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Set-monotonicity implies Kelly-strategyproofness

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  • Felix Brandt

Abstract

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly’s preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity—a new variant of Maskin-monotonicity—implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions—such as the top cycle, the minimal covering set, and the bipartisan set—that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barberà (J Econ Theory 15(2):266–278( 1977a )) and Kelly (Econometrica 45(2):439–446 ( 1977 )). Copyright Springer-Verlag Berlin Heidelberg 2015

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  • 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.
  • Handle: RePEc:spr:sochwe:v:45:y:2015:i:4:p:793-804
    DOI: 10.1007/s00355-015-0881-8
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    Cited by:

    1. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    2. Matías Núñez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 421-441, February.
    3. Brandt, Felix & Geist, Christian & Peters, Dominik, 2017. "Optimal bounds for the no-show paradox via SAT solving," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 18-27.
    4. Hayrullah Dindar & Jean Lainé, 2023. "Vote swapping in irresolute two-tier voting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 221-262, August.
    5. Brandt, Felix & Lederer, Patrick, 2023. "Characterizing the top cycle via strategyproofness," Theoretical Economics, Econometric Society, vol. 18(2), May.
    6. 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).
    7. Demeze-Jouatsa, Ghislain-Herman, 2022. "Ambiguous Social Choice Functions," Center for Mathematical Economics Working Papers 660, Center for Mathematical Economics, Bielefeld University.
    8. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    9. Felix Brandt & Markus Brill & Paul Harrenstein, 2018. "Extending tournament solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 193-222, August.
    10. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    11. Matias Nunez & M. Remzi Sanver, 2021. "On the subgame perfect implementability of voting rules," Post-Print hal-03341697, HAL.
    12. 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.
    13. Felix Brandt & Martin Bullinger & Patrick Lederer, 2021. "On the Indecisiveness of Kelly-Strategyproof Social Choice Functions," Papers 2102.00499, arXiv.org, revised Mar 2022.
    14. Florian Brandl & Felix Brandt & Christian Stricker, 2022. "An analytical and experimental comparison of maximal lottery schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 5-38, January.
    15. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    16. Felix Brandt & Patrick Lederer, 2021. "Characterizing the Top Cycle via Strategyproofness," Papers 2108.04622, arXiv.org, revised Jun 2023.
    17. Nhan-Tam Nguyen & Dorothea Baumeister & Jörg Rothe, 2018. "Strategy-proofness of scoring allocation correspondences for indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 101-122, January.
    18. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, arXiv.org.

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    Keywords

    D71; C70;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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