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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.

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    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/16-2002-cah.pdf
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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;

    References

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    1. Amartya Sen, 1996. "Maximization and the Act of Choice," Harvard Institute of Economic Research Working Papers 1766, Harvard - Institute of Economic Research.
    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. 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.
    4. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    5. 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.
    6. 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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