Rational Preference and Rationalizable Choice

We study a decision maker characterized by two binary relations. The first reflects his judgments about well-being, his mental preferences. The second describes the decision maker's choice behavior, his behavioral preferences, the ones that govern choice (see Rubin- stein and Salant, 2008a,b). Specififically, in the context of decision making under uncertainty, we propose axioms that may describe the rationality of these two relations. These axioms allow a joint representation by a single set of probabilities and a single utility function. It is mentally rational to prefer f over g if and only if the expected utility of f is at least as high as that of g for all probabilities in the set. It is behaviorally rationalizable to choose f over g if and only if the expected utility of f is at least as high as that of g for some probability in the set. In other words, mental and behavioral preferences admit, respectively, a representation a la Bewley (2002) and a la Lehrer and Teper (2011). Our results also provide foundation for a decision analysis procedure called robust ordinal regression and proposed by Greco, Mousseau, and Slowinski (2008).