Maximal-Element Rationalizability

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.