utility Stronger results that requirecardinal measurement are also mentioned Ordinal measurementof instant utility implies that any two moments of experience canbe compared to establish which of them carries the higher he-donic value The measure of instant utility should also permitreliable identication of the hedonically neutral state whichplays a special role in the analysis As was mentioned earlierthese requirements are not beyond the realm of the possible

The following terms will be used formal denitions are pre-sented in the Appendix An episode is a connected time intervaldescribed by its temporal coordinates A group of one or more tem-porally disjoint episodes is called a temporally extended outcome(TEO) The utility prole of a TEO assigns a level of instant util-ity to each time point (see Figure II note that the ordinate isinverted in this gure to correspond to the format of the pa-tientsrsquo ratings)

Utility proles can be concatenated If f is a utility proleof duration x and g is a utility prole of duration y then theirconcatenation is of duration x 1 y coinciding with f on the rstpart and with g on the second For example imagine that the two

BACK TO BENTHAM 389

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

disutility proles shown in Figure II were produced by the sameindividual during two colonoscopies conducted on separate daysThe patientrsquos total experience of colonoscopy could be representedby concatenating the two proles The analysis assumes that thecalibration of the scale of instant utility is constant both for theepisodes included in a TEO and for TEOs that are compared witheach other Of course this requirement is likely to be violatedwhen the situations are radically different as in comparisons ofthe experiences of a person as a baby and as an adult

We now present axioms for total utility that characterize theintegration rule The rst axiom considers neutral utility prolesdened as proles in which instant utilities are hedonically neu-tral ie ldquoneither good nor badrdquo It plays an essential role in com-parisons of TEOs that differ in duration

AXIOM 1 [concatenation of neutral utility proles] The total util-ity of a utility prole is not affected by concatenation with aneutral utility prole

The conditions that we impose next reect the consequen-tialist requirement that a measure of instant utility should com-prise all the information required for the determination of totalutilities

AXIOM 2 [monotonicity in instant utility] Increases of instantutility do not decrease the total utility of a utility prole

The axiom implies that any local improvement of instantutility is perceived as an improvement of total utility irrespectiveof earlier or subsequent instant utilities

AXIOM 3 [monotonicity in total utility] In a concatenation of twoutility proles replacing one prole by another with a highertotal utility will increase the total utility of the concatenation

Axiom 3 implies separability of disjoint time periods If oneutility prole is better than another then this is not affected bythe utility proles that precede and follow them The instant util-ity ratings must be ldquosufcient statisticsrdquo in the sense that all theinformation needed to evaluate the goodness of an episode mustbe incorporated in its utility prole In particular any effects ofprevious or anticipated consumption on the utility of present con-sumption must be incorporated in the measure of instant utilitySeparability is commonly used to characterize additive decompos-

QUARTERLY JOURNAL OF ECONOMICS390

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

ability over disjoint time intervals thus Axiom 3 is the crucialaxiom for the integral representations obtained in this section

THEOREM 1 The three axioms above hold if and only if there ex-ists a nondecreasing (ldquovaluerdquo) transformation function of in-stant utility assigning value 0 to 0 such that total utilityorders utility proles according to the integral of the value ofinstant utility over time5

The normative determination of total utility consists of twoparts Instant utilities are rst measured and then transformedby means of the value function As noted earlier the same norma-tive analysis applies to the subject who reported the instant utili-ties and to an observer with access to the utility prole Thetheorem assumes that the instant utility ratings are ordinal ex-cept for the zero point The transformation yields a ratio scalewhich is unique up to multiplication by a positive scale factorThe present formulation and axioms differ from other treatmentsin the time preference literature mainly in our use of the concate-nation operation This operation is applicable because globalevaluations are undated Our derivation combines techniquesfrom ldquoHoelder rsquos theoremrdquo with Gormanrsquos [1968] result on the rep-resentation of separable preferences

Separability in terms of outcomes is not reasonable andcounterexamples are easily constructed For example the rela-tive values of a strenuous walk and of reading a book in the after-noon depend on whether the individual spent the morningplaying tennis or working at a computer One response to theproblem is a nonadditive model of preferences over outcome pro-les that permits violations of separability as in Gilboa [1989]and Constantinides [1990] Our model retains separability be-cause it assumes that utility proles are specied in terms of in-stant utilities not outcomes Using measurements of instantutility we would expect to nd that the relative instant utilitiesof alternative programs for the afternoon depend strongly on howthe morning was spent Separability is reasonable when out-comes are described in terms of instant utility provided thatinstant utility incorporates all order effects and interactions be-tween outcomes This treatment is similar to Stigler and Becker

