Ratification through referendum or parliamentary vote: When to call a non-required referendum?

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Ratification through referendum or parliamentary vote:When to call a non-required referendum?

George Tridimas ⁎

University of Ulster, School of Economics and Politics, Shore Road, Newtownabbey, Co. Antrim, BT37 0QB, UK

Received 27 April 2006; received in revised form 25 September 2006; accepted 25 September 2006Available online 1 December 2006

Abstract

The paper examines the choice of an incumbent government to call either a non-required referendum ora parliamentary vote to ratify legislation, when there is uncertainty about the preferences of voters andelected representatives. Winning a referendum confers different gains from winning a parliamentary votebut requires different levels of effort to attract support. Differences in the preferences of the majority ofvoters and representatives, personal support for the incumbent and parliamentary party discipline emerge asdeterminants of the decision to call a non-required referendum.© 2006 Elsevier B.V. All rights reserved.

JEL classification: D72; D78Keywords: Non-required referendum; Parliamentary vote; Spatial voting under uncertainty; Incumbent versus opposition

1. Introduction

Settling important constitutional questions by referendum is common in democratic countries.Constitutional amendments around the world and ratification of international treaties in theEuropean Union have been decided by referenda. Switzerland and the USA, at respectively thecanton and state levels, have a long history of deciding important policy decisions by means ofdirect rather than representative democracy. It is unsurprising that important legislation is ratifiedby referendum when the constitution so mandates. However, why do governments call areferendum to approve legislation when this is not required by the constitution?

European integration illustrates the relevance of non-required referenda. During the period1957–2006, out of a total of 43 integration referenda, 23 were not constitutionally required but

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were called at the discretion of the incumbent government; 18 of these 23 resulted in a pro-integration vote as the incumbent government had sought. France has held three EU-related non-required referenda, all initiated by the President of the Republic. The UK approved EECmembership in 1975 in a non-required referendum, the only national UK referendum thus far. In2003, seven of the nine referenda held by the new entrants to approve membership were notrequired.1 Again, none of the four referenda held in 2005 by Spain, France, the Netherlands, andLuxembourg to ratify the EU Constitutional Treaty were constitutionally mandated.2 See theAppendix for the relevant details of the EU referenda.3

Why does the government choose to call a referendum rather than pass legislation throughparliament, despite the fact that the constitution permits to do the latter? After all, the outcome of areferendum that polls the entire electorate is less predictable than a parliamentary vote, where theincumbent typically enjoys the support of the majority of elected representatives. Why does theincumbent choose to risk defeat in a referendum rather than rely on his parliamentary majority?This question is the focus of the present study.

In politics, some issues cause deep intra-party splits between the elected representatives of thesame party rather than inter-party divisions amongst different parties. Constitutional issues, whichconcern questions of governance and national sovereignty of a state, are a prime example. It isthen unlikely that the standard system of parliamentary politics will be able to resolve all thoseissues. On the contrary, it is more likely that the leader of the party in office will call a referendumto decide them.4 Ratifying changes to constitutional arrangements in a referendum conferslegitimacy to their adoption (or rejection) by taking the decision away from parochialparliamentary majorities and putting it into the hands of the citizenry.5

Earlier scholarship has noted the partisan advantage that calling a referendum confers to theincumbent. Bogdanor writes: “In general, where the government has discretion as to whether tocall a referendum, the referendum will strengthen the government… Where the power to call areferendum lies in the hands of government, it is likely to prove a tactical weapon in strengtheningits powers” (1994, p. 31). Similarly, Hug and Sciarini (2000) comment: “First, a governmentmight use a referendum to strengthen its own position. It can do so by attempting to gloss overinternal divisions or by creating divisions in parties of the opposition…Second, a referendum

1 The determinants of the ‘Yes’ votes in the 2003 referenda are studied in detail in Sczcerbiak and Taggart (2004) andDoyle and Fidrmurc (2006).2 On the 2005 French referendum, see Aboura (2005), Franck (2005a,b), Jérôme and Vaillant (2005) and Lemmenicier

(2005) in the Symposium of the European Journal of Political Economy, and Ivaldi (2006).3 Queries have been raised about the nature of votes in EU referenda. Specifically, voters may not care much about

“Europe” but may treat referenda on integration like “second order” national elections and use the opportunity to rewardor punish the conduct of the party in office. Then the referendum outcome will be shaped by the stance of the parties onthe issue and the popularity of the government rather than by intrinsic individual preferences for integration. SeeSchneider and Weitsman (1996), Franklin et al. (1994) and Gabel (1998). Recently a more synthetic view has gainedcurrency (Franklin, 2002). Notably, when integration is an issue of low salience to voters, a referendum tests more thestanding of the government than voter support for integration; however, if integration is an issue of high salience theoutcome of the referendum will depend on the positions taken by the government and the opposition as well as thepreferences of voters.4 See Bogdanor (1994). In addition he identifies moral issues as issues to be resolved by referenda. Moral issues

concern questions of conscience and “right” or “wrong”, such as divorce and abortion, and may give rise to intensefeelings amongst many voters causing divisions within the same party (see also Matsusaka, 2005).5 However, this argument does not automatically justify the referendum as the best way to amend a constitution. For

example, noting that choosing constitutional arrangements requires compromises on a multitude of issues whereinformation and specialised expertise may be necessary, Mueller (1999) suggests that the election of a constitutionalconvention may be a useful alternative to amend a constitution.

675G. Tridimas / European Journal of Political Economy 23 (2007) 674–692


could be held to legitimize a given proposal” (Hug and Scarini, 2000, p. 8–9). Such notions oftactical advantage and political gain are too vague to allow a complete understanding of thebehaviour of the incumbent. They fall short of offering a formal framework to generalise theunderlying intuition. Nor is the extensive formal literature of referenda suitable to tackle thequestion of non-required referenda called by the government. For example, Hug (2004) concludeshis study on the occurrence of various types of referenda by pointing to “… a disconcertingresult… namely that the government should never call a referendum on a voluntary basis” (2004,p. 344). It is the aim of this work to provide such a formal framework.

