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Robust mechanism design and dominant strategy voting rules

Author

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  • Borgers, Tilman
  • Smith, Doug

Abstract

We develop an analysis of voting rules that is robust in the sense that we do not make any assumption regarding voters’ knowledge about each other. In dominant strategy voting rules, voters’ behavior can be predicted uniquely without making any such assumption. However, on full domains, the only dominant strategy voting rules are random dictatorships. We show that the designer of a voting rule can achieve Pareto improvements over random dictatorship by choosing rules in which voters’ behavior can depend on their beliefs. The Pareto improvement is achieved for all possible beliefs. The mechanism that we use to demonstrate this result is simple and intuitive, and the Pareto improvement result extends to all equilibria of the mechanism that satisfy a mild refinement. We also show that the result only holds for voters’ interim expected utilities, not for their ex post expected utilities.

Suggested Citation

  • Borgers, Tilman & Smith, Doug, 2011. "Robust mechanism design and dominant strategy voting rules," MPRA Paper 37027, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:37027
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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," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 447-476.
    2. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    3. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    5. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    6. Bhaskar Dutta & Hans Peters & Arunava Sen, 2008. "Strategy-proof cardinal decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 701-702, May.
    7. repec:cup:apsrev:v:67:y:1973:i:03:p:934-946_14 is not listed on IDEAS
    8. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    9. Jobst Heitzig & Forest Simmons, 2012. "Some chance for consensus: voting methods for which consensus is an equilibrium," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 43-57, January.
    10. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    11. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    12. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    13. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    15. Blin, Jean-Marie & Satterthwaite, Mark A, 1977. "On Preferences, Beliefs, and Manipulation within Voting Situations," Econometrica, Econometric Society, vol. 45(4), pages 881-888, May.
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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
    2. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision, Mechanism Design and Voting," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_11, Max Planck Institute for Research on Collective Goods.
    3. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    4. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    5. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    6. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    7. repec:spr:reecde:v:21:y:2017:i:2:d:10.1007_s10058-017-0201-0 is not listed on IDEAS
    8. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.

    More about this item

    Keywords

    robust mechanism design; dominant strategies; voting; Gibbard-Satterthwaite theorem;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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