Axioms for Minimax Regret Choice Correspondences Jörg Stoye ∗ New York University October 8, 2008 Abstract This paper unifies and extends the recent axiomatic literature on minimax regret. It compares several models of minimax regret, shows how to characterize the according choice correspondences in a unified setting, extends them to choice from convex sets, connects them by defining a behavioral notion of perceived ambiguity, and provides an axiomatization of Hannan regret. Substantively, a main idea is to behaviorally identify ambiguity with failures of independence of irrelevant alter- natives. Regarding proof technique, the core contribution is to uncover a dualism between choice correspondences and preferences in an environment where this dualism is not obvious. This insight can be used to generate results by importing findings from the existing literature on preference orderings. Keywords: Minimax regret, Hannan regret, ambiguity, multiple priors, choice correspon- dences. JEL classification codes: C44, D81. ∗ I thank Efe Ok, Karl Schlag, an associate editor, two extremely helpful referees, and audiences in Bonn (Max Planck Institute for Research on Collective Goods), Budapest (ESEM 2007), and Nashville (Public Economic Theory 2007) for helpful comments. Of course, any errors are mine. Address: Jörg Stoye, Department of Economics, New York University, 19 W. 4th Street, New York, NY 10012, j.stoye@nyu.edu. 1