Aytimur, Emre

Boukouras, Aristotelis

Schwager, Robert

English

We examine the two-candidate equilibria of the citizen-candidate model whenthe implemented policy arises from a compromise between the government andan unelected external power. We show that the equilibria of this model differsignificantly from the original: the distance between the candidates' policies, bothideal and implemented, remains strictly above a threshold. Thus, the medianvoters' ideal policy may not obtain in contested elections if policy control isimperfect, even when the cost of running as a candidate is arbitrarily small

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     Edinburgh Research Explorer                                      The Citizen-Candidate Model with Imperfect Policy ControlCitation for published version:Boukouras, A, Aytimur, E & Schwager, R 2012 'The Citizen-Candidate Model with Imperfect Policy Control'.Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Preprint (usually an early version)Publisher Rights Statement:© Boukouras, A., Aytimur, E., & Schwager, R. (2012). The Citizen-Candidate Model with Imperfect PolicyControl.General rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 20. Feb. 2015The Citizen-Candidate ModelwithImperfect Policy ControlR. Emre Aytimur∗,Aristotelis Boukouras†,Robert Schwager‡August 2012AbstractWe examine the two-candidate equilibria of the citizen-candidate model whenthe implemented policy arises from a compromise between the government andan unelected external power. We show that the equilibria of this model diﬀersigniﬁcantly from the original: the distance between the candidates’ policies, bothideal and implemented, remains strictly above a threshold. Thus, the medianvoters’ ideal policy may not obtain in contested elections if policy control isimperfect, even when the cost of running as a candidate is arbitrarily small.Keywords: elections, polarization, strategic delegation, bureaucracy, foreigninﬂuenceJEL classiﬁcation: D72, D78, H11∗Chair of Public Economics, Georg-August University Go¨ttingen, email: raytimu@gwdg.de†University of Edinburgh Business School, email: aris.boukouras@ed.ac.uk‡Corresponding author. Chair of Public Economics, Georg-August University Go¨ttingen, Platz derGo¨ttinger Sieben 3, D-37073 Go¨ttingen, Germany; phone: +49 551 39-7293, fax: +49 551 39-7417,email: rschwag@uni-goettingen.de11 IntroductionThe citizen-candidate model, pioneered by Osborne and Slivinsky (1996) and Besleyand Coate (1997), has become a major approach to analyze representative democracy.Among the many equilibria of this model (see Dhillon and Lockwood (2002), Roemer(2003)), special attention has been granted to equilibria with two candidates. In suchequilibria, a substantial cost of running for oﬃce prevents a convergence of policyplatforms. Conversely, if the cost of candidacy is small the model allows for equilibriawith two candidates proposing policies which are arbitrarily close to each other andto the median’s preferred policy (see Persson and Tabellini (2002), p. 101-104). Inthe present note, we show that this latter conclusion is no longer true if the electedgovernment cannot fully control the policy to be implemented but has to compromisewith an external power. If the ﬁnal policy is in between the ideal policies of the electedcitizen and the external power, then in any two-candidate equilibrium the distancesbetween the ideal policies and between the policies ﬁnally implemented by the twocandidates remain strictly above a positive threshold, even when the cost of runningfor oﬃce becomes arbitrarily small.The political importance of this result stems from the observation that quite often,elected governments have to share power with an un-elected entity. For example, aself-interested bureaucracy in the spirit of Niskanen (1971) may, by its expertise orits control on executive functions, ’water down’ implemented policies. Similarly, aninterest group1 which has the means to disrupt public life, such as a union or an industryassociation, can inﬂuence the policies eﬀectively enacted by the government. As a thirdexample, in developing countries even elected governments often feel compelled to takethe views of donor countries into account when formulating domestic policies. Finally,when the International Monetary Fund or, recently, the European Union negotiateeconomic programs with countries receiving debt relief, the resulting policies clearlyarise as a compromise between the preferences of the elected government and those ofthe international institution. For these and similar situations, our result