Realism’s Risk: How Should We Interpret Buchak’s Risk Function?

Background: My Question and MotivationsThree Models of Risk Aversion

r and Character Traits?r and Moods?

Conclusion: Constructivism or Sui Generis Realism?

Realism’s Risk: How Should We InterpretBuchak’s Risk Function?

Zachary C. Irving

University of Toronto

[email protected]

July 10, 2013

Zachary C. Irving Realism’s Risk

What is REU Theory?Realism vs. ConstructivismPsychological MotivationDecision Theoretic Motivation

What is REU Theory?

Risk-Weighted Expected Utility Theory

Extension on EU theory aiming to better model risk-aversion andrisk-seeking

Risk Functions

Agents have a probability function, utility function, and a riskfunction r

Risk function: models “. . . the extent to which [the agent] isgenerally willing to accept the risk of something worse inexchange for the possibility of something better” (Buchak2011, p. 48)

What is REU Theory?

Risk-Weighted Expected Utility Theory

Extension on EU theory aiming to better model risk-aversion andrisk-seeking

Risk Functions

Agents have a probability function, utility function, and a riskfunction r

Risk function: models “. . . the extent to which [the agent] isgenerally willing to accept the risk of something worse inexchange for the possibility of something better” (Buchak2011, p. 48)

Strong Realism about r?

My Question

Can we endorse a “strong realist” (Zynda 2000, p. 8) (rather thanconstructivist) interpretation of Buchak’s risk function?

Strong Realism

Each function (in a formal theory of rationality) represents apsychologically real entity, which cannot be reductivelydefined in terms of an agent’s preferences

Example: utility and probability functions represent strengthsof desire and degrees of belief, respectively

Strong Realism about r?

My Question

Can we endorse a “strong realist” (Zynda 2000, p. 8) (rather thanconstructivist) interpretation of Buchak’s risk function?

Strong Realism

Each function (in a formal theory of rationality) represents apsychologically real entity, which cannot be reductivelydefined in terms of an agent’s preferences

Example: utility and probability functions represent strengthsof desire and degrees of belief, respectively

Constructivism

Use a representation theorem to reductively defineprobability/utility/risk functions in terms of preferences

Representation theorem: an agent whose preferences obeyaxioms like transitivity can be represented as having a uniqueprobability, utilitya, and risk function, which maximizeexpected utility

aUtility functions are unique up to positive affine transformations

Example: Revealed Preference Constructivism

Functions are defined in terms of preferences, which are defined interms of choice behaviour

Constructivism

Constructivism (cont.)

Example: Constructivism About Utility

“. . . there is no need to assume, or to philosophize about, theexistence of an underlying subjective utility function, for we are notattempting to account for the preferences. . . . We only wish todevise a convenient way to represent them” (Luce and Raiffa 1957,p. 32)

Motivations

Question

Why should philosophers interpret r?

Three Motivations

One Psychological

Two/Three Decision Theoretic

Motivations

Question

Why should philosophers interpret r?

Three Motivations

One Psychological

Two/Three Decision Theoretic

Psychological Motivation

Psychological Question

Why do humans have the risk-attitudes we do?

REU Theory’s (Surprising) Answer

Option 1: r reduces to folk psychological entities

r represents personality traitsr represents moods

Option 2: Constructivism about r

Option 3: r is a sui generis element of agentive psychology

First Decision Theoretic Motivation

Motivation

Even if you’re a committed realist or constructivist about EUTheory, there’s an open question about whether r ispsychologically real

Argument

1 Both realists and constructivists have reason to think thatagents have a risk function

2 We should investigate realism separately for each function inour best theory of rationality (probability, utility, and riskfunctions)

3 Therefore, we should investigate realism about rindependently

Motivation

Argument

Motivation

Argument

Motivation

Argument

Motivation

Argument

First Decision Theoretic Motivation (cont.)

