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Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized

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  • John Duggan
  • Thomas Schwartz

Abstract

The Gibbard-Satterthwaite Theorem on the manipulability of social-choice rules assumes resoluteness: there are no ties, no multi-member choice sets. Generalizations based on a familiar lottery idea allow ties but assume perfectly shared probabilistic beliefs about their resolution. We prove a more straightforward generalization that assumes almost no limit on ties or beliefs about them.

Suggested Citation

  • John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(1), pages 85-93.
  • Handle: RePEc:spr:sochwe:v:17:y:2000:i:1:p:85-93
    Note: Received: 15 December 1997/Accepted: 16 November 1998
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    Cited by:

    1. Weber, Tjark, 2009. "Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem," MPRA Paper 17836, University Library of Munich, Germany.
    2. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 127-141, January.
    4. Thomas Schwartz, 2011. "Social choice and individual values in the electronic republic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 621-632, October.
    5. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    6. Yasuhito Tanaka, 2001. "Generalized monotonicity and strategy-proofness for non-resolute social choice correspondences," Economics Bulletin, AccessEcon, vol. 4(12), pages 1-8.
    7. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 39-59, June.
    8. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    9. Burak Can & Bora Erdamar & M. Sanver, 2009. "Expected Utility Consistent Extensions of Preferences," Theory and Decision, Springer, vol. 67(2), pages 123-144, August.
    10. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
    11. Fuad Aleskerov & Daniel Karabekyan & M. Sanver & Vyacheslav Yakuba, 2011. "An individual manipulability of positional voting rules," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 431-446, December.

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