Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences

Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji (2005)) describe a decision maker who evaluates each act f according to the twofold expectation V(f)=integral P phi(integral omega u(f)dp)d mu(p) defined by a utility function u, an ambiguity index phi, and a belief mu over a set P of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over Anscombe-Aumann acts. We study a special case where P is a subjective statistical model that is point identified, that is, the decision maker believes that the true law p is an element of P can be recovered empirically. Our main axiom is a joint weakening of Savage's sure-thing principle and Anscombe-Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, a hallmark feature of the smooth ambiguity representation.