Argument: Premise 1

REU Theory avoids paradoxes facing the EU interpretation ofrisk aversion (Rabin 2000; Allais 1979/1953, Hansson 1988)REU is a normative theory of rationality, unlike other theoriesthat avoid paradoxes (e.g. Kahneman and Tversky 1979;Quiggin 1982)

Argument: Premise 1

REU Theory avoids paradoxes facing the EU interpretation ofrisk aversion (Rabin 2000; Allais 1979/1953, Hansson 1988)REU is a normative theory of rationality, unlike other theoriesthat avoid paradoxes (e.g. Kahneman and Tversky 1979;Quiggin 1982)

Argument: Premise 2

Precedent: distinct debates over realism about the probability(e.g. Zynda 2000) and utility functions (e.g. Dreier 1996)Justification: Prima facie, realism about each function is alogically independent psychological hypothesis

Argument: Premise 2

Precedent: distinct debates over realism about the probability(e.g. Zynda 2000) and utility functions (e.g. Dreier 1996)Justification: Prima facie, realism about each function is alogically independent psychological hypothesis

Second Decision Theoretic Motivation

Disanalogy: Realism about r vs. p or u

Folk psychological analogues of probability and utilityfunctions: degrees of belief, strengths of desire

What’s the folk psychological analogue of r?

Problems

If we’re committed to REU Theory, problems for realism

If we’re committed to realism, problems for REU Theory

Upshot

Philosophical work needed to identify candidates for r realism

Problems

Upshot

Problems

Upshot

Problems

Upshot

Outline

1 Three Models of Risk Aversion

2 r and Character Traits?

3 r and Moods?

4 Conclusion: Constructivism or Sui Generis Realism?

EU Theory: SaturationAU Theory: PessimismREU Theory: Sensitivity to Global PropertiesFormalism

Outline

1 Three Models of Risk AversionEU Theory: SaturationAU Theory: PessimismREU Theory: Sensitivity to Global PropertiesFormalism

3 r and Moods?

Three Models of Risk Aversion

John prefers $50 to a coin flip for $100 or $0

Three Explanations of John

1 EU Theory: John has saturated desires

2 Anticipated Utility (AU) Theory: John has pessimistic beliefs

3 REU Theory: John is sensitive to the global properties forgambles

Three Models of Risk Aversion

John prefers $50 to a coin flip for $100 or $0

Three Explanations of John

1 EU Theory: John has saturated desires

2 Anticipated Utility (AU) Theory: John has pessimistic beliefs

3 REU Theory: John is sensitive to the global properties forgambles

EU Theory: Saturation

Formally: Concave UtilityFunction

John prefers $50 to acoin-flip for $0 or $100

EU Interpretation: John’sutility function is concave

Utility

Amount of Good

Psychologically: Saturation ofDesire

Analogy: when I have lots ofapples, I want another appleless than when I had none;my desire becomes saturated

The more money John has,the less he desires $50

u($50)− u($0) >u($100)− u($50)

Utility

Amount of Good

u($50)− u($0) >u($100)− u($50)

Utility

Amount of Good

u($50)− u($0) >u($100)− u($50)

Utility

Amount of Good

u($50)− u($0) >u($100)− u($50)

Utility

Amount of Good

u($50)− u($0) >u($100)− u($50)

Risk Aversion as Saturation

The more money John has, the less he desires $50

Problem: Paradoxes

Generates paradoxes (Rabin 2000; Allais 1979/1953, Hansson1988)

Rabin (2000): “Calibration Theorem”

Moderate risk aversion for small gambles ⇒ extreme riskaversion for large gamblesIf John always prefers $100 over a coin flip for $0 and $110,then he always prefers $1000 over a coin flip of $0 and ∞(Rabin 2000, p. 1282)

Risk Aversion as Saturation

The more money John has, the less he desires $50

Problem: Paradoxes

Generates paradoxes (Rabin 2000; Allais 1979/1953, Hansson1988)

Rabin (2000): “Calibration Theorem”

Moderate risk aversion for small gambles ⇒ extreme riskaversion for large gamblesIf John always prefers $100 over a coin flip for $0 and $110,then he always prefers $1000 over a coin flip of $0 and ∞(Rabin 2000, p. 1282)

AU Theory: Pessimism

w(·): Probability Weighting Function

w(·): known objective probabilities → degrees of belief

Distorts probability judgments, depending on where anoutcome appears in the gamble

Risk Aversion as Pessimism

Risk Aversion Subjective degrees of belief in bad outcomes aremore than their known objective probabilities(opposite for good outcomes)

John In some sense, John knows the coin is fair, but alsobelieves he’s more likely to get $0 than $100

AU Theory: Pessimism (cont.)