5 Because the term utility is already used in another sense we resort to theterm ldquovaluerdquo to designate the transformation of instant utility

BACK TO BENTHAM 391

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

[1977] who achieved separability by redening outcomes as ap-propriate conjunctions of present and past consumption

An implication of Theorem 1 is that the ordering of timepoints in a utility prole does not affect total utility

COROLLARY 1 The total utility of a utility prole and hence of aTEO depends only on the generated time distribution overinstant utility ie the total time spent at each region of in-stant utility

This corollary reects the time neutrality of the modelThe analysis becomes simpler if cardinal measurement of in-

stant utility can be assumed so that differences of instant utilityare meaningful Transformation by the value function is not re-quired in this case The following axiom characterizes cardinalmeasurability of instant utility

AXIOM 4 [cardinality of instant utility] The ordering of total util-ity of two utility proles does not change if for both the in-stant utility level is increased by the same constant over anequally long time period

THEOREM 2 Axioms 1 2 and 4 hold if and only if total utilityorders utility proles according to the integral of instant util-ity over time

Theorems 1 and 2 can be simplied further if total utility ismeasured at a cardinal level (Theorem A2 and Corollary A1 inthe Appendix)

Finally we note the following simple implication which issatised in each of the models and was tested empirically in theexperiments described in the preceding section

COROLLARY 2 [time monotonicity] Axioms 1 (concatenation ofneutral utility episodes) and 2 (monotonicity of instant util-ity) imply that concatenation with a utility prole that liesentirely above zero does not lower total utility and concate-nation with a wholly negative prole does not raise totalutility

IV DISCUSSION

The object of this paper was to show that experienced utilityis governed by a distinctive normative logic that it is potentiallymeasurable and that the empirical study of experienced utility

QUARTERLY JOURNAL OF ECONOMICS392

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

is relevant to some topics of concern to economists We discussthese issues in turn

1 Normative issues Our analysis of total utility assumes atime-neutral perspective and emphasizes duration as a feature ofoutcomes Neither idea is new There is a long history of debateabout the normative status of time preferences especially aboutthe rationality of discounting the future [Loewenstein 1992] andduration is represented in any treatment of utility over timeHowever the context of experienced utility highlights particularaspects of these ideas

Although many authors have argued for a time-neutral per-spective the prevailing position in the economic literature is thatutility discounting is compatible with rationality The exclusivefocus on decisions in economic thinking helps explain the toler-ance for discounting decision utility is evaluated from the per-spective of an agent for whom immediate outcomes indeed loomlarger than more distant ones In contrast the total experiencedutility of an outcome is not evaluated from any particular pointin time The entire utility prole of the outcome must be knownbut the date of the evaluation is irrelevant The same reasoningextends naturally to time-neutral weighting of early and latesegments of extended outcomes Although other models of totalutility could be formulated time neutrality appears most appro-priate for the evaluation of experienced utility The adoption ofthis principle has signicant normative consequences An impor-tant case is the evaluation of actions that produce immediatebenets and long-term costs a category that includes many self-destructive practices Discounting induces a bias in favor of theseactions which is avoided in a time-neutral perspective Time neu-trality is therefore appealing both as a rule of personal prudenceand as a principle of social planning

To appreciate the normative signicance of temporal integra-tion consider an extended outcome that consists of one period ofpleasure and one period of pain Recall that integration impliesthe existence of a suitable monotonic transformation of instantutility (and disutility) to ratio scales (invariant up to a multiplica-tion by a positive constant) with the same zero point The ratio ofthe total durations of positive and negative periods in a mixed-affect TEO which is observable jointly constrains the globalevaluation of the TEOs and the measures of instant utility anddisutility A globally positive evaluation of such a TEO is justiedonly if the ratio of the averages of (suitably transformed) utilities

BACK TO BENTHAM 393

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

and disutilities in the two periods is more extreme than the ratiosof their durations A global positive evaluation can appear im-plausible when the pleasure is very brief in relation to the painHowever an agent who is susceptible to duration neglect in theevaluation of TEOs will tend to assign positive remembered util-ity to outcomes that consisted of periods of intense pleasure andmild pain with little regard for the relative durations of theseexperiences We suspect for example that duration neglect is in-volved in the attitudes of addicts who do not regret their addic-tion Appropriate weighting of the durations of episodes has someforce as a rule of personal prudence and a principle of social plan-ning [Broome 1991]

