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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.

Suggested Citation

  • Johanna Goertz & Francois Maniquet, 2011. "On a Three-Alternative Condorcet Jury Theorem," CESifo Working Paper Series 3457, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_3457
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    File URL: http://www.cesifo-group.de/DocDL/cesifo1_wp3457.pdf
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    References listed on IDEAS

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    1. repec:cup:apsrev:v:93:y:1999:i:02:p:381-398_21 is not listed on IDEAS
    2. Goertz, Johanna M.M. & Maniquet, François, 2011. "On the informational efficiency of simple scoring rules," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1464-1480, July.
    3. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    4. Timothy Feddersen & Wolfgang Pesendorfer, 1997. "Voting Behavior and Information Aggregation in Elections with Private Information," Econometrica, Econometric Society, vol. 65(5), pages 1029-1058, September.
    5. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    6. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    7. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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