John knows the coin is fair, but believes he’s more likely to get $0than $100

Problem One: Automatic Irrationality (Buchak 2011, p. 47)

Risk averse agents are automatically epistemically irrational

Problem Two: Intuitive Phenomenon

Imagine John’s rationale: “the risk of getting $0 doesn’t makeup for the possibility of getting $100”

Pessimism doesn’t capture this rationale; saturation does(kinda), but generates paradoxes

REU Theory avoids both problems

REU Theory: Sensitivity to Global Properties

Risk Function r

r is formally equivalent to w(·), but has a different interpretation

Realist Interpretation: Sensitivity to Global Properties

r : not a feature of beliefs or desires about outcomes

r : general “strategy. . . [for] realizing [your] ends as a whole”(Buchak 2011, pp. 35-36)

Risk averse strategy: prefer gambles that are “less spread out”(that guarantee you something you want) over a chance ofsomething worse or betterStrategies are sensitive to the global properties of gambles(e.g. whether gambles are spread out, top-heavy, etc.)

Risk Function r

Risk averse strategy: prefer gambles that are “less spread out”(that guarantee you something you want) over a chance ofsomething worse or better

Strategies are sensitive to the global properties of gambles(e.g. whether gambles are spread out, top-heavy, etc.)

Risk Function r

REU Theory: Folk Psychological Interpretation of r

Risk Function r

r represents strategies that are sensitive to the global properties ofgambles, not attitudes toward particular outcomes

Constraint on a Folk Interpretation of r

Goal Reduce the risk function to some familiarfolk-psychological entity

Constraint Mental states that are directed toward particularoutcomes (e.g. beliefs, desires) are bad candidates

Candidates Undirected Psychological Entities

Character traits‘Undirected mental states’ like moods (Searle1983, p. 1)

Risk Function r

Outline

1 Three Models of Risk AversionEU Theory: SaturationAU Theory: PessimismREU Theory: Sensitivity to Global PropertiesFormalism

3 r and Moods?

Formalism: EU vs. REU

Expected Utility

EU(G ) = u1 + (∑n

2 pi ) [u2 − u1] + . . . + pn[un − un−1]

The expected utility of a gamble = the utility of its worstoutcome + the utility interval between the worst and secondworst outcome, weighted by the probability that something atleast as good as the second worst outcome will happen, . . .

Risk-Weighted Expected Utility

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

r : [0, 1]→ [0, 1], which weights outcomes, depending onwhere they appear in a gamble

r(0) = 0, r(1) = 1, r is non-decreasing

Expected Utility

EU(G ) = u1 + (∑n

2 pi ) [u2 − u1] + . . . + pn[un − un−1]

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

Expected Utility

EU(G ) = u1 + (∑n

2 pi ) [u2 − u1] + . . . + pn[un − un−1]

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

REU Theory: Formalism (Risk Neutrality)

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

Risk Neutrality: r(p) = p

r(p) = p

If r(p) = p, thenREU(G ) = EU(G )

The agent isindifferent toward risk

REU Theory: Formalism (Risk Aversion)

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

Risk Aversion: r(p) < p (e.g. r(p) = 2p − p2)

r(p) < p

1/2r(p) = p

p 1/2 1

1 If r(p) < p ∀x ∈ (0, 1),then REU(G ) < EU(G )

2 But since r(1) = 1,REU(sure) = EU(sure)

3 Thus, the agent prefersa sure thing to a gamblewith the same EU

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

r(p) < p

1/2r(p) = p

p 1/2 1

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

r(p) < p

1/2r(p) = p

p 1/2 1

REU Theory: Formalism (Risk Seeking)

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

Risk Seeking: r(p) > p (e.g. r(p) = p2)

r(p) > p

r(p) = p

p 1/2 1

1 If r(p) > p∀x ∈ (0, 1),then REU(G ) > EU(G )

2 But sincer(1) = 1,REU(sure) =EU(sure)

3 Thus, the agent prefersa gamble to a sure thingwith the same EU

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

r(p) > p

r(p) = p

p 1/2 1

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

r(p) > p

r(p) = p

p 1/2 1

Background: r as a Character TraitOne-One ViewOne-Many View

Outline

2 r and Character Traits?Background: r as a Character TraitOne-One ViewOne-Many View

3 r and Moods?