implies that apolarization of candidates and policies is inevitable.To arrive at this conclusion, we present a simple model where citizens have single-peaked preferences over an unbounded one-dimensional policy space, decide non-cooperativelywhether to stand in an election, and vote strategically for one of the candidates. To for-1Besley and Coate (2001) study the inﬂuence of lobbying in a citizen-candidate model. However,since the government has full control over the policy in their model, they do not obtain our result.2malize the inﬂuence of the external power, we assume that the ﬁnal policy is a weightedaverage of the winner’s ideal policy and the external power’s preferred choice. We showthat the ideal policies of two candidates running in an equilibrium, and also the policiesﬁnally implemented in case of victory, must diﬀer by a minimum amount. This minimaldistance increases in the strength of the external power and in the diﬀerence betweenthe median voter’s and its preferred policies, but is independent of the cost of candi-dacy. This result obtains since otherwise, if two candidates with similar preferenceswere to run, one of them would prefer the compromise between the other candidateand the external power to the compromise she can obtain herself.Our analysis is in line with several other contributions which show that adding in-stitutional features to the standard citizen-candidate model can cause the candidates’policies to diverge. Thus, Chambers (2007) provides a model where lobbies pay cam-paign contributions to potential candidates so as to convince them to run. He showsthat this induces a minimum distance between the policies chosen in two candidateequilibria. Our approach diﬀers from this result in that we consider an external powerwhich inﬂuences the policy after the election, rather than manipulating the electionitself. It has also been shown that ideal policies in a two-candidate equilibrium mustbe suﬃciently far apart if the ﬁnal policy is a weighted average of the ideal policies ofall candidates (Hamlin and Hjortlund (2000)), or if the decision to stand in the electionmust be taken before the distribution of voter preferences is known (Brusco and Roy(2011)). Both Hamlin and Hjortlund (2000) and Brusco and Roy (2011) assume sincerevoting, and the driving force behind the divergence results is the threat of a third can-didate entering on the fringe of the political spectrum. Contrary to that, in our model,which is based on strategic voting, it does not pay oﬀ for the second candidate to enterif policies are too close to each other. Thus, while these contributions arrive at similarconclusions, our result is based on a fundamentally diﬀerent eﬀect.Our result also contributes to the theory of strategic delegation in a political context.This strand of literature emphasizes that the median voter, by electing someone withpreferences diﬀerent from herself, can compensate for unwelcome inﬂuences in the post-election decision making, and thereby implement her preferred policy. For example,Persson and Tabellini (1992) show that electing a citizen who likes higher taxes thanthe median is a way to counteract the race to the bottom endemic in tax competition.Similarly, Roelfsema (2007) shows that strategic delegation can overcome the free-ridingincentives present when countries set environmental standards in an uncoordinated way.In an inter-temporal set-up, electing a citizen with a high endowment of capital is a way3to commit to a low tax rate on capital, thereby preserving incentives to invest (Perssonand Tabellini (1994)). Other applications of strategic delegation refer, for example, tojoint production of a public good (Harstad (2010)), to monetary policy in the EuropeanCentral Bank (Fatum (2006)), or even to civil conﬂicts (Jennings and Roelfsema (2008)).One-candidate equilibria of our model are perfectly in line with these results: Providedthe cost of candidacy is not too high, there is always an equilibrium where the ﬁnalpolicy coincides with the median’s preferred choice. Contrary to that, in any two-candidate equilibrium, the ﬁnal policies remain bounded away from the median’s idealpolicy, even for arbitrarily small cost of running for oﬃce. Thus, our result shows thatthe power of strategic delegation is limited as long as one considers equilibria whereelections are indeed contested.2 The ModelThere are 푛 citizens with 푛 odd. Each citizen has single-peaked preferences over aunidimensional policy 푝 ∈ ℝ. The ideal policy point of a citizen 푖 is denoted by 푝푖. Themedian voter’s ideal policy is denoted by 푝푚.There are