In common with the existing theoretical literature, at the core of the present study is theuncertainty which surrounds the outcome of different methods of passing legislation. Specifically,some issues cause deep differences amongst the members of the same party. The incumbent maythen be unsure of the voting intentions of the elected representatives of his own governingcoalition, while he may also expect that his proposed legislation will be supported by voters whodo not necessarily vote for his party in parliamentary elections. Attracting the support ofrepresentatives in a parliamentary vote, or of ordinary voters in a referendum, requires to expendresources both pecuniary and non-pecuniary. Similarly, the political benefits of passing legislationby a vote of the legislature may differ from the benefits of passing legislation by the directapproval of voters in a referendum. The choice of the method of ratifying legislation will thendepend on comparing the expected net gains from victory in a referendum and a parliamentaryvote.

The next section offers a selective review of the existing literature on referenda. Section 3presents a formal model of the choice of the incumbent to seek ratification by calling areferendum or a vote in parliament. The model is based on the spatial decision framework andstudies the interactions between the incumbent and the opposition in an environment where theexpected outcome of the two alternative methods of ratification depends on policy preferences,the utility from winning a vote and the effort expended by the incumbent and the opposition tosecure the support of voters and representatives. Section 4 concludes.

2. On the comparative merits of policymaking by referendum

Theoretical and empirical research on referenda has proliferated over the last decade. As thisliterature is surveyed elsewhere – see amongst others, Mueller (1996), Feld and Kirchgässner(2000) and Matsusaka (2005) – there is no reason to provide a survey here. It suffices to indicatehow the present study links with previous work. The existing literature focuses on the choicebetween policy making by referendum and by electoral representation. A range of complementaryquestions have been investigated, notably, why citizens may decide to resolve some issues ofcollective choice by a referendum vote rather than indirectly through their elected representatives;how well-informed voters are; what factors determine referendum outcomes (including voterpreferences and the financial muscle of interest groups); and whether, in comparison to repre-sentative democracy, policy outcomes in referenda are more closely related to the preferences ofthe majority of voters.

Policy making by elected politicians possesses two important advantages. First it minimizesdecision costs of reaching agreements as it restricts the process of negotiation to a small numberof legislators. Second, it achieves superior (welfare increasing) outcomes as policy decisions aremade by elected politicians, who specialise in acquiring the relevant information and expertise onpolicy issues, rather than by ignorant voters. On the other hand, indirect democracy may beplagued by problems of agency, agenda control and logrolling. Agency problems arise because of

676 G. Tridimas / European Journal of Political Economy 23 (2007) 674–692


weak controls of voters on politicians, who may then implement policies which best suit their owninterests. Agenda control problems arise when legislators monopolize the policy issues to bedecided, the order and form of policy decisions. In logrolling legislators trade votes in one projectto secure a favourable vote in another project, which may result in an inefficiently large level oftaxation to finance the sum of public expenditure projects. These problems are largely absentunder direct democracy. Moreover, if the information required on a policy issue is widelydispersed across voters, or if the decision relates to a moral issue, which depends on personalvalues, and there may not be a single “right” or “wrong” answer, involving the entire electorate inpolicy making may result in a superior outcome (welfare increasing) than representativedemocracy. Overall, the greatest benefit of direct democracy is then that it secures policyoutcomes preferred by the majority of voters.6

In pursuit of a systematic understanding, scholars usually draw attention to the institutionalcharacteristics of a referendum.7 In the first instance this refers to whether the referendum isbinding, in which case the authorities will have to implement the policy chosen by the popularvote, or the referendum is simply consultative. Note that in practice a referendum may be formallyconsultative, but become effectively binding when political parties of both government andopposition declare that they will abide by the popular vote. A consultative referendum recordspopular preferences but does not decide an issue. However, it may be politically suicidal forparties to ignore the will of voters. Alternatively, if voters know that their preferences will notdecide an issue, they may not bother to express their preferences, robbing the referendum of anyvalue. The present study focuses on binding referenda. A second useful classification is whether areferendum is called to decide a constitutional issue (that is, one which relates to the rules bywhich policy is made), or a post-constitutional issue (that is, one which concerns the passage ofordinary laws, like taxation and public expenditure).8 A third most significant distinction iswhether or not the constitution mandates that a certain issue is put to the direct approval of thevoters in a referendum, in which case the government has no option but to call a referendum; thisis the required referendum. If a referendum is not required, then an actor as provided by theconstitution may force one. Three types of non-required referenda are distinguished. (a) A non-required referendum called by the opposition (which includes political parties in the parliament aswell as interest groups outside the parliament) on a policy adopted by the government. (b) A non-required referendum on a policy proposed by the opposition, or another actor like an organizationor a group of citizens. Examples of this category are popular initiatives, by which a specifiedminimum number of voters can force a public vote on a policy, and the recall referendum, aprocedure by which voters can remove an elected official from office. (c) A non-requiredreferendum called by the government itself. This type of non-required referendum is also referredto as a “plebiscite” or as “passive” referendum (Christin and Hug, 2002, p. 591). Amongst thecountries with constitutional provisions for this kind of referendum are Austria, Cameroon,Denmark, France, Greece, Ireland and Tunisia (see Hug, 2004). As indicated, the existingliterature has focused on required referenda and the first two types of non-required referenda, tothe neglect of the non-required referendum called by the government.

6 For exceptions to this, see Matsusaka and McCarty (2001) and Kessler (2005), who identify circumstances whererepresentation leads to superior outcomes to direct voting and is preferred by the majority.7 See for example Mueller (1996) and Christin and Hug (2002).8 In this context, Mueller (1996) shows that an informed comparison of the merits of referendum and parliamentary

votes requires accounting for the form of the parliamentary system, two-party or multi-party system, and the size ofmajority required to pass laws.



