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On a Three-Alternative Condorcet Jury Theorem

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  • Johanna Goertz
  • Francois Maniquet

Abstract

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.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3457.

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Date of creation: 2011
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Handle: RePEc:ces:ceswps:_3457

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Related research

Keywords: efficient information aggregation; simple plurality rule; Poisson games; Condorcet Jury Theorem;

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  1. GOERTZ, Johanna M. & MANIQUET, François, 2009. "On the informational efficiency of simple scoring rules," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2009026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Timothy Feddersen & Wolfgang Pesendorfer, 1994. "Voting Behavior and Information Aggregation in Elections with Private Information," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1117, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, Elsevier, vol. 25(1), pages 111-131, October.
  4. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 94(1), pages 7-45, September.
  5. Roger B. Myerson, 2000. "Comparison of Scoring Rules in Poisson Voting Games," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 0686, Econometric Society.
  6. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, Elsevier, vol. 22(2), pages 364-376, February.
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