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A general impossibility result on strategy-proof social choice hyperfunctions

  • Özyurt, Selçuk
  • Sanver, M. Remzi

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
  2. Allan Feldman, 1979. "Nonmanipulable multi-valued social decision functions," Public Choice, Springer, vol. 34(2), pages 177-188, June.
  3. 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.
  4. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
  5. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
  6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  7. 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.
  8. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
  9. 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.
  10. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-46, March.
  11. Barış Kaymak & M. Remzi Sanver, 2003. "Sets of alternatives as Condorcet winners," Social Choice and Welfare, Springer, vol. 20(3), pages 477-494, 06.
  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. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
  14. Selçuk Özyurt & M. Sanver, 2008. "Strategy-proof resolute social choice correspondences," Social Choice and Welfare, Springer, vol. 30(1), pages 89-101, January.
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