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Maximal-Element Rationalizability

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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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Authors and Affiliations

  1. Département de Sciences Economiques and CIREQ, Université de Montréal, H3C 3J7, succursale Centre-ville, Montréal, QC, C.P. 6128, Canada

    Walter Bossert & Yves Sprumont

  2. Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo, 186-8603, Japan

    Kotaro Suzumura

Authors
  1. Walter Bossert
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  2. Yves Sprumont
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  3. Kotaro Suzumura
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Corresponding author

Correspondence to Kotaro Suzumura.

Additional information

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 from the Ministry of Education, Culture, Sports, Science and Technology of Japan is gratefully acknowledged. Thanks are also due to the editor and the two referees for the opportunity to improve the exposition of this paper.

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Bossert, W., Sprumont, Y. & Suzumura, K. Maximal-Element Rationalizability. Theor Decis 58, 325–350 (2005). https://doi.org/10.1007/s11238-005-6849-x

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  • DOI: https://doi.org/10.1007/s11238-005-6849-x

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