Based on the previous classification, Hug and Tsebelis (2002) offer a detailed cross-countrycomparison of institutional provisions about referenda and study how these provisions may affectthe stability of the policy outcome and the role of voter preferences in affecting policy outcomes.They consider referenda as introducing an additional veto player (an actor whose consent isrequired to change the status quo) on the collective choice made by the elected representatives.They show that the possibility of calling a referendum forces the policy outcome to be closer tothe preferences of the median voter. Hug and Sciarini (2000) examine how the institutionalcharacteristics of a referendum (whether required or non-required), may affect the outcome of thevote. They argue that when the government calls a referendum even though it is not required to doso, the supporters of the governing parties treat the vote as a kind of confidence vote and tend tosupport the recommendation of the incumbent. However, the incentive to vote for the incumbentis less strong if the referendum is constitutionally mandated, since in a mandatory referendum agovernment supporter who votes against the proposal of the government may simply signal hisopposition to the specific policy proposed by the government (rather than the government). Usingdata from referenda on European integration, they report empirical estimates in support of thesetheoretical arguments. Similarly, Hug (2004) shows that differences in institutional arrangementsaffect both the occurrence of referenda and the outcome of public policy.9

Missing from the literature is an investigation of the question of the incumbent's choice to call ornot to call a non-required referendum to pass legislation. It is to this task that we turn to in the nextsection. In common with recent literature, uncertainty in our model arises from incompleteknowledge about voter preferences. However the similarities end here. The literature focuses on thecomparative merits of direct and indirect democracy from the viewpoint of voters. Matsusaka andMcCarty (2001) compare policymaking by elected politicians against initiatives triggered by interestgroups assuming that they are both ignorant about the ideal point of the median voter. Similarly, inKessler's (2005)model of citizens–candidates, uncertainty exists because of incomplete informationabout voter preferences and because of stochastic policy outcomes. However, neither of these worksstudies explicitly the competition between government and opposition. Hug (2004) addresses thisissue in a setting of asymmetric information, but in a waywhich lacks generality. He assumes that thegovernment is uncertain about the preferences of the median voter, while the opposition, which isassumed to force a referendum, knows the ideal point of the median voter with certainty. Hisjustification is that the opposition has strong incentives to learn the preferences of voters in aparticular issue, while the government must address several issues simultaneously. The focus of thepresent study is competition between the incumbent and the opposition in a more general setting,where uncertainty arises because both the incumbent and the opposition have incompleteinformation about the preferences of both the voters and those of their elected representatives.

3. A formal model of ratification

3.1. Ratification via referendum

For concreteness, we assume that a decision on a constitutional amendment has to be made andemploy a single dimensional spatial decision framework under a simple majority rule. We

9 He shows that when the constitution provides for the opposition to call a referendum on its own policy proposal, thenreferenda are more likely to occur (but as the cost requirement of the referendum increases, the likelihood of calling onedecreases), and that policy outcomes will reflect more closely the preferences of the voters. Testing these theoreticalpredictions with two samples, one from the States of the USA the other from an international sample, he reports empiricalresults in support of the hypothesis.



envisage a parliamentary democracy with two players, the incumbent denoted by I and theopposition denoted by O. The incumbent is the leader of the governing political coalition. Theopposition is the politician who leads the parties excluded from the governing coalition. Theplayers are assumed to be concerned with both the policy outcome and winning the vote per se.That is, they have policy preferences and derive utility from winning the vote. Let A and B denotethe ideal policy points of the incumbent and the opposition respectively. Let G denote the policyintroduced by the incumbent. G is assumed to have been determined at an earlier stage, likeinternational negotiations; its size is exogenous to the game analysed here. For example, thegovernment of the country negotiates entry to the European Union, or a revision of the foundingtreaties of the EU. Even though at the negotiation stage there may be some leeway concerning theterms of entry, or the adjustment period for harmonization of policies, the new entrant has to adoptthe whole body of European legislation. Thus, when the government of the member-country seeksratification of the treaty of entry (or the like), the choice is one of yes-or-no, rather than a selectionfrom a continuous set. In other words, at the ratification stage the incumbent no longer controlsthe size of G. In general we allow for A ≠ G; that is, given the compromises struck in negotiatinglegislation, the constitutional amendment introduced by the incumbent may differ from his idealpoint. Similarly, the proposed legislation differs from the ideal point of the opposition, B ≠ G. Forconvenience, but without loss of generality, it may be assumed that B < A.

We first analyse the referendum game. In general, the incumbent expects that some, but notnecessarily all, voters who voted for his or her party in the parliamentary election will also supportthe proposed legislation at the referendum. He also expects to pick support amongst those voterswho did not vote for his party at the parliamentary election, but become better off if the proposedlegislation is enacted. Let P be the probability that the incumbent wins the referendum vote andimplements policy G. Since the problem which concerns us here is the choice of the incumbent, itis assumed (as it is indeed the case in plebiscites) that the opposition cannot propose an alternativepolicy to G. Instead, if the incumbent loses the referendum vote, the status quo remains; forsimplicity the policy value of the status quo is set at zero. The probability that the incumbentloses, (correspondingly, the opposition wins the vote) is 1 − P.

We assume that the objective function of the incumbent and the opposition is additive andseparable in its attributes and that utility from the policy outcome is quadratic.10 We then write theobjective function of the incumbent as

UIR ¼ −kI P A−Gð Þ2þ 1−Pð Þ A−0ð Þ2h i

þ 1þ kIð ÞgIP: ð1Þ

The first component of the above sum denotes the expected (loss of) utility from the policyoutcome, the second component captures the utility from winning the vote. The coefficient λIshows the relative weight that the incumbent attaches to implementing policy G. The coefficient(1 − λI) shows the relative weight on winning the vote and ηI is a scale factor which represents thevalue placed on winning the referendum vote. Amongst other factors, this may depend positively

10 This form of objective function was introduced by Nordhaus (1989) in his analysis of the political business cycle. Abroadly similar framework is also assumed by Matsusaka and McCarty (2001). They model the politician as maximizinga utility function which is additive and separable in the preferences of the median voter and the politician himself. On thecontrary, Kessler (2005) assumes that politicians are drawn from the citizens themselves and care about the policy theywill carry out; in her formulation the utility of the citizen-representative depends on preferences about policy (anduncertainty about the outcome of policy measures). As already indicated, the choice of the utility function in the presentstudy reflects the focus on the competition between different parties, rather than the conflict between voters-as-principalsand politicians-as-agents.



on the incumbent politician's intrinsic value of winning a direct vote; the enhanced reputation ofthe incumbent as an election winner and the consequences of the latter for future parliamentaryelections; and the possibility that the referendum splits the opposition, while it avoids splits in thegovernment coalition. An opportunistic party (one without policy preferences) is one with λI =0;a purely ideological party (one which is only interested in policy outcomes) is characterised byηI =0.

