A study of Approval voting on Large Poisson Games

Approval voting features are analysed in a context of large elections with strategic voters: Myerson's Large Poisson Games. I first establish the Magnitude Equiva- lence Theorem (MET) which substantially reduces the complexity of computing the magnitudes of pivotal events. I also show that the Winner of the election coincides with the Profile Condorcet Winner at equilibrium when preferences are restricted to be single-peaked. This is a positive result that strengthens the positive conclusions some scholars have previously drawn over this voting rule. I finally show that, with- out the previous restriction over preferences, both concepts do not generally coincide anymore.

On the informational efficiency of simple scoring rules

efficient information aggregation, scoring rules, Poisson games, approval voting

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

Sincerity in Simple and Complex Voting Mechanisms

We discuss sincere voting when voters have cardinal preferences over alternatives. We interpret sincerity as opposed to strategic voting, and thus define sincerity as the optimal behavior when conditions to vote strategically diminish. When voting mechanisms allow for only one message type (simple voting mechanisms) we show that eliminating some conditions for strategic voting, individuals' optimal behavior coincides with an intuitive and common definition of sincerity. In order to obtain a precise definition of sincerity in voting mechanisms allowing for multiple message types (complex voting mechanisms) further restrictions on strategic voting are required. We illustrate our methodological approach using approval voting (AV) as a prime example of complex voting mechanisms for which no conclusive definition of sincerity exists in the literature.sincere and strategic voting, cardinal utility, approval voting

Maximum Sustainable Government Debt in the Overlapping Generations Model.

The theoretical determinants of maximum sustainable government debt are investigated using Diamond's overlapping-generations model. A level of debt is defined to be 'sustainable' f a steady state with non-degenerate values of economic variables exists. We show that a maximum sustainable level of debt almost always exists. Most interestingly, it normally occurs at a 'catastrophe' ather than a 'degeneracy' , i.e. where variables such as capital and consumption are in the interiors, rather than at the limits, of their economically meaningful ranges. This means that if debt is increased step by step, the economy may suddenly collapse without obvious warning.GOVERNMENT DEBT ; OVERLAPPING GENERATIONS

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.

A networked voting rule for democratic representation

We introduce a general framework for exploring the problem of selecting a committee of representatives with the aim of studying a networked voting rule based on a decentralized large-scale platform, which can assure a strong accountability of the elected. The results of our simulations suggest that this algorithm-based approach is able to obtain a high representativeness for relatively small committees, performing even better than a classical voting rule based on a closed list of candidates. We show that a general relation between committee size and representatives exists in the form of an inverse square root law and that the normalized committee size approximately scales with the inverse of the community size, allowing the scalability to very large populations. These findings are not strongly influenced by the different networks used to describe the individuals interactions, except for the presence of few individuals with very high connectivity which can have a marginally negative effect in the committee selection process.Comment: Submitted for publicatio