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, quasitransitivity, consistency and transitivity.
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|Note:||Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide la Recherche of Qu饕ec, and a Grant-in-Aid for Scientific Research for Priority Areas Number 603 from the Ministry of Education, Science and Culture of Japan is gratefully acknowledged.|
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