Why Character Traits? Boldness and Timidity

Motivating Examples: Boldness and Timidity

Bold (timid) people might have risk functions that make themprefer gambles that are more (less) spread out

DeSousa: Boldness/Timidity as Maximax/maximin

DeSousa’s Hypothesis

Bold (timid) people obey maximax (maximin) (1987, p. 194)Maximax: Choose A over B iff A’s best (worst) outcome isbetter than B’s

Maximax and maximin are limit cases of r (Buchak 2011,pp. 57-59); boldness/timidity are probably less extreme

Maxi Maxine will choose a 1% chance of 2 apples and a 99%chance of violent death over 1 apple

Bold (timid) people obey maximax (maximin) (1987, p. 194)

Maximax: Choose A over B iff A’s best (worst) outcome isbetter than B’s

r as a Character Trait: Two Views

One-to-One vs. One-To-Many View

1 One-To-One View: Character traits like boldness and timiditycorrespond to risk functions

2 One-to-Many View: Character traits like boldness and timiditycorrespond to distributions of risk functions over time

Outline

3 r and Moods?

One-One View: Problem One

Preliminary Result

One-one view implies that risk functions are stable

Argument

1 Character traits stand in a one-to-one relation to riskfunctions (one-one view)

2 Character traits are stable over time (empirical fact)

Personality traits at one time a) predict traits seven years laterand b) become better predictors with age (see Roberts andDelVecchio 2000 for a metaanalysis)

3 Therefore, risk functions are stable over time (from 1 andOne-One View)

Preliminary Result

Argument

Preliminary Result

Argument

Preliminary Result

Argument

Preliminary Result

Argument

Problem with Stable Risk Functions

Risk behaviour varies with temporary states such as moods, andthus isn’t stable over time

Risk Behaviour and Moods: Field and Lab Studies

Field Study: Capital market traders take less (more) risk onsunny (cloudy) days (Kliger and Levy 2003)

Laboratory Results

Good Mood: Subjects who received candy buy more insurance(Arkes, Herren, and Isen 1988) and gamble less (Nygren et al.1996)Bad Mood: Sad subjects are risk-seeking (Raghunathan andPham 1999)

Laboratory Results

Good Mood: Subjects who received candy buy more insurance(Arkes, Herren, and Isen 1988) and gamble less (Nygren et al.1996)

Bad Mood: Sad subjects are risk-seeking (Raghunathan andPham 1999)

Laboratory Results

One-to-One View: Problem Two

Implausible View of Personality

One-One View assumes that character traits manifest inconsistent behaviour (same general strategy toward risk)across situations

Outline

3 r and Moods?

One-To-Many View

Thesis

Character traits like boldness and timidity correspond todistributions of risk functions over time

Stable Character Traits

Doesn’t assume that risk functions are stable

Plausible View of Personality

Fits with the theory of character traits that came out of thePerson/Situation Debate

One-To-Many View

Thesis

One-To-Many View

Thesis

Person Situation Debate

Is behaviour affected by stable traits or mostly determined bysituations?

Situation Datum: Low Cross-Situational Correlations

Individual differences in behaviour are weakly correlated fromone situation to the next (.20-.30; Mischel 1964; Vernon 1964)

Sometimes Jack is more gregarious than Jill, sometimes less

Person Datum: High Aggregate Correlations

Individual differences in behaviour are highly correlated whenaggregated over a week (up to .90 Epstein 1979)

Jack tends to be more gregarious than Jill, on the whole

Person Situation Debate: Fleeson’s Model

Fleeson’s (2001) Model

Personality traits exist, but are characteristic distributions ofbehaviour rather than single ways of acting

Empirical Evidence

Setup Hourly personality measures: e.g.“Over the pasthour, how well does ‘talkative’ describe you?”(Fleeson 2001)

Results Behaviour falls on a distribution with a) highvariance, but b) stable means and standard deviations

Empirical Evidence

Person Situation Debate: Fleeson’s Model (cont.)