2 Measurement issues There has been signicant progresssince Edgeworth fantasized a hedonimeter As illustrated by theresearch described earlier continuous or intermittent measure-ments of affect are feasible in some situations6 where they yieldutility proles that are often quite similar for different individu-als Another promising development is the increasing sophistica-tion of experience sampling techniques in which individuals areprompted by a preprogrammed beeper to record various aspectsof their current experience (eg Brandstatter [1991]) Thesemethods are likely to be supplemented in the future by continu-ous or intermittent measurements of physiological indices ofstress and of hedonic states

The advantage of real-time measures of instant utility is thatthey avoid the biases of memory and evaluation that affect retro-spective judgments of pleasure pain and well-being Becausethey are much easier to obtain however retrospective measureswill remain in frequent use Their effectiveness is likely to be en-hanced by procedures that reduce the impact of known biasesFor example improved estimates of the total utility of an episodecould be obtained by eliciting from the respondent separate as-sessments of its duration and of its average instant utility Moregenerally we propose that the measurement of experienced util-ity should be viewed as a difcult technical problem not a hope-less quest

3 Empirical Issues As Figure I illustrated the considerationof experienced utility raises a complex agenda for both theoretical

6 Several studies have shown that the requirement to report instant utilityhas little or no effect on subsequent global evaluations of the episode [Fredricksonand Kahneman 1993 Kahneman et al 1993 Redelmeier and Kahneman 1996a]

QUARTERLY JOURNAL OF ECONOMICS394

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

and empirical research Our treatment has focused on the norma-tive question of how TEOs should be evaluated (3 in Figure I)and on an empirical study of the remembered and decision utilityof brief aversive episodes We found that remembered utility isdetermined by a Peak-End rule (4) in violation of temporal inte-gration (5) preferences for the repetition of episodes were deter-mined by their remembered utility (8) As a result decisionsfailed to maximize experienced utility (9) although they mayhave maximized remembered utility (10) These ndings shouldbe taken as illustrative because of the narrow range of situationsin which they were obtained

The effects of consumption on the utility of future consump-tion (2 in Figure I) play an important role in numerous economicmodels of individual decisions (eg Becker [1996] Constantin-ides [1990] Gilboa [1989]) The intuitions that drive these modelspertain to the dynamics of experienced utility but the only ob-servables that the models allow are decisions The chain of infer-ences from observed decisions to experienced utility is long andas we illustrated earlier sometimes unreliable We believe thatexperienced utility can only be understood when it is directlymeasured and that a deeper understanding of experienced utilitywill contribute to the development of richer models of economicdecisions

In a book that has been inuential outside economics Scitov-sky [1976] presented numerous ideas about experienced and pre-dicted utility His treatment implies that people are not generallyable to solve the problem of maximizing experienced utility sub-ject to a budget constraint (question 9 in Figure I) at least inpart because of their limited understanding and ability to predicttheir own enjoyment of goods and activities (6) He argued thatAmerican consumers tend to overinvest in comforts and to un-derinvest in pleasures and suggested that members of other cul-tures achieve greater success in the pursuit of happiness In theabsence of measurements of experienced utility Scitovsky couldonly support these strong claims by appealing to his readersrsquo in-tuitions about the psychology of hedonic experience and to theirnormative intuitions about the good life At least in principlehowever his hypotheses could be studied empirically using ap-propriate measures of experienced and predicted utility

Unlike Scitovsky Beckerrsquos analysis of individual behavior as-sumes that people correctly anticipate the effects of consumptionon future preferences and correctly incorporate these predictions

BACK TO BENTHAM 395

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

in their choices [Becker 1996] The available evidence supportsthe more skeptical position Studies of lay beliefs about the dy-namics of taste and hedonic experience have shown these beliefsto be fragmentary and sometimes seriously inaccurate [SnellGibbs and Varey 1995] For example the large effects of sheerfamiliarity in increasing liking and enjoyment are not generallyknown Most people are also very surprised to learn that paraple-gics are not always miserable and that lottery winners are notparticularly happy [Brickman Coates and Janoff-Bulman 1978]reecting a pervasive tendency to underestimate the effects ofhabituation

Experimental studies of predicted utility have produced ad-ditional evidence of poor accuracy Participants in two experi-ments were not able to predict how their own taste for ice creamlow-fat yogurt or music would change over a week of repeatedconsumption [Kahneman and Snell 1992] Failures of individualsto predict their own future choices were reported by Simonson[1990] and by Loewenstein and Adler [1995] These ndings arenot compatible with the assumption that it is easy to anticipatefuture tastes and to plan consumption accordingly