Manipulating, the objective function of the incumbent is written as

UIR ¼ P kI A2− A−Gð Þ2h i

þ 1−kIð ÞgIn o

−kIA2: ð1′Þ

The expression HI≡λI[A2 − (A − G)2] + (1 − λI)ηI denotes the incumbent's marginal benefit

from a vote won in a referendum; we then have

UIR ¼ PHI−kIA2: ð1″ÞFor the objective function of the opposition, denoting the relative weight of policy by λO and

the scale value of winning the vote by ηO, where in general λI ≠ λO and ηI ≠ ηO, we may write

UOR ¼ −kO 1−Pð Þ B−0ð Þ2þP B−Gð Þ2h i

þ 1−kOð ÞgO 1−Pð Þ: ð2Þ

Manipulating and denoting HO≡λO[(B − G)2 − B2]+ (1 − λO)ηO, the opposition's marginalbenefit from a vote won in a referendum, we have

UOR ¼ 1−Pð ÞHO−kO B−Gð Þ2: ð2′ÞThis can be further simplified to

UOR ¼ −PHO−kOB2 þ 1−kOð ÞgO: ð2″ÞThe probability that the incumbent wins the referendum depends on the number of votes polled bythe incumbent, VI, and the opposition, VO. We assume that this probability takes the “Tullockformula”11 and write

P ¼ VI

VI þ VO: ð3Þ

Expression (3) assumes that the vote contest is a fair game. That is, when the incumbent and theopposition poll the same number of votes, VI =VO, the probability of winning the contest must beequal to 1/2.

Both the incumbent and the opposition will expend effort and resources to influence thenumber of votes polled. Specifically, the effort expended by the incumbent to attract the supportof voters in a referendum is assumed to be proportional in the number of voters, and takes theform

CIR ¼ G−Mð Þ2þsI G−Mð Þ2þsIh i

VI: ð4Þ

11 For previous applications of this framework in the choice of institutional settings see amongst others Rubin et al.(2001) and Tridimas (2004). The present treatment of the probability as a continuous function is more general than that ofMatsusaka and McCarty (2001) who assume fixed probabilities for different electoral outcomes.



The term (G − M)2 + sI(G − M)2 + sI represents the marginal effort of attracting an extra vote ina referendum. It depends on two factors. The difference (G − M)2 ≥ 0 represents the deviationof the policy proposed by the incumbent from the policy M most preferred by the median voter,who is assumed to be decisive in a referendum.12 That is, in common with the standard spatialdecision model, it is postulated that the further away the proposed policy from the median is, thecostlier it is for the incumbent to attract votes. Such costs will be incurred irrespective ofwhether the incumbent proposes a policy to the left or the right of M; hence the difference issquared. For convenience and without loss of generality, it is assumed thatM > 0. The term sI ≥0 reflects voter bias, that is, factors other than policy preferences which may influence voters tosupport the proposal of the incumbent. For example, voter support for the incumbent may differat the different phases of the business cycle, and may be influenced by the personal appeal(or lack of it) of the incumbent, his ability to argue his case persuasively, his perceivedcompetence, honesty and integrity in office. It is expected that sI will be decreasing as thepopularity of the incumbent increases. Finally, the term sI(G − M)2 is added to capture thepossible interaction between the policy and non-policy influences on the decision of voters tosupport the incumbent.13

Similarly, it is assumed that the effort expended by the opposition to gain voter support takesthe form

COR ¼ 0−Mð Þ2þsO 0−Mð Þ2þsOh i

VO: ð5Þ

The expression (0 − M)2 + sO(0 − M)2 + sO is the marginal cost. The term (0 − M)2 =M2

shows that the effort made by the incumbent to attract votes rises as the size of the deviationof the median point from the status quo (the alternative supported by the opposition) rises.In strict analogy to the incumbent, the coefficient sO ≥ 0 captures voter bias against theopposition originating from non-policy influences (appeal of the leader of the opposition,etc).

When the incumbent calls a referendum his expected net benefit is RI =UIR − CIR. Substitutingfrom Eqs. (1″), (3) and (4), we obtain

RI ¼ HIVI

VI þ VO−kIA2− G−Mð Þ2þSI G−Mð Þ2þSI

h iVI: ð6Þ

The opposition's expected net benefit from a referendum is RO=UO − COR. Substituting, fromEqs. (2″), (3) and (5), we obtain

RO ¼ −HOVI

VI þ VO−kOB2 þ 1−kOð ÞgO− M2 þ sOM

2 þ sO� �

VO: ð7Þ

The Nash equilibrium of the game is found by assuming that the incumbent maximizes RI withrespect to VI treating VO as given and that the opposition maximizes RO with respect to VO

12 If a supermajority rule applies – a majority greater than 50%+1 of votes is required – M has to be re-interpretedaccordingly.13 In the expression for the marginal cost, each component of the sum is assumed to enter with the same unitarycoefficient. This assumption is made for convenience only, for the more general case of writing the marginal cost as (G −M)2+c1sI(G − M)2+c2sI would have complicated the algebra without an analogous gain in intuition.



treating VI as given. Differentiating and solving yields the expressions for the equilibrium valuesof votes

