Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by the equilibria that they generate for simple elections with three candidates and voters drawn from large Poisson distributions. A calculus for comparing pivot probabilities in Poisson voting games is applied. For a symmetric Condorcet cycle, nonsymmetric discriminatory equilibria exist under best-rewarding scoring rules like plurality voting. A candidate who is universally disliked may still not be out of contention under worst-punishing scoring rules like negative-plurality voting. In elections where two of three candidates have the same position, symmetric equilibria coincide with majority rule only for scoring rules that are balanced between best-rewarding and worst-punishing. When voters also care about continuous functions of vote shares, equilibria may still depend on pivot probabilities.

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by the equilibria that they generate for simple elections with three candidates and voters drawn from large Poisson distributions. A calculus for comparing pivot probabilities in Poisson voting games is applied. For a symmetric Condorcet cycle, nonsymmetric discriminatory equilibria exist under best-rewarding scoring rules like plurality voting. A candidate who is universally disliked may still not be out of contention under worst-punishing scoring rules like negative-plurality voting. In elections where two of three candidates have the same position, symmetric equilibria coincide with majority rule only for scoring rules that are balanced between best-rewarding and worst-punishing. When voters also care about continuous functions of vote shares, equilibria may still depend on pivot probabilites.

Sincere Scoring Rules

Approval Voting is shown to be the unique scoring rule that leads strategic voters to sincere behavior of three candidates elections in Poisson Games. However, Approval Voting can lead to insincere behavior in elections with more than three candidates.Sincerity, Approval Voting, Scoring rules, Poisson Games

Approval Voting and Scoring Rules with Common Values

Consider the problem of deciding a winner among three alternatives when voters have common values, but private information regarding the values of the alternatives. We compare approval voting with other scoring rules. For any finite electorate, the best equilibrium under approval voting is more efficient than either plurality rule or negative voting. If any scoring rule yields a sequence of equilibria that aggregates information in large elections, then approval voting must do so as well

Strategic Approval Voting in a large electorate

L'article est consacré au vote par assentiment pour une grande population de votants. On montre que, partant d'une information statistique sur les scores des candidats, les électeurs rationels votent sincèrement. On montre alors que, si un candidat est vainqueur de Condorcet, ce candidat est élu.Vote par assentiment;Vote stratégique;vote probabiliste;Elections

Maximum Likelihood Equilibria of Games with Population Uncertainty

In the games with population uncertainty introduced in this paper, the number and identity of the participating players are determined by chance.Games with population uncertainty are shown to include Poisson games and random-player games.The paper focuses on those strategy profiles that are most likely to yield a Nash equilibrium in the game selected by chance.Existence of maximum likelihood equilibria is established under mild topological conditions.

Undominated (and) perfect equilibria in Poisson games

In games with population uncertainty some perfect equilibria are in dominated strategies. We prove that every Poisson game has at least one perfect equilibrium in undominated strategies

Manipulation in Elections with Uncertain Preferences

A decision scheme (Gibbard (1977)) is a function mapping profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. Motivated by conditions typically prevailing in elections with many voters, we say that a decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent with her true preferences) by misrepresenting her preferences when her belief about the preferences of other voters is generated by a model in which the other voters are i.i.d. draws from a distribution over possible preferences. We show that if there are at least three alternatives, a decision scheme is necessarily a random dictatorship if it is weakly strategy-proof, never assigns positive probability to Pareto dominated alternatives, and is anonymous in the sense of being unaffected by permutations of the components of the profile. This result is established in two settings- a) a model with a fixed set of voters; b) the Poisson voting model of Meyerson (1998a,b, 2000, 2002).

On a Three-Alternative Condorcet Jury Theorem

We investigate whether the simple plurality rule aggregates information efficiently in a large election with three alternatives. The environment is the same as in the Condorcet Jury Theorem (Condorcet (1785)). Voters have common preferences that depend on the unknown state of nature, and they receive imprecise private signals about the state of nature prior to voting. With two alternatives and strategic voters, the simple plurality rule aggregates information efficiently in elections with two alternatives (e.g., Myerson (1998)). We show that there always exists an efficient equilibrium under the simple plurality rule when there are three alternatives as well. We characterize the set of inefficient equilibria with two alterna- tives and the condition under which they exist. There is only one type of inefficient equilibrium with two alternatives. In this equilibrium, voters vote unresponsively because they all vote for the same alternative. Under the same condition, the same type of equilibrium exists with three alternatives. However, we show that the number and types of coordination failures increase with three alternatives, and that this leads to the existence of other types of inefficient equilibria as well, including those in which voters vote informatively.efficient information aggregation, simple plurality rule, Poisson games, Condorcet Jury Theorem

Sincere Voting with Cardinal Preferences: Approval Voting

We discuss sincere voting when voters have cardinal preferences over alter- natives. We interpret sincerity as opposed to strategic voting, and thus define sincerity as the optimal behaviour when conditions to vote strategically vanish. When voting mechanisms allow for only one message type we show that this op- timal behaviour coincides with an intuitive and common definition of sincerity. For voting mechanisms allowing for multiple message types, such as approval vot- ing (AV), there exists no conclusive definition of sincerity in the literature. We show that for AV, voters' optimal strategy tends to one of the existent definitions of sincerity, consisting in voting for those alternatives that yield more than the average of cardinal utilities.sincere and strategic voting, approval voting