The errors of remembered utility and the consequent errorsof decision that we reviewed earlier do not exhaust the difcultiesthat people have in evaluating extended outcomes nor do theyexhaust the ways in which decisions fail to maximize utilityThus many errors of predicted utility are caused by the practiceof evaluating an entire extended outcome by evaluating the tran-sition to it For example the mistake that most people make inpredicting the well-being of paraplegics may reect their use ofthe tragic event of becoming a paraplegic as a proxy in evaluatingthe long-term state of being a paraplegic A similar bias is thesource of many anomalies of choice Decision makers are suscep-tible to framing effects and are led to inferior choices because ofthe pervasive tendency to evaluate outcomes as changes relativeto a reference point [Tversky and Kahneman 1986 1991] Thefocus on changes sometimes induces an extreme form of myopiawhere decision makers appear to evaluate a transaction by theanticipated pleasure or pain of getting or giving up a good ratherthan by evaluating the state of having it [Kahneman 1994] Adetailed study of remembered utility predicted utility and deci-sion utility can be expected to reveal instructive commonalitiesas well as important differences

4 Consumer Sovereignty Some of the arguments for con-

QUARTERLY JOURNAL OF ECONOMICS396

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

sumer sovereignty are called into question by the observation ofdecisions that systematically fall short of maximizing experi-enced utility The dilemma can be illustrated by the example thatintroduced this paper The amnesic patient attaches the same de-cision utility to the two toasters although the experienced utilitythat the toasters deliver is different The question is whether theamnesicrsquos preferences which clearly do not maximize experi-enced utility should nevertheless be respected This question isof interest because the difference between the patient of the storyand normal people may be smaller than is commonly assumedAs illustrated by the experiments described in Section II normalsubjects also choose to expose themselves to avoidable pain be-cause of the peculiarities of remembered utility Do preferencesthat exhibit almost total duration neglect deserve respect

The point of these observations is not to support paternalismbut to reject one of the arguments commonly raised against itThe claim that agents should be left alone because they generallyknow what is good for them is less secure than is generally as-sumed in economic discourse A sounder case for resisting inter-ventions in the decisions of individuals can be made on othergrounds such as the value of freedom and the high risk that coer-cive power will be abused Invoking the assumption of rationalityin this context merely denies the existence of a real dilemma

V CONCLUSION

The elimination of experienced utility from economic thoughtwas justied by important considerations but it was not costlessPerhaps the heaviest cost was that the exclusive concern withdecision utility removed some important problems from the reachof empirical research In particular the proposition that peoplemaximize utility was granted the status of a maintained hypothe-sis which is used to constrain the interpretation of other factsbut is not itself subject to test Admitting experienced utility as ameasure of outcomes turns utility maximization into an empiri-cal proposition which will probably be found to provide a goodapproximation to truth in many situations and to fail severely inothers The scientic merit of economic analyses that assumeutility maximization will vary accordingly Considerations of ex-perienced utility can help identify situations in which the as-sumption of consumer rationality should be applied with cautionsubjected to empirical test or avoided altogether

BACK TO BENTHAM 397

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

APPENDIX A FORMAL ANALYSIS AND PROOFS

We denote by [BE [ a time interval that contains all timepoints relevant to the analysis to avoid technical details The in-terval is assumed bounded For convenience of notation all timeintervals are assumed left-closed and right-open in this analysisC is a set of outcomes (describing consumed commodity bundleshealth states social states etc) An episode is a mapping from asubinterval [be[ to C for b $ B and e E A TEO is a mappingfrom a nite disjoint union of subintervals of [BE [ to C

The set of levels of instant utilities is denoted by X X is aninterval that contains 0 it may be bounded or unbounded Toeach TEO we assign a dated utility prole ie a function denedon the same domain as the TEO but assigning to each time pointof the domain a level of instant utility instead of an outcome Theinstant utility at a time point depends on the outcome associatedwith that time point but also on outcomes associated with othertime points

Our analysis has been based on the assumption of no dis-counting Hence a dated utility prole dened on some interval[be[ is equivalent to a dated utility prole on an interval [b 1 te1 t[ with corresponding instant utilities for any t We only needto know the time duration e 2 b of the interval and the instantutility prole over that interval and we need not know the valueof b or e Therefore we assign to each dated utility prole f dened on a time interval [be[ a mapping f with domain [0e 2 b[such that f (t) 5 f (b 1 t) for all t f is called the undated utilityprole or utility prole for short Loosely speaking we set theclock at zero at the beginning of each utility prole ie we usestopwatch time instead of calendar time The denition reectsthe assumption that an hour of some specic level of instant util-ity yields the same amount of total utility independent of whenit happens in history

