Public Information: Relevance or Salience?

How does salient public information affect voters’ behavior? In a majoritarian voting game with common preferences, rational voters could use public information as an information device (depending on accuracy) or as a coordination device (regardless of accuracy). A simple lab experiment contradicts both hypotheses – subjects tend to follow public information when it is salient, regardless of the information’s accuracy, but fail to use it as a source of coordination. In particular, it matters whether the information is recent – subjects are more likely to follow public information when it is provided closer to the voting decision. These findings are important because the salience of public information is easily manipulable by political actors.

A Condorcet Jury Theorem for Large Poisson Elections with Multiple Alternatives

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote (simple plurality rule). We also assume that this is a Poisson voting game with population uncertainty. The question is whether the simple plurality rule aggregates information efficiently so that the correct alternative is elected with probability tending to one when the number of voters tends to infinity. The previous literature shows that the CJT holds for large elections with two alternatives, but there is also an example of a large election with three alternatives that has an inefficient equilibrium. We show that there always exists an efficient equilibrium, independent of the number of alternatives. Under certain circumstances (informative types), it is unique in elections with two alternatives. The existence of inefficient equilibria in elections with more than two alternatives is generic.

On the Complexity of the Inverse Semivalue Problem for Weighted Voting Games

Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of the votes exceeds a prespecified threshold. As the influence of a player over the voting outcome is not in general proportional to her assigned weight, various power indices have been proposed to measure each player’s influence. The inverse power index problem is the problem of designing a weighted voting game that achieves a set of target influences according to a predefined power index. In this work, we study the computational complexity of the inverse problem when the power index belongs to the class of semivalues. We prove that the inverse problem is computationally intractable for a broad family of semivalues, including all regular semivalues. As a special case of our general result, we establish computational hardness of the inverse problem for the Banzhaf indices and the Shapley values, arguably the most popular power indices.

A Note on Pivotality

This note provides simple derivations of the equilibrium conditions for different voting games with incomplete information. In the standard voting game à la Austen-Smith and Banks (1996), voters update their beliefs, and, conditional on their being pivotal, cast their votes. However, in voting games such as those of Ellis (2016) and Fabrizi, Lippert, Pan, and Ryan (2019), given a closed and convex set of priors, ambiguity-averse voters would select a prior from this set in a strategy-contingent manner. As a consequence, both the pivotal and non-pivotal events matter to voters when deciding their votes. In this note, I demonstrate that for ambiguous voting games the conditional probability of being pivotal alone is no longer sufficient to determine voters’ best responses.

Spatial Social Choice

A key concept of social choice is the idea of the Condorcet point or core. For example, consider a voting game with four participants so any three will win. If voters have Euclidean preferences, then the point at the center will be unbeaten. Earlier spatial models of social choice focused on deterministic voter choice. However, it is clear that voter choice is intrinsically stochastic. This chapter employs a stochastic model based on multinomial logit to examine whether parties in electoral competition tend to converge toward the electoral center or respond to activist pressure to adopt more polarized policies. The chapter discusses experimental results of the idea of the core explores empirical analyses of elections in Israel and the United States.

GROWTH, UNEMPLOYMENT, AND FISCAL POLICY: A POLITICAL ECONOMY ANALYSIS

This study presents an overlapping-generations model featuring capital accumulation, collective wage-bargaining, and probabilistic voting over fiscal policy. The study characterizes a Markov-perfect political equilibrium of the voting game within and across generations, and it derives the following results. First, the greater bargaining power of unions lowers the capital growth rate and creates a positive correlation between unemployment and public debt. Second, an increase in the political power of elderly persons lowers the growth rate and shifts government expenditure from unemployed persons to elderly ones. Third, prohibiting debt finance increases the growth rate and benefits future generations; however, it worsens the state of present-day employed and unemployed persons.