Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal-element rationalizability. All but one notion of consistent rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.
|Date of creation:||Apr 2002|
|Date of revision:|
|Note:||June 2002, Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche of Québec, and a Grant-in-Aid for Scientific Research for Priority Areas (B) Number 603 from the Ministry of Education, Science and Culture of Japan is gratefully acknowledged.|
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- Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2001.
"Rationalizability of Choice Functions on General Domains Without Full Transitivity,"
28, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
- Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2006. "Rationalizability of choice functions on general domains without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 435-458, December.
- Bossert, W. & Sprumont, Y. & Suzumura, K., 2001. "Rationalizability of Choice Functions on General Domains without Full Transitivity," Cahiers de recherche 2001-13, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2001. "Rationalizability of Choice Functions on General Domains without Full Transitivity," Cahiers de recherche 2001-13, Universite de Montreal, Departement de sciences economiques.
- Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 149-158.
- Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
- Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
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