V I⁎ ¼ H2

I HO M 2 þ sOM 2 þ sO½ �HI½M 2 þ sOM 2 þ sO

n iþ HO G−Mð Þ2þsI G−Mð Þ2þsI

h ig2 : ð8Þ

V O⁎ ¼

HIH2O G−Mð Þ2þsI G−Mð Þ2þsIh i

HI½M 2 þ sOM 2 þ sOn i

þ HO G−Mð Þ2þsI G−Mð Þ2þsIh ig2 : ð9Þ

The probability that the incumbent wins the referendum is then given by

P⁎¼ HI M2 þ sOM 2 þ sO½ �HI½M 2 þ sOM 2 þ sO� þ HO G−Mð Þ2þsI G−Mð Þ2þsI

h i : ð10Þ

It can easily be checked that the above probability is increasing in the size of bias against theopposition, sO, and the incumbent's marginal benefit of a referendum vote HI. On the other hand,it is decreasing in the size of voter bias against the incumbent, sI, the incumbent's policy deviationfrom the median, (G − M)2, and the opposition's marginal benefit of a referendum vote, HO.However, the effect of a change in the size of the median, M, is ambiguous.

To gain a better understanding of the equilibrium formula of the probability that the incumbentwins the referendum, Eq. (10) can be expressed as

P⁎ ¼ M 2 þ sOM 2 þ sO½ � � HO

f½M 2 þ sOM 2 þ sO� � HOg þ G−Mð Þ2þsI G−Mð Þ2þsIh i

� HI

n o : ð10′Þ

The term qOuM2þsOM2þsO

HOis the ratio of the opposition's marginal effort for a referendum vote

divided by the marginal benefit of a referendum vote; it can be thought as the opposition's net

marginal effort for a referendum vote. By the same token, the term qIuG−Mð Þ2þsI G−Mð Þ2þsI

HIis the

incumbent's net marginal effort for a referendum vote. The probability that the incumbent winsthe referendum may then be rewritten as

P⁎ ¼ qOqO þ qI

: ð10″Þ

Substituting from Eqs. (8) and (9) back into Eq. (6), the net benefit of the incumbent in areferendum is written as

R I⁎ ¼ H2

I M 2 þ sOM 2 þ sO½ �2

HI½M 2 þ sOM 2 þ sO� þ HO G−Mð Þ2þsI G−Mð Þ2þsIh in o2 −kIA

2: ð11Þ

Using Eq. (10″) Eq. (11) can be expressed more compactly as

R I⁎ ¼ P⁎ð Þ2−kIA2: ð11′Þ



The incumbent's expected net benefit from a referendum is a quadratic function of theprobability of winning the referendum. More generally, it is clear that the expected net benefit ofthe incumbent depends on the parameters of his objective function as well as those of theopposition, the parameters of the functions which describe the effort to secure votes, thepreferences of the median voter and the deviation of the policy implemented from the medianpreferences.

Since in the present setting the opposition cannot force the incumbent to hold a referendum, itsexpected net benefit from the game is not studied any further.

3.2. Ratification through parliament

We now assume that the incumbent seeks to ratify the constitutional amendment through theparliament. In the case of ordinary legislation the governing coalition is supported by the majorityof elected representatives and the incumbent can rely on their votes to pass his proposed policymeasures. Analogously, the opposition consists of a minority of elected representatives and, witha few exceptions (typically involving some issues of national defence), the representatives of theopposition vote against the proposals of the incumbent. With the number of governmentrepresentatives greater than the number of opposition representatives and all the representativesvoting on party lines, it is certain that the incumbent will pass his proposed legislation. The gameplayed between the incumbent and the opposition is then rather simple and uninteresting. In thiscircumstance, the contest for votes takes place between the parties in the national vote forparliamentary seats rather than in parliament.

However, as already discussed, for some controversial pieces of legislation (like constitutionalamendments) the usual parliamentary confrontation which ends with the certain victory of thegovernment is not applicable. Elected representatives of the governing coalition for reasons ofideology or political expediency (especially if their party is unpopular), or other personal reasonsmay conclude that they are better off by voting against the legislation proposed by the incumbent.Intuitively, when voting against the incumbent's proposal politicians of the government coalitionhave to weigh the benefits from voting against a policy they dislike and the cost of punishment bythe leadership (being bypassed for promotion and so on), or in the worst case precipitating the fallof the government and the call of an election whose outcome is uncertain. Equally, someopposition politicians for ideological or personal reasons may prefer to support the legislationintroduced by the government and vote against the official line adopted by the leadership of theopposition. As before, in voting for the incumbent's proposal opposition politicians have to weighup the benefits from supporting a policy they prefer and the cost of possibly forgoing theopportunity to bring down the government. If a free vote amongst representatives is called, or ifthe party whips are unable to marshal representatives to follow party lines, the outcome of theparliamentary vote becomes uncertain. It is this game which concerns us here.

Let Q denote the probability that the incumbent wins the parliamentary vote. The objectivefunction of the incumbent is written as

UIE ¼ −kI Q A−Gð Þ2þ 1−Qð Þ A−0ð Þ2h i

þ 1−kIð ÞhIQ: ð12Þ

This is similar to Eq. (1), the difference being that the utility from winning the parliamentaryvote is in general different from the utility of winning the referendum vote. Specifically, onepresumes that, ηI ≥ θI. This recognizes that victory in a referendum, which relies on the directapproval of the voters, may be valued higher than a parliamentary victory, where the incumbent



enjoys the support of the majority of the representatives and lacks the direct involvement of theelectorate. Even if the incumbent enjoys a solid parliamentary majority, winning a vote inparliament may be considered as “softer” than winning a referendum. Moreover, the leader ofthe party in office calculates that calling a referendum, even though not required, signals to theelectorate his willingness to subject himself to the test of voters and his commitment todemocracy, factors which may enhance his reputation and help win a later parliamentaryelection too.

