Advanced Search
MyIDEAS: Login

Set-rationalizable choice and self-stability

Contents:

Author Info

  • Brandt, Felix
  • Harrenstein, Paul
Registered author(s):

    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.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000251
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

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

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

    as in new window
    Handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1721-1731

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/inca/622869

    Related research

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

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Jean-FranÚois Laslier, 2000. "Aggregation of preferences with a variable set of alternatives," Social Choice and Welfare, Springer, vol. 17(2), pages 269-282.
    2. Amartya Sen, 1996. "Maximization and the Act of Choice," Harvard Institute of Economic Research Working Papers 1766, Harvard - Institute of Economic Research.
    3. Bordes, Georges, 1976. "Consistency, Rationality and Collective Choice," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 451-57, October.
    4. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-79, May.
    5. Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
    6. 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.
    7. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    8. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    9. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    10. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
    11. 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.
    12. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    13. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    14. 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.
    15. 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.
    16. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    17. 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.
    18. 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.
    19. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:146:y:2011:i:4:p:1721-1731. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.