A utility prole or prole for short is a bounded functionfrom an interval [0d[ to X where 0 d M with M the maximalduration that is conceivable ie M 5 E 2 B7 The utility proleis complete if its domain is [0M[ For two proles fg dened on[0a[ and [0b[ respectively with a 1 b M the concatenationfampg is dened on [0a1 b[ and coincides with f on [0a[ and with gon [aa1 b[ (after appropriate translation of the arguments)

7 We make the usual measurability assumptions ie utility proles areldquoLesbesgue-measurablerdquo [Halmos 1950]

QUARTERLY JOURNAL OF ECONOMICS398

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

Next we dene utility proles for TEOs A TEO can be consid-ered a concatenation of episodes and we can consider the utilityproles belonging to the separate episodes of a TEO The utilityprole belonging to a TEO is dened as the concatenation of theutility proles of the episodes that the TEO consists of Its dura-tion is therefore the total duration of the TEO ie the sum ofthe durations of the separate episodes By using the concatena-tion of the separate utility proles we drop the information re-garding the time spans between the separate episodes That isagain a reection of our assumption of zero discounting The as-sumption would be eminently unreasonable if utility proleswould assign outcomes to time points instead of instant util-ities and illustrates the essential role of instant utility in ouranalysis

To each episode and TEO a utility prole is assigned throughthe above process and the total utility of an episode or TEO issimply the total utility of the belonging utility prole The rest ofthe analysis will only concern utility proles

f is the weak ordering of proles represented by total utilityie f f g if and only if the total utility of f is at least as high asthat of g We assume at rst that total utility is measured at anordinal level meaning that f comprises all relevant informationTherefore the rst part of our analysis is in terms of f The re-striction of f to complete proles is denoted by f c

We next turn to Axiom 3 monotonicity of f with respect tototal utility We rst give a formal statement of the axiom

AXIOM A1 [monotonicity in total utility formal statement ofAxiom 3] If f f g then famph f gamph and hampf f hampg wheneverthese concatenations are dened Strict preference in thepremise implies strict preference in the conclusion

We next demonstrate how versions of separability of f followfrom monotonicity with respect to total utility We say that f c

satises separability if

(A2) f g f gc c implies f f9 9

whenever for a partition IR of [0M[ f 5 g and f 9 5 g9 onI and f 5 f 9 g 5 g9 on R f c satises left separability if (A2)holds only for the special case in which I 5 [0e[ for some eand f c satises right separability if (A2) holds only for thespecial case in which I 5 [bM[ for some b

BACK TO BENTHAM 399

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

LEMMA A1 Under Axiom 1 (neutral concatenation) monoton-icity in total utility implies left- and right-separability for f c

Proof For left-separability let ff 9 gg9 be as above and as-sume that I 5 [0e[ We can write f 5 campx g 5 campy f 9 5 c9 ampxg9 5 c 9 ampy (dene c as the restriction of f ( 5 g) on [0e[ x as therestriction of f ( 5 f 9 ) on [eM[ ldquoshifted leftwardsrdquo etc) By mono-tonicity in total utility we have

x y c x c y c x c yx y c x c y c x c yx y c x c y c x c y

implies amp and also implies amp and also ~ implies ~ amp and also ~

(apply thecondition bothwith and

s s sa a a

f d

amp amp amp amp amp amp amp amp amp

)

9 99 99 9

That is in each case the preference between f and g agrees withthat between f 9 and g 9 This is what left-separability requires

Right-separability is derived similarly considering f 9 5 xampcg 5 yampc f 5 xampc g9 5 yampc9

Our technical condition concerns continuity with respect tothe supremum norm A sequence of proles f j converges to a pro-le f (in supremum norm) if these proles are all of the sameduration and for each positive e there exists a natural number Nsuch that [ f j (t) 2 f(t)| e for all j $ N and t in the domainSupnorm-continuity means that for every sequence f j convergingto f in supremum norm and every g s f there exists a naturalnumber N such that g s f j for all j $ N and the same holds witha instead of s everywhere We now state the main theoremformally

THEOREM A1 [formal version of Theorem 1] Let M 0 For abinary relation f dened over the (utility) proles ie allmeasurable bounded mappings from subintervals [0e[ of[0M[ to an interval X containing 0 the following two state-ments are equivalent(i) There exists a nondecreasing continuous (ldquovaluerdquo) func-tion v X reg IR assigning value 0 to 0 such that proles areordered according to the integral of the value of instant util-ity over time(ii) f is a supnorm-continuous weak order Axiom 1 (neutralconcatenation) Axiom 2 (monotonicity in instant utility) andAxiom 3 (monotonocity in total utility ie Axiom A1) hold

