Allais, Ellsberg, and preferences for hedging

Abstract

Two of the most well-known regularities of preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behavior of an agent who can display both tendencies at the same time. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts, and captures both aversion to ambiguity and attraction towards certainty in objective lotteries. We show that this axiom, together with other standard axioms, is equivalent to two representations that generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both representations the agent evaluates ambiguity using multiple priors, but does not use Expected Utility to evaluate objective lotteries. In the rst representation, lotteries are evaluated by distorting probabilities as in the Rank Dependent Utility model, but using the worst from a set of such distortions. In the second, equivalent, representation the agent treats objective lotteries as ‘ambiguous objects,’ and uses a set of priors to evaluate them. We show that a preference for hedging is not sucient to guarantee an Ellsberg-like behavior if the agent violates Expected