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Maximal-Element Rationalizability

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  • Walter Bossert
  • Yves Sprumont
  • Kotaro Suzumura

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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. Copyright Springer 2005

Suggested Citation

  • Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Maximal-Element Rationalizability," Theory and Decision, Springer, vol. 58(4), pages 325-350, June.
  • Handle: RePEc:kap:theord:v:58:y:2005:i:4:p:325-350
    DOI: 10.1007/s11238-005-6849-x
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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. 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.
    3. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Consistent Rationalizability," Economica, London School of Economics and Political Science, vol. 72(286), pages 185-200, May.
    4. 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.
    5. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
    6. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    7. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
    8. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
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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. Apesteguia, Jose & Ballester, Miguel A., 2013. "Choice by sequential procedures," Games and Economic Behavior, Elsevier, vol. 77(1), pages 90-99.
    3. 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.
    4. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 03-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. 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).
    7. Miguel Costa-Gomes & Carlos Cueva & Georgios Gerasimou & Matus Tejiscak, 2014. "Choice, Deferral and Consistency," Discussion Paper Series, Department of Economics 201416, Department of Economics, University of St. Andrews, revised 26 Dec 2016.
    8. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques.
    9. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.
    10. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Rational Choice on Arbitrary Domains: A Comprehensive Treatment," Cahiers de recherche 2005-13, Universite de Montreal, Departement de sciences economiques.

    More about this item

    Keywords

    choice functions; maximal-element rationalizability; D11;

    JEL classification:

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

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