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.     

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.     

A passion for voting

We model expressive voting as a dynamic game with informed and ignorant voters. A voter has selective memory for actions and he is aware of it. We find a unique symmetric equilibrium with ignorant voting. Public signal in favor of one particular alternative creates the bandwagon and underdog effects. When the signal is sufficiently strong, the majority outcome is biased. This is a possible reason for persistence of public policies.     

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.     

Bandwagons and Momentum in Sequential Voting

In this paper I show that an equilibrium exists to the sequential voting game in which a bandwagon begins with probability 1. These bandwagons are driven by a combination of beliefs and the desire of voters to vote for the winning candidate. Significantly, in this equilibrium the pivot probability for each voter is non-zero, even in an infinite population. Consequently, the bandwagons do not always start after one (or at most two) favourable decisions (as do economic cascades) and varying levels of informative voting are observed, consistent with observations from sequential voting in U.S. presidential primaries. Further, voters are exposed to counterintuitive incentives, referred to as "buyers' remorse", that have been attributed to real primary voters.
I also derive equilibrium behaviour in this environment when voting is simultaneous and compare the quality of information aggregation within each mechanism. I relate the conclusions to U.S. presidential primaries and find they are consistent with a common conclusion about the front-loading of the primary process: that in tight elections (with no front-runner) simultaneous voting is preferred, whereas in lopsided elections sequential voting is preferred. The superior performance of sequential voting in lopsided races is precisely because bandwagons occur.     

An IMPOSSIBILITY THEOREM IN PURE PUBLIC GOODS ECONOMIES WITH FEASIBILITY CONSTRAINTS: VOTING BY COMMITTEES IN NON-RECTANGULAR FEASIBLE SETS*

We consider the problem of choosing an alternative in a pure public goods economy with feasibility constraints when voters have "additively-separable and single-peaked"preferences.Our purpose is to identify tops-only voting procedures satisfying "nonmanipulability" and "voter sovereignty". First, we show that such procedures are generalizations of the schemes of "voting by committees"¹)introduced by Barbera, Sonnenschein and Zhou (1991) in the sense that these procedures are defined similarly for the generalized feasible set. Second, we establish that when no two goods can be simultaneously produced at their maximal feasible levels, the procedures are characterized by the existence of a very powerful voter.     

Counterexamples on the Superiority of Approval versus Plurality

We present a simple voting environment with three candidates where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability. We also analyze the robustness of such an example to changes in the number of voters and their preferences. To conclude, we present a generic four‐candidate voting environment with the same properties.     

Compulsory versus voluntary voting: An experimental study

We report on an experiment comparing compulsory and voluntary voting institutions in a voting game with common preferences. Rational choice theory predicts sharp differences in voter behavior between these two institutions. If voting is compulsory, then voters may find it rational to vote insincerely, i.e., against their private information. If voting is voluntary so that abstention is allowed, then sincere voting in accordance with a voter's private information is always rational while participation may become strategic. We find strong support for these theoretical predictions in our experimental data. Moreover, voters adapt their decisions to the voting institution in place in such a way as to make the group decision accuracy differences between the two voting institutions negligible. The latter finding may serve to rationalize the co-existence of compulsory and voluntary voting institutions in nature.     

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.     

Voting by Successive Elimination and Strategic Candidacy

We study the impact of strategic choices of self-interested candidates of whether or not to enter an election. We focus on strategic candidacy in the context of the tree and binary voting procedures used by small groups such as committees. We offer a comprehensive analysis for the special but important case of voting by successive elimination. Strategic candidacy slightly enlarges the set of candidates that can be equilibrium outcomes relative to the traditional analysis which takes the set of candidates as fixed. Pareto-dominated candidates can be elected in equilibrium under voting by successive elimination when strategic candidacy is considered, in contrast with a fixed set of candidates. Journal of Economic Litterature Classification Numbers: D71, D72.     

The politics of progressive income taxation with incentive effects

This paper studies majority voting over quadratic taxation and investigates under which conditions marginal progressivity emerges as a voting outcome. In our model with endogenous income, there is no majority (Condorcet) winning tax schedule. We then investigate less demanding political equilibrium concepts in order to see under which conditions the set of equilibria is composed only of progressive tax functions. We follow three strategies: (i) reduction of the policy space to the tax functions that are ideal for some voter; (ii) elimination of weakly dominated strategies and the use of mixed strategies in a standard Downsian two-party competition game; (iii) assumption that political parties interact repeatedly and care about the size of their majority. Although each approach captures a different aspect of political behavior, they point to the same (simulation-based) conclusion that progressivity is more likely to emerge for most distributions of abilities and that it is actually the only possible voting outcome if the distribution is sufficiently concentrated at the middle.     