Traits as Distributions of Behavior

Extroversion at a given moment

1 2 76543

Trait Differences as Distribution Differences

Jill Jack

High variance, butstable means andstandard deviations.Explains:

1 Lowcross-situationalcorrelations

2 High aggregatecorrelations

Person Situation Debate: Fleeson’s Model (cont.)

Traits as Distributions of Behavior

Extroversion at a given moment

1 2 76543

Trait Differences as Distribution Differences

Jill Jack

High variance, butstable means andstandard deviations.Explains:

1 Lowcross-situationalcorrelations

2 High aggregatecorrelations

One-Many View

Character Traits as Distributions of Risk Functions

Character traits like boldness and timidity correspond tocharacteristic distributions of risk functions over time

Advantages

Risk Aversion at a given moment

r(p)<<p r(p)=pr(p)<p

Risk Attitudes as Frequency Distributions

Timid Tim Bold Billy

r(p)>p r(p)>>p

1 Risk functions can varyover time

2 Character traitscorrespond to a realdifference in riskfunctions

3 Psychologically plausible

One-Many View

Advantages

r(p)>p r(p)>>p

One-Many View

Advantages

r(p)>p r(p)>>p

One-Many View

Advantages

r(p)>p r(p)>>p

Limitation of the One Many View

Incomplete Interpretation of r

Character traits (at best) predict the distribution of someone’srisk function over time

Remaining Explanandum: what psychological entities (if any)bring about changes in the risk function

Prima facie candidate: Moods

Moods and Optimism/PessimismCautious Optimism and Daring PessimismCautious Optimism as Mood MaintenanceCautious Optimism as r?

Outline

3 r and Moods?Moods and Optimism/PessimismCautious Optimism and Daring PessimismCautious Optimism as Mood MaintenanceCautious Optimism as r?

r as a Mood

Thesis

Moods cause us to use strategies that are sensitive to certainglobal properties of gambles (e.g. whether it’s “spread out”)

Motivations

1 Moods aren’t directed at particular outcomes: “. . . the bestavailable description of [what a mood is about] is ‘everything’or ‘nothing in particular”’ (Goldie 2002, p. 144)

2 Moods correlate with risk behaviour in the world and lab

Empirical Question

Do moods cause risk behaviour by changing our risk functions,saturation, or optimism/pessimism?

r as a Mood

Thesis

Motivations

Empirical Question

r as a Mood

Thesis

Motivations

Empirical Question

r as a Mood

Thesis

Motivations

Empirical Question

Outline

Moods and Optimism/Pessimism

Empirical Result

Positive (negative) affect makes us more optimistic (pessimistic)when we estimate the probabilities of good and bad events

Empirical Evidence: Johnson and Tversky (1984)

Setup Read emotionally charged newspaper articles, thenestimate annual deaths from car crashes, cancer etc.

Results Subjects in a good (bad) mood estimate that badevents are less (more) likely

Upshot

Insofar as we seem more risk-seeking when in a good mood, this isattributable to Quiggin-style optimism (rather than r)

Empirical Result

Upshot

Empirical Result

Upshot

Empirical Result

Upshot

Outline

Cautious Optimism and Daring Pessimism

Moods and Risk Aversion: Conflicting Effects

Good moods can cause risk averse behaviour, unlike optimism(opposite for bad moods)

Good (bad) mood must change some other psychologicalentity to cause this risk behaviour (candidate: r)

Empirical Evidence for “Cautious Optimism”

Capital market traders are more (less) risk averse on sunny(cloudy) days (Kliger and Levy 2003)

Experimental participants will buy more insurance (Arkes,Herren, and Isen 1988) and gamble less when given candy(Nygren et al. 1996; Arkes, Herren, and Isen 1988)

Outline

Nygren et al. 1996: Mood-induced risk preferences

Background: Nygren et al. 1996

Experiment 1: Good mood increases optimism, decreaseswillingness to gamble (Nygren et al. 1996)