Similarly, assuming that for the opposition it is also ηO ≥ θO, its objective function is writtenas

UOE ¼ −kO 1−Qð Þ B−0ð Þ2þQ B−Gð Þ2h i

þ 1−kOð ÞhO 1−Qð Þ: ð13Þ

If a free vote takes place in parliament neither the representatives in the governing coalition northose of the opposition have to follow party lines, but they vote according to their preferences.Then the probability that the incumbent wins the parliamentary vote Q depends on the number ofrepresentatives who vote for it, NI, and the number of representatives who vote against it, NO.Assuming again a non-discriminatory Tullock probability, we may write

Q ¼ NI

NI þ NO: ð14Þ

The effort of the incumbent to secure the support of representatives, CIE, is assumed to take theform

CIE ¼ G−lð Þ2þrI G−lð Þ2þrIh i

NI: ð15Þ

μ > 0 denotes the ideal point of the median elected representative. There are good reasons toexpect that the ideal point of the median voter in the electorate, M, differs from the ideal point ofthe median voter in the parliament, μ. The referendum aggregates the preferences of all voterssimultaneously by treating the electorate as a single constituency, a process which (under theusual conditions) can elicit the preferences of the median voter. On the other hand, parliamentaryelections aggregate the geographical constituencies, which differ in their socio-economic make-up and therefore voter preferences. As different electoral systems apply different representationthresholds and majority rules, the distribution of the policy preferences of the politicians electedby different constituencies does not necessarily replicate the distribution of policy preferences ofthe electorate. Then, in general we have M ≠ μ.

The difference (G − μ)2 in Eq. (15) captures the difference between the platform proposed bythe leader of the government and the preferences of the median representative. The larger thisdifference, the more effort the incumbent has to expend to pass his proposed policy. The non-policy bias of the representatives against the incumbent is captured by the σI coefficient, withσI > 0.

In a parliamentary system, where the government assumes office after being voted in by amajority of the representatives, one expects that the representative with median preferencessupports the incumbent. If in addition the coalition of politicians who support the government iscohesive, the value of σI will be very small reflecting that a majority of the representativessupport the incumbent, who then needs comparatively little effort to persuade them to vote for hisproposed policy. At the limit, with σI =0 and (G − μ)2 =0, the policy introduced by the incumbent



passes with certainty, so that we may write CIE=0 and Q=1. In the more general caseexamined here, CIE > 0 and 0 < Q < 1. Intra-party policy differences are then reflected in thesize of the (G − μ)2, while weak party discipline – inability to control the representatives – isreflected in the size of σI.

14 Moreover, one may presume that σI and (G − μ)2 are positivelycorrelated, in the sense that when the difference between the preferences of the leader and themedian representative is large, so is the weakness of the leader to control the representativesof his party.

The effort function of the opposition is assumed to be

COE ¼ 0−lð Þ2þrO 0−lð Þ2þrOh i

NO: ð16Þ

As before, the term (0 − μ)2 =μ2 captures the effort expended by the opposition because ofpolicy differences between its platform and the ideal point of the median representative inparliament. The parameter σO > 0 denotes the bias of representatives against the opposition.Similarly to the governing coalition, a well-disciplined party of opposition representatives will becharacterised by a very small σO.

When the incumbent calls a parliamentary vote, his net expected benefit is EI=UIE − CIE, whilethat of the opposition is EO=UOE − COE. Denoting ΘI≡λI [A2 − (A − G)2]+(1 − λI)ΘI, theincumbent's expected marginal benefit from a vote won in parliament, and ΘO≡λO [(B − G)2 −B2]+(1 − λO)ΘO, the opposition's expected marginal benefit from a vote won in parliament, wehave

EI ¼ HINI

NI þ NO−kIA2− G−lð Þ2þrI G−lð Þ2þrI

h iNI: ð17Þ

EO ¼ −HONI

NI þ NO−kOB2 þ 1−kOð ÞhO− l2 þ rOl

2 þ rO� �

NO: ð18Þ

The Nash equilibrium of the game is again found by assuming that the incumbent maximizes EIwith respect toNI treatingNO as given and analogously for the opposition. Upon differentiating andafter the relevant manipulations we obtain that in equilibrium the probability that the incumbentwins the parliamentary vote is

Q⁎ ¼ HI l2 þ rOl2 þ rO½ �HI½l2 þ rOl2 þ rO� þHO G−lð Þ2þrI G−lð Þ2þrI

h i : ð19Þ

Or,

Q⁎ ¼ l2 þ rOl2 þ rO½ � �HO

f½l2 þ rOl2 þ rO� �HOg þ G−lð Þ2þrI G−lð Þ2þrIh i

�HI

n o : ð19′Þ

14 Note that even if G=μ, it is still possible for the incumbent not to control his representatives completely. Somebackbenchers, who share the same preferences with the leader, may nonetheless vote against the leadership for personalreasons, or because they have been bypassed for promotion to office and the like.



The term pOul2þrOl2þrO

HOis the ratio of the opposition's marginal effort for a parliamentary vote

divided by the marginal benefit of a parliamentary vote, and can be thought as the opposition's netmarginal effort of a parliamentary vote. By the same token, the term pIu

G−lð Þ2þrI G−lð Þ2þrIHI

is theincumbent's net marginal effort for a parliamentary vote. The probability that the incumbent wins inparliament may then be rewritten as

Q⁎ ¼ pOpO þ pI

: ð19″Þ

The expected net benefit of the incumbent is written as

E I⁎ ¼ H2

I l2 þ rOl2 þ rO½ �2

HI½l2 þ rOl2 þ r2O

n iþHO G−lð Þ2þrI G−lð Þ2þrI

h ig2 −kIA2: ð20Þ

Using Eq. (15), Eq. (16) can be expressed more compactly as

E I⁎ ¼ Q⁎ð Þ2−kIA2: ð20′Þ

The latter has an interpretation analogous to that given for R I⁎ in Eqs. (11) and (11′).

3.3. The choice between referendum and parliamentary vote

The incumbent will call a non-required binding referendum when the expected net benefitfrom the referendum is greater than the expected net benefit from the parliamentary vote, that is,when R I⁎ > E I⁎. He will opt for parliamentary ratification when RI⁎ < E I⁎, while he will beindifferent between the two routes to ratification when R I⁎=E I⁎.

