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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.

Suggested Citation

  • , & 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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    13. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    14. 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..
    15. 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).
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    Cited by:

    1. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-329, May.
    2. Jobst Heitzig & Forest W. Simmons & Sara M. Constantino, 2025. "Fair group decisions via non-deterministic proportional consensus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(1), pages 345-371, February.
    3. Martin Hellwig, 2015. "Financial Stability and Monetary Policy," Discussion Paper Series of the Max Planck Institute for Behavioral Economics 2015_10, Max Planck Institute for Behavioral Economics.
    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 Behavioral Economics 2021_19, Max Planck Institute for Behavioral Economics.
    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 Behavioral Economics 2015_12, Max Planck Institute for Behavioral Economics.
    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. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    14. 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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    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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