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A general impossibility result on strategy-proof social choice hyperfunctions

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  • 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.

Suggested Citation

  • Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:2:p:880-892
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    References listed on IDEAS

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    1. Allan Feldman, 1979. "Nonmanipulable multi-valued social decision functions," Public Choice, Springer, vol. 34(2), pages 177-188, June.
    2. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 569-580.
    3. 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.
    4. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    5. 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.
    6. Barbera, Salvador, 1977. "The Manipulation of Social Choice Mechanisms That Do Not Leave "Too Much" to Chance," Econometrica, Econometric Society, vol. 45(7), pages 1573-1588, October.
    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. Allan Feldman, 1980. "Strongly nonmanipulable multi-valued collective choice rules," Public Choice, Springer, vol. 35(4), pages 503-509, January.
    9. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
    10. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
    11. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
    12. Jerry S. Kelly & Donald E. Campbell, 2002. "A leximin characterization of strategy-proof and non-resolute social choice procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 809-829.
    13. 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.
    14. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    15. Selçuk Özyurt & M. Sanver, 2008. "Strategy-proof resolute social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 89-101, January.
    16. Barış Kaymak & M. Remzi Sanver, 2003. "Sets of alternatives as Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 477-494, June.
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    Cited by:

    1. Laslier, Jean-François & Núñez, Matías & Remzi Sanver, M., 2021. "A solution to the two-person implementation problem," Journal of Economic Theory, Elsevier, vol. 194(C).
    2. 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.
    3. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    4. Carmelo Rodríguez-à lvarez, 2017. "On single-peakedness and strategy-proofness: ties between adjacent alternatives," Economics Bulletin, AccessEcon, vol. 37(3), pages 1966-1974.
    5. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    6. 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).
    7. Shin Sato, 2014. "A fundamental structure of strategy-proof social choice correspondences with restricted preferences over alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 831-851, April.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Kutlu, Levent, 2007. "Arrovian aggregation for preferences over sets," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 255-258, May.
    13. 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.
    14. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.

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