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Characterizing the top cycle via strategyproofness

Author

Listed:
  • Brandt, Felix

    (Department of Computer Science, Technische Universität München)

  • Lederer, Patrick

    (Computer Science Department, Technische Universität München)

Abstract
Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In this paper, we consider set-valued social choice correspondences (SCCs) that are strategyproof according to Fishburn's preference extension and, in particular, the top cycle, an attractive SCC that returns the maximal elements of the transitive closure of the weak majority relation. Our main theorem shows that, under mild conditions, the top cycle is the only non-imposing strategyproof SCC whose outcome only depends on the quantified pairwise comparisons between alternatives. This result effectively turns the Gibbard-Satterthwaite impossibility into a complete characterization of the top cycle by moving from SCFs to SCCs. We also leverage key ideas of the proof of this statement to obtain a more general characterization of strategyproof SCCs.

Suggested Citation

  • Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    • Handle: RePEc:the:publsh:5120
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    References listed on IDEAS

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    1. 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.
    2. Miller, Nicholas R & Grofman, Bernard & Feld, Scott L, 1990. "The Structure of the Banks Set," Public Choice, Springer, vol. 66(3), pages 243-251, September.
    3. 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.
    4. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    5. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    6. 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.
    7. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    8. Ehlers, Lars & Sprumont, Yves, 2008. "Weakened WARP and top-cycle choice rules," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 87-94, January.
    9. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    10. 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).
    11. Feldman, Allan, 1979. "Manipulation and the Pareto rule," Journal of Economic Theory, Elsevier, vol. 21(3), pages 473-482, December.
    12. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
    13. Nicolas Houy, 2011. "Common characterizations of the untrapped set and the top cycle," Theory and Decision, Springer, vol. 70(4), pages 501-509, April.
    14. MacIntyre, I. & Pattanaik, Prasanta K., 1981. "Strategic voting under minimally binary group decision functions," Journal of Economic Theory, Elsevier, vol. 25(3), pages 338-352, December.
    15. Georges Bordes, 1976. "Consistency, Rationality and Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 451-457.
    16. Ehlers, Lars & Majumdar, Dipjyoti & Mishra, Debasis & Sen, Arunava, 2020. "Continuity and incentive compatibility in cardinal mechanisms," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 31-41.
    17. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    18. Shasikanta Nandeibam, 2013. "The structure of decision schemes with cardinal preferences," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 205-238, September.
    19. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    20. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
    21. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 557-568, October.
    22. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    23. Felix Brandt & Hans Georg Seedig, 2016. "On the Discriminative Power of Tournament Solutions," Operations Research Proceedings, in: Marco Lübbecke & Arie Koster & Peter Letmathe & Reinhard Madlener & Britta Peis & Grit Walther (ed.), Operations Research Proceedings 2014, edition 1, pages 53-58, Springer.
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    Cited by:

    1. 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).
    2. Brandt, Felix & Lederer, Patrick & Suksompong, Warut, 2023. "Incentives in social decision schemes with pairwise comparison preferences," Games and Economic Behavior, Elsevier, vol. 142(C), pages 266-291.

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    More about this item

    Keywords

    Top cycle; strategyproofness; Condorcet; preference extension;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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