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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 agentsʼ ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules. But in some environments where the agentsʼ 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, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
  • Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:651-665 DOI: 10.1016/j.geb.2011.08.002
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    Cited by:

    1. Börgers, Tilman & Hernando-Veciana, Angel & Krähmer, Daniel, 2013. "When are signals complements or substitutes?," Journal of Economic Theory, Elsevier, vol. 148(1), pages 165-195.
    2. repec:eee:gamebe:v:104:y:2017:i:c:p:468-485 is not listed on IDEAS
    3. Giles, Adam & Postl, Peter, 2014. "Equilibrium and effectiveness of two-parameter scoring rules," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 31-52.
    4. Rafael Hortala-Vallve, 2012. "Qualitative voting," Journal of Theoretical Politics, , vol. 24(4), pages 526-554, October.
    5. Shao, Ran & Zhou, Lin, 2016. "Voting and optimal provision of a public good," Journal of Public Economics, Elsevier, vol. 134(C), pages 35-41.
    6. Rosar, Frank, 2015. "Continuous decisions by a committee: Median versus average mechanisms," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 15-65.
    7. Felix J. Bierbrauer & Pierre C. Boyer, 2016. "Efficiency, Welfare, and Political Competition," The Quarterly Journal of Economics, Oxford University Press, vol. 131(1), pages 461-518.
    8. Pivato, Marcus, 2015. "Condorcet meets Bentham," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 58-65.
    9. repec:oup:restud:v:84:y:2017:i:2:p:688-717. is not listed on IDEAS
    10. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    11. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    12. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. repec:eee:gamebe:v:104:y:2017:i:c:p:350-371 is not listed on IDEAS
    14. Börgers, Tilman & Smith, Doug, 2014. "Robust mechanism design and dominant strategy voting rules," Theoretical Economics, Econometric Society, vol. 9(2), May.
    15. Kwiek, Maksymilian, 2014. "Efficient voting with penalties," Discussion Paper Series In Economics And Econometrics 1419, Economics Division, School of Social Sciences, University of Southampton.
    16. Rafael Hortalà-Vallvé, 2010. "Qualitative Voting," Cuadernos de Economía - Spanish Journal of Economics and Finance, ELSEVIER, vol. 33(92), pages 5-44, Mayo-Sept.
    17. Engelmann, Dirk & Grüner, Hans Peter, 2013. "Tailored Bayesian Mechanisms: Experimental Evidence from Two-Stage Voting Games," CEPR Discussion Papers 9544, C.E.P.R. Discussion Papers.
    18. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    19. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.
    20. Vijay Krishna & John Morgan, 2015. "Majority Rule and Utilitarian Welfare," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 339-375, November.
    21. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
    22. Kleiner, Andreas & Drexl, Moritz, 2013. "Why Voting? A Welfare Analysis," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79886, Verein für Socialpolitik / German Economic Association.
    23. NAKADA, Satoshi & NITZAN, Shmuel & UI, Takashi, 2017. "Robust Voting under Uncertainty," Discussion paper series HIAS-E-60, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.

    More about this item

    Keywords

    Majority rule; Mechanism design; Correlated values; Utilitarianism;

    JEL classification:

    • 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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