Set-rationalizable choice and self-stability
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.
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.
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.
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.:
- Laslier, J.F., 1996.
"Aggregation of Preferences with a Variable set of Alternatives,"
9628, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- Jean-FranÚois Laslier, 2000. "Aggregation of preferences with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 269-282.
- J.-F. Laslier, 1996. "Aggregation of preferences with a variable set of alternatives," THEMA Working Papers 96-28, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Amartya Sen, 1996.
"Maximization and the Act of Choice,"
Harvard Institute of Economic Research Working Papers
1766, Harvard - Institute of Economic Research.
- 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.
- Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 185-192.
- 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.
- Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
- Georges Bordes, 1976. "Consistency, Rationality and Collective Choice," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 451-457.
- Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
- Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
- Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
- 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.
- Bhaskar Dutta & Jean-Francois Laslier, 1999.
"Comparison functions and choice correspondences,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
- Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
- Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
- Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
- Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
- Moulin, Herve, 1985. "From social welfare ordering to acyclic aggregation of preferences," Mathematical Social Sciences, Elsevier, vol. 9(1), pages 1-17, February.
- 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.
- Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
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: (Dana Niculescu)
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.