Repeated Elections with Asymmetric Information

An infinite sequence of elections with no term limits is modelled. In each period a challenger with privately known preferences is randomly drawn from the electorate to run against the incumbent, and the winner chooses a policy outcome in a one-dimensional issue space. One theorem is that there exists an equilibrium in which the median voter is decisive: an incumbent wins re-election if and only if his most recent policy choice gives the median voter a payoff at least as high as he would expect from a challenger. The equilibrium is symmetric, stationary, and the behavior of voters is consistent with both retrospective and prospective voting. A second theorem is that, in fact, it is the only equilibrium possessing the latter four conditions — decisiveness of the median voter is implied by them.     

Mixed Equilibrium in a Downsian Model with a Favored Candidate

This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate (A) enjoys an advantage over the other candidate (D). Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some fixed distance δ. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fail to exist in this model, except under special conditions about δ and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium with no-gaps, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies. We find that both players' equilibrium strategies converge to the expected median voter as A's advantage shrinks to 0. Journal of Economic Literature Classification Numbers: C72, D72.     

Candidate reputations and the ‘incumbency effect’

A major shortcoming of the classical median voter model is that its central prediction — convergence of platforms to the median voter's ideal — is seldom observed. One reason is that the classical model neglects the importance of voter expectations as a determinant of votes. Here we associate voters' expectations about candidates with past as well as current candidate pronouncements, and assume that incumbents whose actions are consistent with their ‘reputations’ are perceived as less risky than challengers. In equilibrium candidates choose distinct platforms. Typically neither adopts the median voter's ideal point. Either candidate may win depending on how well the incumbent's reputation reflects current voter tastes and how relatively ‘risky’ the electorate perceives the challenger to be.     

Electoral competition with privately-informed candidates

This paper formulates and analyzes a general model of elections in which candidates receive private signals about voters' preferences prior to committing to political platforms. We fully characterize the unique pure-strategy equilibrium: After receiving her signal, each candidate locates at the median of the distribution of the median voter's location, conditional on the other candidate receiving the same signal. Sufficient conditions for the existence of pure strategy equilibrium are provided. Though the electoral game exhibits discontinuous payoffs for the candidates, we prove that mixed strategy equilibria exist generally, that equilibrium expected payoffs are continuous in the parameters of the model, and that mixed strategy equilibria are upper hemicontinuous. This allows us to study the robustness of the median voter theorem to private information: Pure strategy equilibria may fail to exist in models “close” to the Downsian model, but mixed strategy equilibria must, and they will be “close” to the Downsian equilibrium.     

Dynamic enfranchisement

Why would an enfranchised elite voluntarily dilute its power by expanding the franchise? The central intuition behind our analysis is that the dilution of power by an enfranchised elite is equivalent to the delegation of power by one member of the elite—a pivotal voter—to another citizen, who in turn becomes the pivotal voter in the new (expanded) elite. Such delegation might be useful if it allows the current pivotal voter to credibly commit to future policy choices. The current pivotal voter realizes that the agent to whom authority is delegated will face similar incentives to subsequently transfer power, and this effect tempers the extent to which the franchise is extended. We develop a recursive, infinite horizon model that generates the possibility of gradual franchise expansion. We show that, in equilibrium, expansion occurs if and only if the private decisions of the citizenry have a net positive spillover to the dynamic payoff of the current pivotal voter. The class of games we study can accommodate a number of proposed explanations for franchise extension, including the threat of insurrection, and ideological or class conflict within the elite.     

Candidate strategies in primaries and general elections with candidates of heterogeneous quality

I consider a model in which candidates of differing quality must win a primary election to compete in the general election. I show that there is an equilibrium in which Democrats choose liberal policies and Republicans choose conservative policies, but higher quality candidates choose more moderate policies than lower quality candidates. In this equilibrium, higher quality candidates choose more moderate policies if they have a larger quality advantage or there is less uncertainty about the median voterʼs ideal point in the general election, and the candidates in a given primary choose closer policies to one another when there is a smaller quality difference between the candidates in a primary. I further show that if the candidates have policy motivations, then a low quality candidate may strategically choose to enter a primary even if running for office is costly and the candidate will lose the primary election with certainty in equilibrium.     

Coordinated voting in sequential and simultaneous elections: some experimental evidence

This paper studies a situation wherein a set of voters choose between two alternatives in the presence of a payoff externality. Specifically, regardless of her intrinsic preference, a voter’s payoff is maximized should she vote for the alternative that garners a majority of the votes cast. Are votes coordinated on a single alternative? Using laboratory experiments, we examine voting patterns in sequential voting and simultaneous voting elections. Across both election types, we also vary the amount of information that an individual voter has regarding the intrinsic preferences of the other voters. Our main findings are as follows. In the “low” information treatment, sequential voting elections facilitate coordinated voting. However, in the “high” information treatment, voting patterns are not dependent on how the election is structured.     

