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The (sub-)optimality of the majority rule

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  • Schmitz, Patrick W.
  • Tröger, Thomas

Abstract

We consider collective choice from two alternatives. Ex ante, each agent is uncertain about which alternative she prefers, and may be uncertain about the intensity of her preferences. An environment is given by a probability distribution over utility vectors that is symmetric across agents and neutral across alternatives. In many environments, the majority voting rule maximizes agents' ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agents' utilities are stochastically correlated, other dominant-strategy choice rules are better for all agents. If utilities are stochastically independent across agents, majority voting is ex-ante optimal among all anonymous and incentive-compatible rules. We also compare rules from an interim viewpoint.

Suggested Citation

  • Schmitz, Patrick W. & Tröger, Thomas, 2011. "The (sub-)optimality of the majority rule," MPRA Paper 32716, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:32716
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    References listed on IDEAS

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    1. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 447-476.
    2. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    3. Schofield, Norman, 1972. "Ethical Decision Rules for Uncertain Voters," British Journal of Political Science, Cambridge University Press, vol. 2(2), pages 193-207, April.
    4. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    5. Casella, Alessandra, 2005. "Storable votes," Games and Economic Behavior, Elsevier, vol. 51(2), pages 391-419, May.
    6. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    7. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, January.
    8. repec:tpr:qjecon:v:119:y:2004:i:3:p:1011-1048 is not listed on IDEAS
    9. Salvador Barbera & Matthew O. Jackson, 2002. "Choosing How to Choose: Self Stable Majority Rules," Microeconomics 0211003, University Library of Munich, Germany.
    10. Matthias Messner & Mattias K. Polborn, 2004. "Voting on Majority Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(1), pages 115-132.
    11. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    12. Tilman Borgers, 2004. "Costly Voting," American Economic Review, American Economic Association, vol. 94(1), pages 57-66, March.
    13. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    14. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    15. Alessandra Casella & Thomas Palfrey & Raymond Riezman, 2013. "Minorities and Storable Votes," World Scientific Book Chapters, in: Raymond Riezman (ed.), International Trade Agreements and Political Economy, chapter 15, pages 247-282, World Scientific Publishing Co. Pte. Ltd..
    16. Ledyard, John O., 1978. "Incentive compatibility and incomplete information," Journal of Economic Theory, Elsevier, vol. 18(1), pages 171-189, June.
    17. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 1011-1048.
    18. Krasa, Stefan & Polborn, Mattias K., 2009. "Is mandatory voting better than voluntary voting?," Games and Economic Behavior, Elsevier, vol. 66(1), pages 275-291, May.
    19. Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 379-389.
    20. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    21. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
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    More about this item

    Keywords

    majority rule;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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