Experiment 2: Tests “mood maintenance” explanation ofcautious optimism

Happy people avoid large risks because it might spoil theirmood

Nygren et al. 1996: Mood-induced risk preferences

Background: Nygren et al. 1996

Experiment 1: Good mood increases optimism, decreaseswillingness to gamble (Nygren et al. 1996)

Experiment 2: Tests “mood maintenance” explanation ofcautious optimism

Happy people avoid large risks because it might spoil theirmood

Nygren Gambles: Probability/Payout Tradeoff

Pairs of Gambles: Probability/Payout Tradeoff

Gambles are identical except one has a good chance ofwinning (pwpl > 2) and one has a good payout for winningrelative to losing ( vwvl > 2)

Risk preference: do you prefer a better chance of winning, ormore potential winnings (relative to losses)?

Nygren Gambles: Probability/Payout Tradeoff

Pairs of Gambles: Probability/Payout Tradeoff

Gambles are identical except one has a good chance ofwinning (pwpl > 2) and one has a good payout for winningrelative to losing ( vwvl > 2)

Risk preference: do you prefer a better chance of winning, ormore potential winnings (relative to losses)?

Nygren Gambles: Probability/Payout Tradeoff (cont.)

Example

GProb = {〈1/8,−8〉, 〈3/8, 0〉, 〈1/2, 2〉}More than twice as likely to win as lose, but you can lose morethan twice as much as you can win

GPay = {〈1/2,−2〉, 〈3/8, 0〉, 〈1/8, 8〉}

-8 84-4

Prob Pay

Results and Interpretations

Results

Neutral Mood: GProb � GPay (Strong)

Positive Mood: GPay � GProb (Mild)

Mood Maintenance Interpretation Nygren et al.

Subjects in a good mood avoid the possibility of losing largeamounts, and thus spoiling their good mood (also why theygamble less)

r Interpretation

Subjects in good versus neutral moods have different r

Is this plausible? If yes, does it explain how r changes overtime?

Results

r Interpretation

Results

r Interpretation

Results

r Interpretation

Outline

r and Nygren Gambles

Theses

1 Some r can explain preferences over Nygren Gambles

2 Important class of r are Nygren Risk Neutral; thus,mood-induced preferences for Nygren Gambles can’t explainwhy we token them

r and Nygren Gambles

Theses

1 Some r can explain preferences over Nygren Gambles

2 Important class of r are Nygren Risk Neutral; thus,mood-induced preferences for Nygren Gambles can’t explainwhy we token them

Nygren Risk Neutrality

Theorem

On the assumption that u(v) is linear,REU(GProb) = REU(GPay )⇔ r ′′(p) = r ′′(1− p),∀p ∈ [0, 1]

r ′′(p) = r ′′(1− p),∀p ∈ [0, 1]says that r ′′ is symmetric alongthe axis 1− p

p 1/2 1

Why A Linear Utility Function?

If r is sufficient to generate Nygren-Risk-Aversion/Seeking, rshould do so without saturated utility

Theorem

r ′′(p) = r ′′(1− p), ∀p ∈ [0, 1]says that r ′′ is symmetric alongthe axis 1− p

p 1/2 1

Theorem

r ′′(p) = r ′′(1− p), ∀p ∈ [0, 1]says that r ′′ is symmetric alongthe axis 1− p

p 1/2 1

Nygren Risk Neutrality (NRN)

REU(GProb) = REU(GPay )⇔ r ′′(p) = r ′′(1− p), ∀p ∈ [0, 1]

r ′′ is symmetric along the axis 1− p

NRN Is A Weak Condition

NRN is a weak condition that manyrisk- averse/seeking agents wouldsatisfy (e.g. any with constant r ′′)

If agents token risk functions likethese, evidence for mood-inducedNygren Risk Aversion/Seekingcan’t explain why

E.g. r(p) = p2

r(p) < p

1/2r(p) = p

p 1/2 1

E.g. r(p) = p2

r(p) < p

1/2r(p) = p

p 1/2 1

E.g. r(p) = p2

r(p) < p

1/2r(p) = p

p 1/2 1

Plausibility Argument: Agents Satisfy NRN

Deny that any real agents are NRN

Some rational risk functionsrepresent attitudes that no one has

Problem

Constant r ′′ is a natural attitude toward risk: representsespecially consistent, pure aversion/attraction to gambling

Ad hoc to suppose no agents have these attitudes

Problem

Plausibility Argument: Agents Satisfy NRN (cont.)