IMPERFECTLY INFORMED VOTERS AND STRATEGIC EXTREMISM

We analyze a two‐candidate Downsian model considering that voters use shortcuts (e.g., interest‐group/media endorsements) to infer candidates' policy platforms. That is, voters do not observe candidates' exact platforms but only which candidate offers the more leftist/rightist platform (relative positions). In equilibrium, candidates' behavior tends to maximum extremism, but it may converge or diverge depending on how voters behave when indifferent policywise between the candidates. When the tie‐breaking rule used by the voters is sufficiently fair, candidates converge to the extreme preferred by the median voter, but when it strongly favors a certain candidate, each candidate specializes in a different extreme.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.     

Civic duty and political advertising

Should voter awareness policies and get-out-the-vote movements be promoted? This paper addresses the question using a model of political advertising that incorporates both the mobilization and the persuasion aspects of advertising. We characterize the equilibrium and conduct comparative statics analysis allowing evaluation of the effect of voter awareness policies or the activity of get-out-the-vote movements on political advertising and the information aggregated by the electoral outcome. We find that such policies or movements may lead to either an increase or a decrease in political advertising as well as in the probability that the candidate preferred by a majority of (all informed) citizens is elected.     

Impermanent types and permanent reputations

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.     

Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.     

MISINFORMATION*

A candidate for political office has private information about his and his rival’s qualifications. A more informative positive (negative) campaign generates a more accurate public signal about his own (his rival’s) qualifications, but costs more. A high type candidate has a comparative advantage in negative campaigns if, relative to the low type, he can lower the voter’s belief about his rival more effectively than he can raise her belief about himself and vice versa. In equilibrium, this comparative advantage determines whether the high type chooses a positive or negative campaign. Further, competition helps the high type separate.     

SEQUENTIAL VOTING WHEN LONG ELECTIONS ARE COSTLY

This paper analyzes sequential voting in binary elections when voters are motivated by a desire both to elect their preferred candidate and to avoid a long and costly election. I find a unique equilibrium in which a voter's action depends both on the intensity of the voter's preferences as well as how well the candidates have done in earlier voting rounds. This equilibrium results in momentum in which voters are more likely to vote for the candidate currently in the lead. Furthermore, the probability a voter votes for a candidate is increasing in the size of the candidate's lead. As a consequence, a candidate is more likely to win the election if the candidate's stronger supporters vote earlier in the election.     

Computationally restricted unmediated talk under incomplete information

Summary. We show the role of unmediated talk with computational complexity bounds as both an information transmission and a coordination device for the class of two-player games with incomplete information and rational parameters. We prove that any communication equilibrium payoff of such games can be reached as a Bayesian-Nash equilibrium payoff of the game extended by a two phase universal mechanism of interim computationally restricted pre-play communication. The communication protocols are designed with the help of modern cryptographic tools. A familiar context in which our results could be applied is bilateral trading with incomplete information.Received: 9 September 2002, Revised: 14 March 2003, JEL Classification Numbers: C72. Correspondence to: Amparo UrbanoWe wish to thank financial aid from the Valencian Institute of Economic Research (IVIE) and partial support by DIGCYT under project PB95 - 1074. A previous version of this work appears as IVIE Working Paper WP-AD 99-07, under the title: "Unmediated talk under incomplete information".     

EXTREMIST PLATFORMS: POLITICAL CONSEQUENCES OF PROFIT-SEEKING MEDIA

We analyze how information about candidate quality affects the choice of electoral platforms made by an office-motivated political challenger. The incumbent is of known quality and located at the ideal policy of the voter. The voter cares for both policy and the candidates' quality and can learn about the challenger's quality by buying information. A high-quality challenger then has an incentive to signal her quality by choosing a policy that induces the voter to buy information. We first study the benchmark case in which the information is supplied exogenously, and its quality is independent of the challenger's platform; this yields multiple equilibria and indeterminacy of equilibrium platforms. By contrast, when the information is supplied by a profit-maximizing media outlet, its quality depends on the challenger's platform and we obtain a unique equilibrium platform. In particular, when the incumbent's quality is relatively low, the media coverage rises and the challenger's platform diverges further from the voter's ideal policy as the voter's preference for quality increases.     

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.     

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.     

The strategic sincerity of Approval voting

We show that Approval voting need not trigger sincere behavior in equilibrium of Poisson voting games and hence might lead a strategic voter to skip a candidate preferred to his worst preferred approved candidate. We identify two main rationales for these violations of sincerity. First, if a candidate has no votes, a voter might skip him. Notwithstanding, we provide sufficient conditions on the voters’ preference intensities to remove this sort of insincerity. On the contrary, if the candidate gets a positive share of the votes, a voter might skip him solely on the basis of his ordinal preferences. This second type of insincerity is a consequence of the correlation of the candidates’ scores. The incentives for sincerity of rank scoring rules are also discussed.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.