three stages. In the ﬁrst stage, each citizen decides whether to stand forelection or not. Being a candidate costs 푐 > 0. In the second stage, voting takes placeaccording to the plurality rule. In case of a tie, every candidate which ties for the ﬁrstplace is selected as the winner with equal probability. In the third stage, if citizen 푖 isthe winner of the election, then the ﬁnal policy 푝푖푥 is a weighted average of her idealpolicy (푝푖) and the ideal policy of an external power (푝푥):푝푖푥 = 훾푝푖 + (1− 훾)푝푥 (1)with 0 ≤ 훾 ≤ 1. If no one runs for the election, then the ﬁnal policy becomes 푝푥.The formula of the ﬁnal policy captures the idea that, ideally, the election’s winnerwould like to implement her most preferred policy, but has to compromise with theexternal power. 1− 훾 measures the power of this un-elected entity.The equilibrium concept is subgame perfect equilibrium together with the elimina-tion of weakly dominated voting strategies. From Proposition 3 in Besley and Coate(1997) we know that a two-candidate equilibrium, which is the focus of the presentnote, exists only if (a) both candidates attract an equal number of votes, and (b) forboth candidates, the gain in expected utility arising from changing the ﬁnal policy with4probability 1/2 outweighs the cost of running.2Making use of the necessary conditions (a) and (b), our result characterizes the setof candidate pairs which can be observed in a two-candidate equilibrium.Proposition 1. In any equilibrium with two candidates 푖 and 푗, ∣푝푖−푝푗∣ > 1−훾훾 ∣푝푥−푝푚∣.Proof: Note that 푝푖 ∕= 푝푗, since otherwise one of the candidates would be better oﬀ notrunning for the election and saving the cost 푐. Assume without loss of generality that푝푗 = 푝푖 + 푑 with 푑 > 0. With (1), this implies 푝푗푥 > 푝푖푥. The key observation is that푝푗 > 푝푖푥, since otherwise 푗 would prefer 푝푖푥 to 푝푗푥 (due to single-peaked preferences)and would be certainly better oﬀ not running for the election (even with 푐 = 0). Thiscan be equivalently written as푝푖 + 푑 > 훾푝푖 + (1− 훾)푝푥which gives푑 > (1− 훾)(푝푥 − 푝푖) (2)As it is well known, in a two-candidate equilibrium, two candidates should tie. Dueto single-peaked preferences this is possible only if 푝푗푥 > 푝푚 > 푝푖푥. By substitutingequation (1) for 푝푖푥 into 푝푚 > 푝푖푥 and rearranging, we get:푝푥 − 푝푖 > 푝푥 − 푝푚훾Combining this with inequality (2) gives푑 >1− 훾훾(푝푥 − 푝푚) (3)In the same way, using the inequalities 푝푖 < 푝푗푥 (since otherwise 푖 would be better oﬀnot being a candidate) and 푝푗푥 > 푝푚, it can be also shown that푑 >1− 훾훾(푝푚 − 푝푥) (4)Inequalities (3) and (4) together complete the proof. Q.E.D.2Besley and Coate (1997) also show that the necessary conditions (a) and (b) together are suﬃcientfor existence of a two-candidate equilibrium if in addition, (c) all voters strictly prefer the candidatethey vote for to the other candidate and the set of indiﬀerent voters is smaller than one third of theelectorate.5Proposition 1 says that it is not possible to have two candidates whose ideal policiesare at a distance lower than 1−훾훾∣푝푥−푝푚∣ from each other, even if the cost of running asa candidate is arbitrarily small. While this result relates only to the ideal points of thecandidates, the next corollary, which follows directly from Proposition 1 and equation(1), shows that also the two potential ﬁnal policies are distant from each other by atleast (1− 훾)∣푝푥 − 푝푚∣.Corollary 1. In any equilibrium with two candidates 푖 and 푗, ∣푝푖푥−푝푗푥∣ > (1−훾)∣푝푥−푝푚∣.3 Comments and ConclusionThe “standard” case with perfect policy control. If we set 훾 = 1 in (1), then the politi-cian implements her ideal policy and we have the standard citizen-candidate model. Inthis case it is easy to construct examples of two-candidate equilibria displaying arbi-trarily close distance between the two candidates, by choosing a suﬃciently small costof running and an appropriate distribution of citizens’ ideal policy points.3 However,if 훾 < 1, Proposition 1 tells us that any two candidates running must have substan-tially diﬀerent ideal points, and that also the two potential ﬁnal policies diverge fromeach other by a non-negligible amount. Put diﬀerently, our result shows that the pres-ence of the external power precludes convergence of platforms and ﬁnal policies intwo-candidate equilibria of the citizen-candidate model.Moreover, since the median’s preferred policy must be located between the policiesimplemented by the two potential winners, in the standard model the two-candidateequilibrium provides an institutional framework for (almost) implementing the median’spreferences. Contrary to that, when an external power inﬂuences the policy