Comparison of the expected payoffs of the incumbent under a referendum and a parliamentarybenefit, Eqs. (11′) and (20′), and ruling out negative values of the probabilities, yields

R I⁎−E I

⁎ ¼ pIpO

−qIqO

¼G−lð Þ2þrI G−lð Þ2þrI

HI

l2þrOl2þrOHO

−G−Mð Þ2þsI G−Mð Þ2þsI

HI

M2þsOM2þsOHO

: ð21Þ

Whether or not the incumbent calls a non-required binding referendum depends on whether or not

pIpO

>qIqO

: ð22Þ

That is, the incumbent will call a referendum when his net marginal effort for aparliamentary vote relative to the opposition's net relative marginal effort, πI/πO, exceeds hisnet marginal effort for a referendum vote relative to that of the opposition, ρI/ρO. Recallingthe terms involved in the relative marginal efforts, it is clear that all factors identified bythe model affect the choice of the incumbent whether or not to call a referendum. That is,the choice will depend on the parameters of the utility function of the incumbent and theopposition, the configuration of non-policy biases of the elected representatives and theelectorate, the policy preferences of the median voter in the referendum, the median voter inthe parliament and the policy proposed by the incumbent. The model predicts that the leaderof the government is likely to call a referendum when he exercises only weak control overhis own parliamentary party (large value of σI) and his party is split over the legislation that



he wants to ratify (large difference between G and μ). The incentive to call a referendum iscompounded when the parliamentary opposition is united (small value of σO), theincumbent thinks that his policy is closer to the preferences of the voters (small differencebetween G and M), he is personally popular amongst the electorate (small sI), while theopposition is unpopular (large sO), and when he values direct endorsement of the policymore than parliamentary endorsement (large HI in comparison to ΘI). Table 1 summarizesthe expected effect of these factors on the likelihood that the incumbent will call areferendum. These conclusions formalize and generalise the intuition of the earlierscholarship reviewed above.

More specific results are obtained for special values of the parameters. Specifically, let usassume that both the incumbent and the opposition value equally a win in a referendum and aparliamentary vote, so that ηI =θI and ηO=θO,

15 in which case, HI =ΘI and HO=ΘO. Substitutinginto Eq. (18) we obtain that the incumbent will call a referendum (R I⁎ > E I⁎ ) when

G−lð Þ2þrI G−lð Þ2þrIl2 þ rOl2 þ rO

>G−Mð Þ2þsI G−Mð Þ2þsIM2 þ sOM 2 þ sO

: ð23Þ

The first term of the above inequality is the ratio of the incumbent's marginal effort in aparliamentary vote relative to that of the opposition. Similarly, the second term of the inequality isthe incumbent's marginal effort in a referendum relative to that of the opposition. The expressionin Eq. (23) then postulates that the incumbent will call a referendum when he perceives theparliamentary vote as requiring more effort per vote relative to the referendum.

These comparisons formalize the intuition that governments use non-required referenda to“gloss over” divisions in their own ranks, captured by the σI coefficient of the model, andopen up divisions in the opposition, captured by the σO coefficient, as well as the differencebetween M, μand G, and to legitimize policies by involving voters directly, captured by themedian points of the electorate and the representatives, M and μ, respectively.

Table 1Comparative static properties of the ratification choice

An increase in Implies that the Likelihood of a referendum

Incumbent's valuation of ratification by referendum, HI IncreasesIncumbent's valuation of ratification by parliament, ΘI DecreasesPolicy deviation from the median voter, (G−M)2 DecreasesVoter bias against the incumbent, sI DecreasesElected representative bias against the incumbent, σI IncreasesOpposition's valuation of ratification by referendum, HO DecreasesOpposition’s valuation of ratification by parliament, ΘO IncreasesPolicy deviation from the median elected representative, (G−μ)2 IncreasesVoter bias against the opposition, sO IncreasesElected representative bias against the opposition, σO Decreases

15 Note that this condition necessarily holds when the two parties have purely ideological preferences, that is, whenηI =θI =ηO=θO=0.



Expression (23) can be simplified even further if the voting biases in the effort functions of theincumbent and the opposition are assumed away, so that the only reason why the incumbent andthe opposition need to expend effort is differences in policy preferences. Formally, with sI = sO=σI =σO=0, the inequality in Eq. (23) is transformed into

G−ll

� �2

>G−MM

� �2

: ð24Þ

That is, the choice for or against a referendum will depend entirely on the sizes of normalizeddeviations from the median preferences in parliament and the electorate. There are seven possibleconfigurations of G,M and μ. These and the resulting choices for calling or not a referendum areshown in Table 2.

Inspection of Table 2 reveals that when the policy introduced by the incumbentgovernment lies between the parliamentary and electorate median preferences, the choice ofone or another method is ambiguous (see the second and the seventh rows). On the otherhand, when the policy lies outside the segment defined by the two medians, and irrespectiveof whether M is greater or lower than μ, the choice of the route of ratification becomesunambiguous. If the policy is “extreme” from the point of view of the electorate, that is, G issmaller than μ and μ is smaller than M, or G is larger than μ and μ is larger than M, theincumbent seeks ratification through the parliament (see the first and the last rows). In theopposite case, where the policy is “extreme” from the standpoint of the representatives, thatis, G is larger than M and M is larger than μ, or G is smaller than M and M is smaller thanμ, the incumbent opts for a referendum (third and fifth rows). Finally, in the case where theelectorate and parliamentary medians coincide, the incumbent is indifferent between the tworoutes of ratification.

4. Conclusions

The existing literature on referenda compares the benefits that voters expect from referendavis-à-vis from representation. The focus of this literature is on the conflict between voters andpoliticians, the sources of this conflict and its consequences for policy under the referendumand the parliamentary methods of decision making. The present study has focused on theconflict between the government and the opposition, and has compared the benefits thegovernment derives by winning a referendum and a parliamentary vote. We began from theobservation that in practice governments often call referenda to resolve an important issue, like

Table 2Incumbent's choice of ratification method

Configuration of policy preferences Sign of ð G−ll Þ2− G−M

M

� �2Incumbent's choice: Ratification by

0<G<μ<M − Parliament0<μ<G<M ? Ambiguous0<μ<M<G + Referendum0<μ=M 0 Indifference0<G<M<μ + Referendum0<M<G<μ ? Ambiguous0<M<μ<G − Parliament



constitutional arrangements and national sovereignty, even though the government has therequired parliamentary support to pass legislation and the constitution provides that the issueunder consideration can be decided by a parliamentary vote only. Previous research has paidonly scant attention to this question. Although the tactical advantage held by the incumbentgovernment when calling such a non-required referendum has been recognized, no formalmodel has studied the phenomenon.

