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Robust mechanism design and dominant strategy voting rules

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  • ,

    (Department of Economics, University of Michigan)

  • Smith, Doug

    (Federal Trade Commission)

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.

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  • , & Smith, Doug, 2014. "Robust mechanism design and dominant strategy voting rules," Theoretical Economics, Econometric Society, vol. 9(2), May.
    • Handle: RePEc:the:publsh:1111
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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. 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.
    3. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    4. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. 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..
    9. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    11. Zeckhauser, Richard, 1973. "Voting Systems, Honest Preferences and Pareto Optimality," American Political Science Review, Cambridge University Press, vol. 67(3), pages 934-946, September.
    12. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    13. 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.
    14. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    15. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    16. Yamashita, Takuro, 2014. "Implementation in Weakly Undominated Strategies, with Applications to Auctions and Bilateral Trade," TSE Working Papers 14-513, Toulouse School of Economics (TSE).
    17. 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.
    18. 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).
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    20. 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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    Cited by:

    1. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    2. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    3. Martin Hellwig, 2015. "Financial Stability and Monetary Policy," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_10, Max Planck Institute for Research on Collective Goods.
    4. Martin F. Hellwig, 2021. "Public-Good Provision with Macro Uncertainty about Preferences: Efficiency, Budget Balance, and Robustness," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2021_19, Max Planck Institute for Research on Collective Goods.
    5. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    6. Saori CHIBA, 2018. "Hidden Profiles and Persuasion Cascades in Group Decision-Making," Discussion papers e-18-001, Graduate School of Economics , Kyoto University.
    7. 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.
    8. Tilman Börgers, 2017. "(No) Foundations of dominant-strategy mechanisms: a comment on Chung and Ely (2007)," Review of Economic Design, Springer;Society for Economic Design, vol. 21(2), pages 73-82, June.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    10. Yasunori Okumura, 2019. "What proportion of sincere voters guarantees efficiency?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 299-311, August.
    11. Mukherjee, Saptarshi & Muto, Nozomu & Sen, Arunava, 2024. "Implementation in undominated strategies with applications to auction design, public good provision and matching," Journal of Economic Theory, Elsevier, vol. 216(C).
    12. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    13. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.

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    More about this item

    Keywords

    Robust mechanism design; Gibbard-Satterthwaite theorem;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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