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Set-rationalizable choice and self-stability

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  • Brandt, Felix
  • Harrenstein, Paul

Abstract

Rationalizability and similar notions of consistency have proved to be highly problematic in the context of social choice, as witnessed by a range of impossibility results, among which Arrow[modifier letter apostrophe]s is the most prominent. We propose to rationalize choice functions by preference relations over sets of alternatives (set-rationalizability) and introduce two consistency conditions, and , which are defined in analogy to Sen[modifier letter apostrophe]s [alpha] and [gamma]. We find that a choice function satisfies if and only if it is set-rationalizable and that it satisfies and if and only if it is self-stable, a new concept based on earlier work by Dutta. The class of self-stable social choice functions contains a number of appealing Condorcet extensions.

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  • Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1721-1731
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    Cited by:

    1. Josep E., Peris & Begoña, Subiza, 2015. "Rationalizable Choice and Standards of Behavior," QM&ET Working Papers 15-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    2. Yang, Yi-You, 2020. "Rationalizable choice functions," Games and Economic Behavior, Elsevier, vol. 123(C), pages 120-126.
    3. Hans Peters & Panos Protopapas, 2021. "Set and revealed preference axioms for multi-valued choice," Theory and Decision, Springer, vol. 90(1), pages 11-29, February.
    4. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    5. 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.
    6. Koshevoy, Gleb & Savaglio, Ernesto, 2023. "On rational choice from lists of sets," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    7. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    8. 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.
    9. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, arXiv.org.
    10. Chris Dong & Patrick Lederer, 2023. "Characterizations of Sequential Valuation Rules," Papers 2302.11890, arXiv.org.
    11. Felix Brandt & Markus Brill & Felix Fischer & Paul Harrenstein, 2014. "Minimal retentive sets in tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 551-574, March.
    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. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    14. Stefano Vannucci, 2011. "Widwast Choice," Department of Economics University of Siena 629, Department of Economics, University of Siena.

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