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Set-rationalizable choice and self-stability

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  • Brandt, Felix
  • Harrenstein, Paul
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 146 (2011)
    Issue (Month): 4 (July)
    Pages: 1721-1731

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    Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1721-1731

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    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

    Keywords: Choice theory Rationalizability Consistency Stable sets Social choice theory;

    References

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    1. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    2. Sen, A., 1996. "Maximisation and the Act of Choice," Papers 270, Banca Italia - Servizio di Studi.
    3. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
    4. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    5. Bordes, Georges, 1976. "Consistency, Rationality and Collective Choice," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 451-57, October.
    6. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
    7. Laslier, J.F., 1996. "Aggregation of Preferences with a Variable set of Alternatives," Papers 9628, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    8. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
    9. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    10. Bordes, Georges, 1983. "On the possibility of reasonable consistent majoritarian choice: Some positive results," Journal of Economic Theory, Elsevier, vol. 31(1), pages 122-132, October.
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    12. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-79, May.
    13. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    14. B. Dutta & J-F. Laslier, 1998. "Comparison functions and choice correspondences," THEMA Working Papers 98-12, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    15. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
    16. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    17. Mas-Colell, Andreu & Sonnenschein, Hugo, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Wiley Blackwell, vol. 39(2), pages 185-92, April.
    18. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
    19. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
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    Cited by:
    1. Felix Brandt & Markus Brill & Felix Fischer & Paul Harrenstein, 2014. "Minimal retentive sets in tournaments," Social Choice and Welfare, Springer, vol. 42(3), pages 551-574, March.

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