Furthermore v in (i) is a ratio scale

QUARTERLY JOURNAL OF ECONOMICS400

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

Proof Since the implication (i) THORN (ii) is easily establishedwe assume (ii) and derive (i) as well as the uniqueness result Asthe theorem is trivial if all levels of instant utility are equivalent(then all proles are equivalent by Axiom 2 and v 5 0) we as-sume that there are two levels of instant utility that are notequivalent Because of neutral concatenation we will mostly re-strict attention to the weak ordering f c of the complete prolesdened on all of [0 M[ By Lemma A1 monotonicity in total util-ity implies left- and right-separability of f c

For some n f 3 we now partition the interval [0 M[ into nsubintervals [m0m1[ [mn 2 1mn[ of equal length M n (m0 5 0mn 5 M) By (x1 xn) we denote the complete prole that as-signs xj to all time points in the jth interval This set of completeproles denoted by F n is isomorphic to Xn and we now study therestriction f r of f c to F n We rst show that any interval [mj 2 1mj[is essential with respect to f r ie proles from F n that agreeoutside of the interval need not be equivalent

Assume that the level of instant utility x is strictly preferredto y ie the complete prole that is constant x is strictly pre-ferred to the complete prole that is constant y Assume for con-tradiction that x[mj 2 1mj[ ~ y[mj 2 1mj[ where we follow theconvention of using the set [mj 2 1mj[ to denote also the indicatorfunction that is 1 on [mj 2 1mj[ and 0 on the rest of [0 M[ By Ax-iom 1 x[mi 2 1mi[ ~ y[mi 2 1mi[ also holds for all i different than jThen by left- and right-separability y[0 M[ ~ x[0m1[ 1 y[m1M[ ~ x[0m2[ 1 y[m2 M[ ~ ~ x[0mn 2 1[ 1 y[mn 2 1 M[ ~ x[0 M[contradicting our assumption that y[0 M[ a x[0 M[ So every in-terval [mj 2 1mj[ is essential with respect to f r

Because all intervals are essential and n $ 3 and f r is acontinuous weak order that satises left- and right-separabilityit satises full-force separability by Gorman [1968] and there ex-ist functions V1 Vn such that V1(x1) 1 1 Vn(xn) representsf r of F n We may and will assume that Vj(0) 5 0 for all j BecauseAxiom 1 (x0 0) ~ (0x0 0) ~ ~ (0 0x) and thisimplies that V1(x) 5 5 Vn(x) for all x We dene v(x) 5 V1(x)(m1 2 m0) We can then conclude that the integral of v representspreferences over F n By Axiom 2 v is nondecreasing As the aboveanalysis holds true for all n and thus for a dense subset of thecomplete proles supnorm-continuity implies that f c is repre-sented by the integral of v on the whole set of complete prolesBy zero-concatenation it now follows that the representation ex-tends to all proles

Gorman [1968] also demonstrated that the Vj functions de-

BACK TO BENTHAM 401

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

rived above are unique up to location and a common scale Thistheir unique relatedness to v and v(0) 5 0 imply that v is a ra-tio scale

Proof of Theorem 2 We assume the same technical condi-tions (M domain and supnorm-continuity) as in Theorem A1The necessity of Axiom 4 for linearity of the value function is obvi-ousmdashhence we assume the axiom and derive the representationNote that we do not have Axiom 3 (A1) available Therefore wemust derive it in some way A step prole is a nite concatenationof constant proles ie it is nite-valued and it is constantover intervals

LEMMA A2 Axiom 4 implies Axiom 3 (A1) for step proles

Proof Assume that for step proles xyc we have x f y andthat campx and campy are dened First assume that c is constant c9denotes the neutral prole of the same duration as c By neutralconcatenation we get c9 ampx ~ x f y ~ c9 ampy By Axiom 4 we can addup the instant utility of c over the duration of c and get campx f ecampy We can repeat this for other constant proles c1 cn toget cnamp amp c1 amp c amp x f cnamp amp c1 amp c amp y Every step-prolec0 can be written as a concatenation cn amp amp c1 amp c and hencewe get c0 ampx f c 0 ampy for all step proles c0 Similarly xampc 0 f yampc 0follows The same reasoning also applies to strict instead ofweak preferences

