A Condorcet Jury Theorem for Large Poisson Elections with Multiple Alternatives

Johanna M. M. Goertz
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Johanna M. M. Goertz: Department of Economics and Finance, Gordon S. Lang School of Business and Economics, University of Guelph, 50 Stone Road East, Guelph, ON N1G 2W1, Canada

Games, 2019, vol. 11, issue 1, 1-12

Abstract: 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.

Keywords: efficient information aggregation; simple plurality rule; Poisson games; condorcet jury theorem (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2019
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