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Maximal-Element Rationalizability

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  • Walter BOSSERT
  • Yves SPRUMONT
  • Kotaro SUZUMURA

Abstract

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 16-2002.

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Length: 19 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:mtl:montec:16-2002

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Keywords: choice functions; maximal-element rationalizability;

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References

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  1. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
  2. Sen, A., 1996. "Maximisation and the Act of Choice," Papers 270, Banca Italia - Servizio di Studi.
  3. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
  4. 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.
  5. 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.
  6. Schwartz, Thomas, 1976. "Choice functions, "rationality" conditions, and variations on the weak axiom of revealed preference," Journal of Economic Theory, Elsevier, vol. 13(3), pages 414-427, December.
  7. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Consistent Rationalizability," Cahiers de recherche 2002-12, Universite de Montreal, Departement de sciences economiques.
  8. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
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Cited by:
  1. Apesteguia, Jose & Ballester, Miguel A., 2013. "Choice by sequential procedures," Games and Economic Behavior, Elsevier, vol. 77(1), pages 90-99.
  2. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 2005-21, Universite de Montreal, Departement de sciences economiques.
  3. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.

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