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A general impossibility result on strategy-proof social choice hyperfunctions

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Author Info

  • Özyurt, Selçuk
  • Sanver, M. Remzi

Abstract

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D[lambda] of lexicographic orderings which exhibits an impossibility of the Gibbard-Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D[lambda]. As most of the standard extension axioms induce superdomains of D[lambda] while social choice correspondences are particular social choice hyperfunctions, we are able to generalize many impossibility results in the literature.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 66 (2009)
Issue (Month): 2 (July)
Pages: 880-892

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Handle: RePEc:eee:gamebe:v:66:y:2009:i:2:p:880-892

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Strategy-proofness Manipulation Gibbard-Satterthwaite theorem Social choice correspondences Hyperfunctions;

References

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  1. Selçuk Özyurt & M. Sanver, 2008. "Strategy-proof resolute social choice correspondences," Social Choice and Welfare, Springer, vol. 30(1), pages 89-101, January.
  2. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  3. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  4. Barış Kaymak & M. Remzi Sanver, 2003. "Sets of alternatives as Condorcet winners," Social Choice and Welfare, Springer, vol. 20(3), pages 477-494, 06.
  5. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
  6. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
  7. Jerry S. Kelly & Donald E. Campbell, 2002. "A leximin characterization of strategy-proof and non-resolute social choice procedures," Economic Theory, Springer, vol. 20(4), pages 809-829.
  8. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
  9. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-46, March.
  10. Allan Feldman, 1979. "Nonmanipulable multi-valued social decision functions," Public Choice, Springer, vol. 34(2), pages 177-188, June.
  11. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
  12. Benoit, Jean-Pierre, 2002. "Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted," Journal of Economic Theory, Elsevier, vol. 102(2), pages 421-436, February.
  13. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
  14. 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.
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Citations

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Cited by:
  1. Shurojit Chatterji & Arunava Sen, 2009. "Tops-Only Domains," Working Papers 06-2009, Singapore Management University, School of Economics.
  2. Fuad Aleskerov & Daniel Karabekyan & M. Sanver & Vyacheslav Yakuba, 2011. "An individual manipulability of positional voting rules," SERIEs, Spanish Economic Association, vol. 2(4), pages 431-446, December.
  3. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer, vol. 39(2), pages 371-398, July.
  4. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
  5. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
  6. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  7. Fuad Aleskerov & Daniel Karabekyan & Remzi Sanver & Vyacheslav Yakuba, 2009. "Evaluating the Degree of Manipulability of Certain Aggregation Procedures under Multiple Choices," Journal of the New Economic Association, New Economic Association, issue 1-2, pages 37-61.
  8. Kutlu, Levent, 2007. "Arrovian aggregation for preferences over sets," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 255-258, May.
  9. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
  10. Sanver, M. Remzi, 2007. "A characterization of superdictatorial domains for strategy-proof social choice functions," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 257-260, December.

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