outcome, atleast one of the ﬁnal policies necessarily stays bounded away from the median preferredpolicy, no matter how small the cost of running is.One-candidate equilibria. If we consider one-candidate equilibria, then our modelproduces similar results to the “standard” model: if there is a citizen 푖 who compensatesthe external power’s policy inﬂuence in such a way that the ﬁnal policy becomes (almost)3For instance, if voter 푚 is indiﬀerent between 푝푖 and 푝푗 and half of the remaining 푛 − 3 votersrespectively have ideal policies smaller than 푝푖 and larger than 푝푗 , then a two-candidate equilibriumwith 푖 and 푗 running exists whenever the cost of running is small enough.6the median voter’s ideal policy (i.e. 푝푖푥 = 푝푚 or arbitrarily close to it) then this citizen푖 running unopposed constitutes a one-candidate equilibrium (given the cost of entryis appropriately small). Even though citizen 푖 is not the median voter, the ﬁnal policyis close to the median-voter’s ideal. But this result does not hold if we consider two-candidate equilibria. In the latter case, as Corollary 1 shows, it is not possible forthe median voter to fully neutralize the inﬂuence of the external power by strategicdelegation.To summarize, this note shows that the citizen candidate model implies a diver-gence of ideal policies between candidates, and of ﬁnal policies implemented from thepreferences of the median, if one considers equilibria with two candidates running foroﬃce and if the ﬁnal policy arises from a compromise between the elected governmentand some un-elected entity such as a bureaucracy or foreign inﬂuences. Thus, while themedian voter result provides a useful benchmark in many political economic analyses,it may be misleading if such an outside inﬂuence is relevant and elections are contested.ReferencesBesley, T. and S. Coate (1997). An economic model of representative democracy. TheQuarterly Journal of Economics 112 (1), 85–114.Besley, T. and S. Coate (2001). Lobbying and welfare in a representative democracy.Review of Economic Studies 68 (234), 67–82.Brusco, S. and J. Roy (2011). Aggregate uncertainty in the citizen candidate modelyields extremist parties. Social Choice and Welfare 36 (1), 83–104.Chambers, C. (2007). Citizen-candidates, lobbies, and strategic campaigning. EconomicTheory 33 (2), 285–309.Dhillon, A. and B. Lockwood (2002). Multiple equilibria in the citizen-candidate modelof representative democracy. Journal of Public Economic Theory 4 (2), 171–184.Fatum, R. (2006). One monetary policy and 18 central bankers: The european monetarypolicy as a game of strategic delegation. Journal of Monetary Economics 53 (4), 659–669.Hamlin, A. and M. Hjortlund (2000). Proportional representation with citizen candi-dates. Public Choice 103 (3/4), 205–230.7Harstad, B. (2010). Strategic delegation and voting rules. Journal of Public Eco-nomics 94 (1/2), 102–113.Jennings, C. and H. Roelfsema (2008). Civil conﬂict, federalism and strategic delegationof leadership. Journal of Peace Research 45 (4), 557–573.Niskanen, W. A. (1971). Bureaucracy and Representative Government. Chicago:Aldine-Atherton.Osborne, M. and A. Slivinsky (1996). A model of political competition with citizen-candidates. The Quarterly Journal of Economics 111 (1), 65–96.Persson, T. and G. Tabellini (1992). The politics of 1992: Fiscal policy and europeanintegration. The Review of Economic Studies 59 (4), 689–701.Persson, T. and G. Tabellini (1994). Representative democracy and capital taxation.Journal of Public Economics 55 (1), 53–70.Persson, T. and G. Tabellini (2002). Political Economics: Explaining Economic Policy.Cambridge, Mass.: The MIT Press.Roelfsema, H. (2007). Strategic delegation of environmental policy making. Journal ofEnvironmental Economics and Management 53 (2), 270–275.Roemer, J. (2003). Indeterminacy of citizen-candidate equilibrium. Cowles FoundationDiscussion Paper no. 1410.8

A model of political competition with citizencandidates.

Aggregate uncertainty in the citizen candidate model yields extremist parties.

An economic model of representative democracy.

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Citizen-candidates, lobbies, and strategic campaigning.

Civil con federalism and strategic delegation of leadership.

Indeterminacy of citizen-candidate equilibrium.

Lobbying and welfare in a representative democracy.

Multiple equilibria in the citizen-candidate model of representative democracy.

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The Citizen-Candidate Model with Imperfect Policy Control

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