Information Manipulation in Election Campaigns

We provide a game‐theoretical model of manipulative election campaigns with two political candidates and a Bayesian voter. The latter is uncertain about how good the candidates are. Candidates take unobservable, costly actions to manipulate voter's opinion about their positions. We show that if the candidates differ in campaigning efficiency, and the voter receives the biased campaign messages with some noise, then the cost‐efficient candidate can win the election with higher probability than her opponent even when she is ex‐post an inferior choice for the voter. Our paper offers a novel informational justification for imposing limits on campaign spending and encouraging diversity in the supply of political information.     

Unidimensional median voter results in probabilistic voting models

This paper studies the policy outcomes that can be expected to occur when candidates are uncertain about voter behavior. Its analysis begins with an example that illustrates how the ‘Comaner–Hinich effect’ (i.e., the possibility of non-median outcomes) can occur under such circumstances. This example is then modified in ways which restore a median outcome. After this is done, the method of restoration is generalized to obtain a unidimensional median voter result for probabilistic voting models.     

Learning in Elections and Voter Turnout

Voter turnout in game theoretic models of voting has typically been difficult to predict because of the problem of multiple Nash equilibria ( Palfrey and Rosenthal 1983, 1985 ). Many of these equilibria require an extreme precision of beliefs among voters that is unlikely to be reached in real elections. At the same time, mechanisms like pre‐election polls exist to shape the beliefs of voters about expected turnout. We combine these two features in a model of voter learning in elections and characterize the asymptotically stable equilibria of both complete and incomplete information games in a simple symmetric setting with two candidates. We also show how the model can be used to qualitatively explain several phenomena observed in reality: increases in costs of voting affect turnout adversely but there may be persistence of turnout levels between elections even though costs and other parameters change. Increase in uncertainty increases turnout while increases in the size of the electorate decrease it, in line with intuition.     

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.     

The ratio equilibrium and a voting game in a public goods economy

An economic model of the allocation process with public goods is presented. We define a concept of equilibrium and prove the existence. Next we present a voting game in which a level of the public goods to be produced is decided. We prove that the core of the voting game and the equilibria exist simultaneously, and that they coincide.     

Let the experts decide? Asymmetric information,abstention, and coordination in standing committees

We examine abstention when voters in standing committees are asymmetrically informed and there are multiple pure-strategy equilibria – swing voterʼs curse (SVC) equilibria where voters with low-quality information abstain and equilibria when all participants vote their information. When the asymmetry in information quality is large, we find that voting groups largely coordinate on the SVC equilibrium which is also Pareto optimal. However, we find that when the asymmetry in information quality is not large and the Pareto optimal equilibrium is for all to participate, significant numbers of voters with low-quality information abstain. Furthermore, we find that information asymmetry induces voters with low-quality information to coordinate on a non-equilibrium outcome. This suggests that coordination on “letting the experts” decide is a likely voting norm that sometimes validates SVC equilibrium predictions but other times does not.     

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.     

Mixed equilibria in runoff elections

We demonstrate that the Hotelling–Downs model with runoff voting always admits symmetric mixed strategy equilibria for any (even or odd) number of office-motivated candidates (provided they are at least four). In specific, (a) we show that the game does not admit any symmetric atomless equilibrium, (b) we fully characterize a class of symmetric atomic mixed equilibria which exist for any distribution of the voters' ideal policies and (c) we argue that these equilibria are more robust than pure strategy equilibria to introduction of uncertainty about the voters' preferences.     

Exit polls,turnout, and bandwagon voting: Evidence from a natural experiment

We exploit a voting reform in France to estimate the causal effect of exit poll information on turnout and bandwagon voting. Before the change in legislation, individuals in some French overseas territories voted after the election result had already been made public via exit poll information from mainland France. We estimate that knowing the exit poll information decreases voter turnout by about 11 percentage points. Our study is the first clean empirical design outside of the laboratory to demonstrate the effect of such knowledge on voter turnout. Furthermore, we find that exit poll information significantly increases bandwagon voting; that is, voters who choose to turn out are more likely to vote for the expected winner.