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Robust mechanism design and dominant strategy voting rules

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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.

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File URL: https://mpra.ub.uni-muenchen.de/37027/1/MPRA_paper_37027.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37027.

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Date of creation: 03 Nov 2011
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Handle: RePEc:pra:mprapa:37027
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Keywords: robust mechanism design; dominant strategies; voting; Gibbard-Satterthwaite theorem;

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Find related papers by JEL classification:
  • D7 - Microeconomics - - Analysis of Collective Decision-Making
  • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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  1. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
  3. Bengt Holmstrom & Roger B. Myerson, 1981. "Efficient and Durable Decision Rules with Incomplete Information," Discussion Papers 495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. Jeff Ely, 2003. "Foundations of Dominant Strategy Mechanisms," Theory workshop papers 658612000000000064, UCLA Department of Economics.
  6. Stephen Morris & Dirk Bergemann, 2004. "Robust Mechanism Design," Yale School of Management Working Papers ysm380, Yale School of Management.
  7. 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.
  8. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
  9. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
  10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  11. 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).
  12. Blin, Jean-Marie & Satterthwaite, Mark A, 1977. "On Preferences, Beliefs, and Manipulation within Voting Situations," Econometrica, Econometric Society, vol. 45(4), pages 881-88, May.
  13. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-29, 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. Martin Hellwig, 2015. "Financial Stability and Monetary Policy," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2015_10, Max Planck Institute for Research on Collective Goods.
  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. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
  5. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.
  6. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
  7. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.

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