Essays on Strategic Voting

Theory and Decision, 2017

In this study, we are concerned with how agents can best amalgamate their private information about a binary state of Nature. The agents are heterogeneous in their "ability", the quality of their private information. The agents cannot directly communicate their private information but instead can only vote between the two states (say "Innocent" or "Guilty" on a criminal jury). We first describe possible methods of sequential majority voting, and then we analyze a particular one: the first n -1 jurors vote simultaneously and, in the case of a tie, the remaining juror has the casting vote. We prove that when n = 3 (a common situation for a tribunal of three judges), the probability of a correct verdict is maximized when the agent of median ability has the casting vote.

Public Choice, 2018

This paper studies the collective decision-making processes of voters who have heterogeneous levels of rationality. Specifically, we consider a voting body consisting of both rational and sincere voters. Rational voters vote strategically, correctly using both their private information and the information implicit in other voters' actions to make decisions; sincere voters vote according to their private information alone. We first characterize the conditions under which the presence of sincere voters increases, reduces, or does not alter the probabilities of making correct collective decisions. We also discuss how the probabilities change when the incidence of sincere voters in the population varies. We then characterize the necessary and sufficient condition under which informational efficiency can be achieved when sincere voters coexist with rational voters. We find that when sincere voters are present, supermajority rules with high consensus levels are not as desirable as they are in rational voting models, as informational efficiency fails under such voting rules.

2012

We analyze committees of voters who take a decision between two options as a twostage process. In a discussion stage, voters share non verifiable information about a private signal concerning what is the best option. In a voting stage, votes are cast and one of the options is implemented. We introduce the possibility of leadership whereby a certain voter, the leader, is more influential than the rest at the discussion stage even though she is not better informed. We study information transmission and find, amongst others, a non-monotonic relation between how influential the leader is and how truthful voters are at discussion stage.

In a model of majority voting with common values and costly but voluntary participation, we show that in the vicinity of equilibrium, it is always Pareto-improving for more agents, on the average, to vote. This demonstrates that the negative voting externality identified by Borgers(2001) in the context of private values is always dominated by a positive informational externality. In addition, we show that multiple Pareto-ranked voting equilibria may exist and moreover, majority voting with compulsory participation can Pareto dominate majority voting with voluntary participation. Finally, we show that the inefficiency result is robust to limited preference heterogeneity.

Proceedings of the 24th ACM Conference on Economics and Computation

We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the "correct" decision, outperforming the common non-strategic behavior of informative voting and sincere voting. Our results give merit to strategic voting for making good decisions. To this end, we investigate a natural model, where voters' preferences between two alternatives depend on a discrete state variable that is not directly observable. Each voter receives a private signal that is correlated with the state variable. We reveal a surprising equilibrium between a strategy profile being a strong equilibrium and leading to the decision favored by the majority of agents conditioned on them knowing the ground truth (referred to as the informed majority decision): as the size of the vote goes to infinity, every-strong Bayes Nash Equilibrium with converging to 0 formed by strategic agents leads to the informed majority decision with probability converging to 1. On the other hand, we show that informative voting leads to the informed majority decision only under unbiased instances, and sincere voting leads to the informed majority decision only when it also forms an equilibrium. CCS Concepts: • Theory of computation → Algorithmic game theory; • Computing methodologies → Distributed artificial intelligence.

2006

Whether made explicit or implicit, knowledge theoretic properties such as common knowledge of rationality are important in understanding and modeling game-theoretic, or strategic, situations. There is a large literature devoted to exploring these and other issues related to the epistemic foundations of game theory. Much of the literature focuses on what the agents need to know about the other agents' strategies, rationality or knowledge in order to guarantee that a particular solution concept, such as the Nash equilibrium, is realized. This paper, which is based on two recent papers 1 [7] and [16], develops a framework that looks at similar issues relevant to the field of voting theory. Our analysis suggests that an agent must possess information about the other agents' preferences in order for the agent to decide to vote strategically. In a sense, our claim is that the agents need a certain amount of information in order for the Gibbard-Satterthwaite theorem to be "effective".

University of Copenhagen Economics Working Paper No. 08-25, 2008

We examine abstention when voters in standing committees are asymmetrically informed and there are multiple pure strategy equilibria-swing voter's 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 …nd that voting groups largely coordinate on the SVC equilibrium which is also Pareto Optimal. However, we …nd that when the asymmetry in information quality is not large and the Pareto Optimal equilibrium is for all to participate, signi…cant numbers of voters with low quality information abstain. Furthermore, we …nd 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.

University of Copenhagen Economics Working Paper No. 14-18, 2014

We investigate experimentally the effects of corrupt experts on information aggregation in committees. We find that non-experts are significantly less likely to delegate through abstention when there is a probability that experts are corrupt. Such decreased abstention, when the probability of corrupt experts is low, actually increases information efficiency in committee decision-making. However, if the probability of corrupt experts is large, the effect is not sufficient to offset the mechanical effect of decreased information efficiency due to corrupt experts. Our results demonstrate that the norm of "letting the expert decide" in committee voting is influenced by the probability of corrupt experts, and that influence can have, to a limited extent, a positive effect on information efficiency.

Economics and Philosophy, 2015

We present a model of collective decision making in which aggregation and deliberation are treated simultaneously. In our model, individuals debate in a public forum and potentially revise their judgements in light of deliberation. Once this process is exhausted, a rule is applied to aggregate post-deliberation judgements in order to make a social choice. Restricting attention to three alternatives, we identify conditions under which a democracy is "truth-revealing". This condition says that the deliberation path and the aggregation rule always * Financial support from the Irish Research Council for the Humanities and Social Sciences, the Spanish Ministry of Science and Innovation through MICINN/FEDER grants ECO2010-21624 and ECO2010-14929, and the NUI Galway Millennium Fund is gratefully acknowledged. We are grateful for comments received at a Choice Group seminar at LSE and also those received at a seminar at the Université de Caen. In particular, we would like to thank