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Robust mechanism design and dominant strategy voting rules

  • Borgers, Tilman
  • Smith, Doug

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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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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  1. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  2. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-29, May.
  5. 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.
  6. Tilman Börgers & Peter Postl, 2008. "Efficient Compromising," Discussion Papers 06-11R, Department of Economics, University of Birmingham.
  7. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Jeffrey C. Ely & Kim-Sau Chung, 2004. "Foundations of Dominant Strategy Mechanisms," Econometric Society 2004 North American Summer Meetings 169, Econometric Society.
  9. 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.
  10. 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.
  11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  12. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
  13. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
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