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Maximal-Element Rationalizability

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  • BOSSERT, Walter
  • SPRUMONT, Yves
  • SUZUMURA, Kotaro

Abstract

We examine the maximal-element rationalizability of choice functions with arbitrary do-mains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier litera-ture, 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 rationaliz-ability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as re exivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.

Suggested Citation

  • BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Maximal-Element Rationalizability," Cahiers de recherche 2002-16, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2002-16
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    File URL: http://hdl.handle.net/1866/487
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    References listed on IDEAS

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    1. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
    2. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
    3. 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.
    4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro & 鈴村, 興太郎, 2002. "Consistent Rationalizability," Discussion Paper 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    5. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    6. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    7. 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.
    8. repec:bla:econom:v:43:y:1976:i:172:p:381-90 is not listed on IDEAS
    9. Unknown, 2001. "General Discussion," Proceedings of the 6th Agricultural and Food Policy Systems Information Workshop, 2000: Trade Liberalization Under NAFTA: Report Card on Agriculture 16839, Farm Foundation, Agricultural and Food Policy Systems Information Workshops.
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    Citations

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    Cited by:

    1. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    2. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    3. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Apesteguia, Jose & Ballester, Miguel A., 2013. "Choice by sequential procedures," Games and Economic Behavior, Elsevier, vol. 77(1), pages 90-99.
    5. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," SIRE Discussion Papers 2015-17, Scottish Institute for Research in Economics (SIRE).
    6. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques.
    7. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques.
    8. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Rational Choice on Arbitrary Domains: A Comprehensive Treatment," Cahiers de recherche 17-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-17, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.
    11. Georgios Gerasimou, 2016. "Partially dominant choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 127-145, January.

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    More about this item

    Keywords

    Choice Functions; Maximal-Element Rationalizability.;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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