STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.     

Would letting people vote for multiple candidates yield policy moderation?

We investigate whether letting people vote for multiple candidates would yield policy moderation. We do so in a setting that takes three key features of elections into account, namely, strategic voting, endogenous candidacy and policy motivation on the part of the candidates. We consider two classes of voting rules. One class consists of the voting rules where each voter casts several equally-weighed votes for the different candidates. The other class consists of the voting rules where each voter rank-orders the candidates. We identify conditions under which these voting rules yield policy moderation. We also show that these voting rules may yield policy extremism instead of policy moderation if one (or several) of the conditions is not satisfied! Finally, we find that amongst these voting rules the extent of policy moderation is maximal under the Borda Count if we consider only equilibria where all candidates are serious contenders. However, this result does not carry over to spoiler equilibria, where Approval Voting can yield more moderate policy outcomes than the Borda Count.     

Candidate stability and probabilistic voting procedures

Summary. We extend the analysis of Dutta, Jackson and Le Breton (Econometrica, 2001) on strategic candidacy to probabilistic environments. For each agenda and each profile of voters preferences over running candidates, a probabilistic voting procedure selects a lottery on the set of running candidates. Assuming that candidates cannot vote, we show that random dictatorships are the only unanimous probabilistic voting procedures that never provide unilateral incentives for the candidates to withdraw their candidacy at any set of potential candidates. More flexible probabilistic voting procedures can be devised if we restrict our attention to the stability of specific sets of potential candidates.Received: 4 February 2003, Revised: 14 September 2004, JEL Classification Numbers: D71, D72.This is a revised version of a chapter of my Ph.D. Dissertation submitted to the Universitat Autónoma de Barcelona. I am indebted to my supervisor Salvador Barberá for his advice and constant support. I am grateful to Dolors Berga and an anonymous referee for their detailed comments and suggestions. I thank José Alcalde, Walter Bossert, Bhaskar Dutta, Lars Ehlers, Jordi Massó, Diego Moreno, Clara Ponsatí, Yves Sprumont, and William Thomson for many helpful comments and discussions. I thank the hospitality of the C.R.D.E. at the Université de Montréal and the Department of Economics of the University of Warwick where parts of this research were conducted. Financial support through Research Grant 1998FI00022 from Comissionat per Universitats i Recerca, Generalitat de Catalunya, Research Project PB98-870 from the Ministerio de Ciencia y Tecnología, and Fundación Barrié de la Maza is gratefully acknowledged.     

Approval voting with endogenous candidates

We present a formal model of political competition under approval voting which allows for endogenous candidate entry. Our analysis yields a number of novel insights. First, we develop a notion of sincere voting behavior under approval voting, called relative sincerity. We then show that the relatively sincere voting behavior is consistent with the strategic calculus of voting. Second, we show that in a one-dimensional model with distance preferences, equilibria in relatively sincere strategies and without spoiler candidates always generate outcomes close to the median voter. Moreover, approval voting satisfies Duverger's Law in the sense that there are at most two winning positions! Finally, we extend our analysis to arbitrary policy spaces. In the general setting, approval voting is shown to be susceptible to the same kinds of problems as the plurality rule, such as the possibility of non-majoritarian outcomes, failure to elect the Condorcet winner and existence of spoiler candidates.     

Sampling equilibrium, with an application to strategic voting

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.     

Size approval voting

We propose a new class of voting procedures, called Size Approval Voting, according to which, the effective weight of a vote from a given individual depends on how many other candidates that individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved candidates. Then, for a given profile of individual votes, all candidates with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting procedures is characterized by a set of natural properties.     

Strategic candidacy for multivalued voting procedures

Dutta et al. (Econometrica 69 (2001) 1013) (Dutta, Jackson, and Le Breton—DJLeB) initiate the study of manipulation of voting procedures by a candidate who withdraws from the election. A voting procedure is candidate stable if this is never possible. We extend the DJLeB framework by allowing: (a) the outcome of the procedure to be a set of candidates; (b) some or all of the voters to have weak preference orderings of the candidates. When there are at least three candidates, any strongly candidate stable voting selection satisfying a weak unanimity condition is characterized by a serial dictatorship. This result generalizes Theorem 4 of DJLeB.     

Hotelling–Downs Competition with Free Entry When Voters Have an Option to Contest

Osborne shows that for almost all distributions of voters’ preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling–Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side‐by‐side with office‐seeking players. The model studied in this paper renders Osborne and the celebrated citizen‐candidate model à la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office‐seeking players possible? We also show that in our general setting, extremists are typically voter‐candidates so that in every two‐party contest, office‐seeking politicians stay out of competition.     

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by their equilibria in simple voting games with Poisson population uncertainty, using new techniques for computing pivot probabilities. Best-rewarding rules like plurality voting can generate discriminatory equilibria where the voters disregard some candidate as not a serious contender, although he may be universally liked, or may be symmetric to other candidates as in the Condorcet cycle. Such discriminatory equilibria are eliminated by worst-punishing rules like negative voting, but then even a universally disliked candidate may have to be taken seriously. In simple bipolar elections, equilibria are always majoritarian and efficient under approval voting, but not other scoring rules. Journal of Economic Literature Classification: D72.     

