Ambiguity Aversion: An Axiomatic Approach Using Second Order Probabilities

This paper presents an axiomatic characterization of preferences which allow ambiguity aversion. It is assumed that decision makers treat risky lotteries and ambiguous lotteries separately, with preferences governed by the von Neumann-Morgenstern axioms for risk and a variant of the Savage axioms for ambiguity. These axioms imply that the decision maker chooses among risks according to expected utility, forms subjective second order probabilities over possible risks, and chooses among ambiguous lotteries according to a modi…ed version of subjective expected utility. Furthermore, the decision maker has two utility functions, one governing attitudes toward risk and one governing attitudes toward ambiguity. Conditions governing ambiguity aversion, comparative ambiguity aversion, and decreasing ambiguity aversion are derived, and are similar to the familiar Arrow-Pratt characterizations for risk aversion.