In the proof of Theorem 1A1 we only needed Axiom 3 (A1)and its implications (eg left- and right-separability) and in factall conditions except weak ordering and supnorm-continuity forstep proles Hence we can invoke the representation of the theo-rem Partition [0 M[ into [0 M2[ and [M2 M[ The notation(x1 x2) designates here the prole that is x1 on the rst intervaland x2 on the second Now (x0) ~ (x0)mdashhence by Axiom 4 (xe )~ (x 1 e 0) This implies that v(x 1 e ) 2 v(x) 5 v( e ) for all x and e ie v satises the Cauchy equation For the nondecreasing v thatimplies that v is linear

QED

All the results above have assumed total utility only at theordinal level and have characterized total utility as an increas-ing transform of an integral (because it induces the same order-ing over proles as the integral) We next consider the case inwhich total utility is measurable at the cardinal level That canbe tested by the following axiom

QUARTERLY JOURNAL OF ECONOMICS402

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

AXIOM A2 [cardinal total utility] The total utility of two concate-nated proles is the sum of their separate total utilities

In the presence of Axiom A2 Theorems 1 and 2 can bestrengthened to provide total utility as an integral of the value ofinstant utility and the integral of instant utility respectively Weassume in the theorems below the same technical conditions (Mdomain weak ordering supnorm-continuity) as in Theorem A1

THEOREM A2 Axioms 1 2 and A2 hold if and only if total utilityis an integral of the value of instant utility

Proof Necessity of the axioms is obviousmdashhence we assumethe axiom and derive the representation Axiom A2 impliesAxiom 3 and hence we obtain the integral representation ofTheorem A1 Note that the integral of the value function doessatisfy Axiom A2

Let (x1 x2) be the complete prole that is x1 on [0 M2[ and x2

on [M2 M[ Both total utility and the integral of the value func-tion provide additively decomposable representations for f thatboth assign 0 to the neutral prole By standard uniqueness re-sults on additive conjoint measurement (continuity of total utilityneed not be presupposed here but is implied see Wakker [1988])total utility must be a positive scalar times the integral We candivide the value function by that positive scalar

COROLLARY A1 Under the technical conditions of Theorem A3Axioms 1 2 4 and A2 hold if and only if total utility is theintegral of instant utility

WOODROW WILSON SCHOOL OF PUBLIC AFFAIRS PRINCETON UNIVERSITY

MEDICAL DECISION MAKING UNIT LEIDEN UNIVERSITY THE NETHERLANDS

ANDERSON SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA LOS ANGELES

REFERENCES

Becker G S Accounting for Tastes (Cambridge MA Harvard University Press1996)

Bentham J An Introduction to the Principle of Morals and Legislations (1789)reprinted (Oxford UK Blackwell 1948)

Brandstatter H ldquoEmotions in Everyday Life Situations Time Sampling of Sub-jective Experiencerdquo in F Strack M Argyle and N Schwarz eds SubjectiveWell-Being An Interdisciplinary Perspective (Oxford Pergamon 1991) pp173ndash92

Brickman P D Coates and R Janoff-Bulman ldquoLottery Winners and AccidentVictims Is Happiness Relativerdquo Journal of Personality and Social Psychol-ogy XXXVII (1978) 917ndash27

Broome J Weighing Goods (Oxford UK Blackwell 1991)Cabanac M ldquoPhysiological Role of Pleasurerdquo Science CLXXIII (1971) 1103ndash07

BACK TO BENTHAM 403

Clark A E and A J Oswald ldquoUnhappiness and Unemploymentrdquo EconomicJournal CIV (1994) 648ndash659

Constantinides G M ldquoHabit Formation A Resolution of the Equity PremiumPuzzlerdquo Journal of Political Economy XCVIII (1990) 519ndash43

Dasgupta P An Inquiry into Well-Being and Destitution (Oxford Clarendon1993)

Edgeworth F Y Mathematical Psychics An Essay on the Application of Mathe-matics to the Moral Sciences (1881) reprinted (New York M Kelly 1967)

Frank R H Passions within Reason The Strategic Value of the Emotions (NewYork Norton 1988)

Fredrickson B L and D Kahneman ldquoDuration Neglect in Retrospective Evalua-tions of Affective Episodesrdquo Journal of Personality and Social PsychologyLXV (1993) 45ndash55

Gilboa I ldquoExpectations and Variations in Multi-Period Decisionsrdquo EconometricaLVII (1989) 1153ndash69

Gorman W M ldquoThe Structure of Utility Functionsrdquo Review of Economic StudiesXXXV (1968) 367ndash90

Gottman J M and R W Levenson ldquoA Valid Procedure for Obtaining Self-Reportof Affect in Marital Interactionrdquo Journal of Consulting and Clinical Psychol-ogy LIII (1985) 51ndash160