Recent non-required referenda on EU integration, amongst other examples, attest tothe relevance of this inquiry. For European democracies European integration, which impliestransferring some sovereign decision making powers to the EU supranational bodies,has turned out to be a vexing constitutional issue cutting across traditional party lines andcausing intra-party rifts. As a result, the governments of several European countries haveoften called non-required referenda to settle questions of EU membership and furtherintegration.

Acknowledging that the outcome of a vote, either plebiscital or parliamentary, is uncertain,a model of spatial decision making has investigated the interactions between the governmentand the opposition in an environment of incomplete information about the preferences of thevoters in a referendum and the preferences of the elected representatives in a parliamentaryvote. Ratification of legislation confers utility in allowing the incumbent government to realisepolicy preferences and in the intrinsic value of winning the contest against the opposition.Winning the referendum contest is costly as it involves expending effort to attract votersupport. This effort increases as the difference between the proposed legislation and the idealpoint of the median-decisive voter increases, and as the non-policy biases of voters against theincumbent increase. Similarly, a parliamentary victory requires effort, which is increasing inthe difference between the incumbent's proposal and the ideal point of the median-decisiverepresentative and the non-policy preferences of the representatives. The effort for winning thereferendum differs from the effort for winning the parliamentary vote because the ideal pointof the median voter in the electorate differs from the ideal point of the median representativein the parliament and because the non-policy biases of voters differ from the non-policy biasesof representatives. Whether the incumbent calls a referendum to ratify a policy choice orsubmits the decision to a parliamentary vote depends on the comparison of the expectedpayoffs in the two different contests given the status quo.

The model predicts that the incumbent government is likely to call a non-requiredreferendum rather than a parliamentary vote when (a) the policy proposed is close to thatpreferred by the median voter in the electorate, while it differs significantly from thatpreferred by the representatives of the government's own party; (b) the government values areferendum victory more than a parliamentary victory; (c) the leader of the governmentenjoys high personal (that is, not related to the specific legislation) support amongst theelectorate, while the opposition is held in low esteem; (d) the government exercises weakcontrol over the elected representatives of its party, while the representatives of the oppositionare split over the policy proposed by the government. These predictions accord well withintuition and the actions of incumbents in calling and, to a large extent winning, referenda inpolitical practice.

Of course, the present study represents a first attempt to study formally the calculus of non-required referenda. Subjecting the predictions of the model to rigorous statistical testing is anobvious next step for further research. Equally important is to examine additional constraints onthe incumbent originating from the precedent of having held referenda and the interaction withother veto players like the constitutional court.



Acknowledgments

I wish to thank two anonymous referees and Arye Hillman for various helpful com-ments and suggestions. Of course, responsibility for any remaining errors or omissions ismine alone.

Appendix

Referenda on European Integration

Year Issue Country % of Votes Referendum type

‘Yes’ ‘No’

1972 Enlargement Francea 68 32 Non-required1972 Membership Ireland 83 17 Required

Norway 46 54 Non-requiredDenmark 63 37 Required

1972 Free trade with EEC Switzerland 72 28 Required1975 Membership UK 67 33 Non-required1982 Membership Greenland 46 54 Non-required1986 Single European Act Denmark 56 44 Non-required1987 Single European Act Ireland 70 30 Required1989 Euroconstitutional process Italy 88 12 Initiative1992 Maastricht Treaty Ireland 69 31 Required

France 51 49 Non-requiredDenmark 48 52 Required

1992 EEA accession Switzerland 49 51 Required1992 EEA accession Lichtenstein 56 44 Required1993 Maastricht Treatyb Denmark 57 43 Non-required1994 Membership Austria 67 33 Required

Finland 57 43 Non-requiredSweden 53 47 Non-requiredNorway 47 53 Non-requiredAland Islands 74 26 Non-required

1995 Membership Lichtenstein 56 44 Required1997 EU access procedures Switzerland 26 74 Initiative1998 Amsterdam Treaty Denmark 55 45 Required

Ireland 62 38 Required2000 Bilateral EU treaties Switzerland 67 33 Initiative2000 Euro accession Denmark 47 53 Required2001 Nice Treaty Ireland 46 54 Required2001 EU access procedures Switzerland 23 77 Initiative2002 Nice Treatyc Ireland 63 37 Non-required2003 Membership Malta 54 46 Non-required

Slovenia 90 10 Non-requiredHungary 84 16 Non-requiredLithuania 90 10 RequiredSlovakia 92 8 Non-requiredPoland 77 23 Non-requiredCzechRepublic 77 23 RequiredEstonia 67 33 Non-requiredLatvia 67 33 Non-required

2005 European Constitution Spain 77 23 Non-requiredFrance 45 55 Non-required



Year Issue Country % of Votes Referendum type‘Yes’ ‘No’

2005 European Constitution Netherlands 38 62 Non-requiredLuxembourg 57 43 Non-required

Notes: As all governments which called consultative referenda promised to abide by their outcome, the binding–consultative distinction is not reported.

aFrench referendum on the accession of the UK, Ireland and Denmark.bAfter Denmark negotiated opt-outs from specific policies.cAfter the Irish government took various measure to assuage public concerns about Irish neutrality.Source: For referenda in the period 1972–2002: Huatala et al. (2002); Christin and Hug (2002). For the 2003 referenda:

Sczcerbiak and Taggart (2004). For the 2005 referenda: author's compilations.

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Ratification through referendum or parliamentary vote: When to call a non-required referendum?

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