Consistency of Constant r ′′

The simpler r ’s functional form,the more consistent your attitudetoward risk

Risk Averse/Seeking r : The effectof small changes in an outcome’sprobability (r ′) depends on it’slocation in the gamble

E.g. r(p) = 2p − p2

r(p) > p

r(p) = p

p 1/2 1

Constant r ′′ : r ′ changes in a consistent way over the wholegamble

E.g. r(p) = 2p − p2

r(p) > p

r(p) = p

p 1/2 1

E.g. r(p) = 2p − p2

r(p) > p

r(p) = p

p 1/2 1

Constant r ′′ as Pure Risk Aversion/Seeking

Agents with a constant r ′′ can be averse/attracted to gamblingsimpliciter, without caring about other properties of gambles

Contrast: Reasonable MaxiMin (S-Shaped r)

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

1 Cares more about theworst outcomes than thebest

2 Will prefer some surethings to gambles withthe same EU, and viceversa

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

REU(G ) = u1 + r (∑n

2 pi ) [u2 − u1] + . . . + r(pn)[un − un−1]

Conclusion: Risk Functions and Moods

Ad hoc to deny that people have pure and consistent aversionto gambling

Evidence for mood-induced Nygren Risk Aversion/Seekingcan’t explain why we have these attitudes

Conclusion: Risk Functions and Moods

Ad hoc to deny that people have pure and consistent aversionto gambling

Evidence for mood-induced Nygren Risk Aversion/Seekingcan’t explain why we have these attitudes

Folk Psychological InterpretationsConstructivismSui Generis Realism

Outline

3 r and Moods?

Folk-Psychological Interpretation of r?

r as Character Traits

One-One One-One Mapping of character traits to riskfunctions

Psychologically Implausible

One-Many Character traits are distributions of risk functions

Psychologically plausibleOpen question: what psychological entities (ifany) explain why risk functions vary over time?

r as Moods

Hypothesis Moods explain why risk functions vary over time

Problem Evidence for the effect of mood on risk-behavior iseither

Directly attributable to a psychologicalphenomenon other than r (optimism/pessimism)Consistent with only a narrow range of riskfunctions (ones that aren’t NRN)

Looking Forward: Constructivist Option

Constructivism about r

r is defined in terms of preferences, which are ontologicallyfundamental

Looking Forward: Realist Option

Sui Generis Realism about r

r represents a real psychological entity, which isn’t reducibleto preferences or folk-psychological moods/character traits

Roughly: Momentary strategy toward risk

Looking Forward: Realist Option

Sui Generis Realism about r

r represents a real psychological entity, which isn’t reducibleto preferences or folk-psychological moods/character traits

Roughly: Momentary strategy toward risk

Looking Forward: Realist Option (cont.)

Analogy: Jamesian Epistemic Strategy

James How much an epistemic agent cares about believingtruths or avoiding falsehoods is part of herpsychology (irreducible to preferences)

Risk A practical agent’s strategy toward risk is part of hispsychology

Analogy: Jamesian Epistemic Strategy

James How much an epistemic agent cares about believingtruths or avoiding falsehoods is part of herpsychology (irreducible to preferences)

Risk A practical agent’s strategy toward risk is part of hispsychology

Worry: Wrong Order of Explanation

Shouldn’t psychology inform our (descriptive) decision theory, notthe other way around?

Rationality and Psychological Discovery

Theories of rationality can identify elements of our mental lifethat philosophers have ignored

Analogy: Bratman on Intentions

Remember John: doesn’t John’s psychology include hisattitude toward risk?

Acknowledgements

Thanks to Jonathan Weisberg, Avi Kulkarni, Lara Buchak, CarlosAvnanciao, Sheisha Kulkarni, and Nathan Howard. This researchwas supported by the Social Sciences and Research Council ofCanada

Realism’s Risk: How Should We Interpret Buchak’s Risk Function?

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Realism’s Risk: How Should We Interpret Buchak’s Risk Function?

Transcript of Realism’s Risk: How Should We Interpret Buchak’s Risk Function?