Halmos P R Measure Theory (New York Van Nostrand 1950)Kahneman D ldquoNew Challenges to the Rationality Assumptionrdquo Journal of Insti-

tutional and Theoretical Economics CL (1994) 18ndash36Kahneman D B L Fredrickson C A Schreiber and D A Redelmeier ldquoWhen

More Pain Is Preferred to Less Adding a Better Endrdquo Psychological ScienceIV (1993) 401ndash05

Kahneman D and J S Snell ldquoPredicting a Changing Taste Do People KnowWhat They Will Likerdquo Journal of Behavioral Decision Making V (1992)187ndash200

Kahneman D and C Varey ldquoNotes on the Psychology of Utilityrdquo in J Elsterand J E Roemer eds Interpersonal Comparisons of Well-Being Studies inRationality and Social Change (New York Cambridge 1991) pp 127ndash63

Kapteyn A ldquoThe Measurement of Household Cost Functions Revealed Prefer-ence versus Subjective Measuresrdquo Journal of Population Economics VII(1994) 333ndash50

Loewenstein G ldquoThe Fall and Rise of Psychological Explanations in the Econom-ics of Intertemporal Choicerdquo in G Loewenstein and J Elster eds ChoiceOver Time (New York Russell Sage Foundation 1992) pp 3ndash34

Loewenstein G and D Adler ldquoA Bias in the Prediction of Tastesrdquo EconomicJournal CV (1995) 929ndash37

Mowrer O H and L N Solomon ldquoContiguity vs Drive-Reduction in Condi-tioned Fear The Proximity and Abruptness of Drive-Reductionrdquo AmericanJournal of Psychology LXVII (1954) 15ndash25

Nussbaum M C and A Sen The Quality of Life (Oxford UK Clarendon 1993)Redelmeier D and D Kahneman ldquoPatientsrsquo Memories of Painful Medical Treat-

ments Real-Time and Retrospective Evaluations of Two Minimally InvasiveProceduresrdquo Pain CXVI (1996a) 3ndash8

Redelmeier D and D Kahneman ldquoImproving the Memory of a ColonoscopyrdquoWorking Paper 1996b

Schelling T C Choice and Consequence Perspectives of an Errant Economist(Cambridge MA Harvard University Press 1984)

Scitovsky T The Joyless Economy (New York Oxford University Press 1976)Schreiber C A and D Kahneman ldquoBeyond the Peak and End Hypothesis Ex-

ploring the Relation between Real-Time Displeasure and Retrospective Eval-uationrdquo Working Paper Princeton University 1996

Sen A K ldquoWelfare Preference and Freedomrdquo Journal of Econometrics L(1991) 15ndash29

Simonson I ldquoThe Effect of Purchase Quantity and Timing on Variety-SeekingBehaviorrdquo Journal of Marketing Research XXVII (1990) 150ndash62

Snell J B J Gibbs and C Varey ldquoIntuitive Hedonics Consumer Beliefs aboutthe Dynamics of Likingrdquo Journal of Consumer Psychology IV (1995) 33ndash60

Stevens S S Psychophysics Introduction to its Perceptual Neural and SocialProspects (New York Wiley 1975)

QUARTERLY JOURNAL OF ECONOMICS404

Stigler G J ldquoThe Development of Utility Theory I IIrdquo Journal of Political Econ-omy LVIII (1950) 307ndash27 373ndash96

Stigler G J and G S Becker ldquoDe Gustibus non Est Disputandumrdquo AmericanEconomic Review LXVII (1977) 76ndash90

Tinbergen J ldquoOn the Measurement of Welfarerdquo Journal of Econometrics L(1991) 7ndash13

Tversky A and D Kahneman ldquoRational Choice and the Framing of DecisionsrdquoJournal of Business CIX (1986) S251ndash78

Tversky A and D Kahneman ldquoReference Theory of Choice and ExchangerdquoQuarterly Journal of Economics CVI (1991) 1039ndash61

Van Praag B M S ldquoOrdinal and Cardinal Utility An Integration of the TwoDimensions of the Welfare Conceptrdquo Journal of Econometrics L (1990)69ndash89

Varey C and D Kahneman ldquoExperiences Extended across Time Evaluation ofMoments and Episodesrdquo Journal of Behavioral Decision Making V (1992)169ndash86

Wakker P P ldquoThe Algebraic versus the Topological Approach to Additive Repre-sentationsrdquo Journal of Mathematical Psychology XXII (1988) 421ndash35

Wegener B ed Social Attitudes and Psychophysical Measurements (HillsdaleNJ Lawrence-Erlbaum 1982)

BACK TO BENTHAM 405