A Hotelling–Downs model of electoral competition with the option to quit

We study a variant of the multi-candidate Hotelling–Downs model that recognizes that politicians, even after declaring candidacy, have the option of withdrawing from the electoral contest before the election date and saving the cost of continuing campaign. We find that this natural variant significantly alters equilibrium predictions. We give conditions for the existence of an equilibrium for an arbitrary finite number of candidates and an arbitrary distribution of single-peaked preferences of voters. We also provide a partial characterization of the equilibrium outcomes that addresses whether policy convergence can be a feature of equilibrium outcomes when more than two candidates enter the electoral contest.     

Information and strategic voting

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting. Voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur and focus on how information about the preference distribution affects strategic behavior. We also vary the relative importance of the second preferred option. Quantal response equilibrium analysis is used to analyze the game and derive predictions. Our results indeed show that strategic voting arises. Its extent depends on (i) information availability; (ii) the relative importance of the intermediate candidate; (iii) the electorate’s relative support for one’s preferred candidate; (iv) the relative position of the plurality-supported candidate in one’s preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate’s chances of winning.     

THE POLITICAL CHOICE OF THE EXCHANGE RATE REGIME*

The purpose of this paper is to present a model in which the choice of the optimal exchange rate regime is envisaged in a political setting. We consider a country whose voting population comprises three types of agents, importers, exporters and speculators, who select their position on exchange rate policy according to welfare maximization. As a result, well-defined interest groups are shown to emerge. Each coalition makes contributions to one of two political candidates running for political office in support for their optimal policy intervention. When policy pronouncements by the two candidates are made in terms of exchange rate volatility, the equilibrium consists of two extremes: a fixed versus flexible exchange regime, the latter with bounded volatility [JEL D72, F31].     

Universality of Nash components

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.     

Coalition and Party Formation in a Legislative Voting Game

We examine a legislative voting game where decisions are to be made over both ideological and distributive dimensions. In equilibrium legislators prefer to make proposals for the two dimensions together, despite having preferences that are separable over the two dimensions. The equilibria exhibit interaction between the ideological and distributive dimensions, and the set of legislators who approve winning proposals does not always consist of ideologically adjacent legislators. There is more than one ideological decision that has a positive probability of being proposed and approved. We show that legislators can gain from forming political parties, and consider examples where predictions can be made about the composition of parties. Journal of Economic Literature Classification Numbers: D72, C71, C78.     

VOTING AND SOCIAL PRESSURE UNDER IMPERFECT INFORMATION

We develop a model in which costly voting in a large, two‐party election is a sequentially rational choice of strategic, self‐interested players who can reward fellow voters by forming stronger ties in a network formation coordination game. The predictions match a variety of stylized facts, including explaining why an individual's voting behavior may depend on what she knows about her friends' actions. Players have imperfect information about others' voting behavior, and we find that some degree of privacy may be necessary for voting in equilibrium, enabling hypocritical but useful social pressure. Our framework applies to any costly prosocial behavior.     

Voting Equilibria in Multi-candidate Elections

We consider a general plurality voting game with multiple candidates, where voter preferences over candidates are exogenously given. In particular, we allow for arbitrary voter indifferences, as may arise in voting subgames of citizen-candidate or locational models of elections. We prove that the voting game admits pure strategy equilibria in undominated strategies. The proof is constructive: we exhibit an algorithm, the "best winning deviation" algorithm, that produces such an equilibrium in finite time. A byproduct of the algorithm is a simple story for how voters might learn to coordinate on such an equilibrium.     

On the Generic Finiteness of Equilibrium Outcomes in Plurality Games

In this paper we prove that for generic (noncooperative) voting games under plurality rule the set of equilibria that induce a mixed distribution over the outcomes (i.e., with two or more candidates elected with positive probability) is finite and, furthermore, each of these equilibria is regular. From that we deduce the finiteness of the set of equilibrium distributions over outcomes. Furthermore we offer an example (S. Govindan and A. McLennan, 1997, “On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms,” mimeo) that shows the impossibility of extending such results to a general framework, even just to voting games. Journal of Economic Literature Classification Numbers: C72, D72.     

Sequential voting with abstention

Dekel and Piccione [2000. Sequential voting procedures in symmetric binary elections. J. Polit. Economy 108, 34–55] have proven that information cascades do not necessarily affect the properties of information aggregation in sequential elections: under standard conditions, any symmetric equilibrium of a simultaneous voting mechanism is also an equilibrium of the correspondent sequential mechanism. We show that when voters can abstain, these results are sensitive to the introduction of an arbitrarily small cost of voting: the set of equilibria in the two mechanisms are generally disjoint; and the informative properties of the equilibrium sets can be ranked. If an appropriate q-rule is chosen, when the cost of voting is small the unique symmetric equilibrium of the simultaneous voting mechanism dominates all equilibria of the sequential mechanism.     

On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.     

Political salaries,electoral selection and the incumbency advantage: Evidence from a wage reform

Incumbents tend to gain solid electoral advantage in many voting systems. In this study, we examine the relationship between salaries prescribed to politicians and the incumbency advantage by exploiting a political wage reform and data from close elections in a proportional semi-open list system in the Czech Republic. We show that higher salaries reduce the average incumbency advantage, as they increase the probability to run again for previously non-elected candidates much more than for incumbents. Still, we find that higher wages improve candidate selection, especially by encouraging repeated candidacy from university-educated incumbents. Higher wages also improve relative positions of re-running incumbents on candidate lists compared to previously non-elected re-running candidates. Our results overall suggest that incumbency per se changes the relationship between political wages and candidate selection.