Allais, Ellsberg, and preferences for hedging

Two of the most well known regularities observed in preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behav- ior of an agent who can display both tendencies simultaneously. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts. We show that this axiom, together with other standard ones, is equivalent to a representation in which the agent (i) evaluates ambiguity using multiple priors, as in the model of Gilboa and Schmeidler (1989), and (ii) evalu- ates objective lotteries by distorting probabilities, as in the rank dependent utility model, but using the worst from a set of distortions. We show that a preference for hedging is not suf?cient to guarantee Ellsberg-like behavior if the agent violates expected utility for objective lotteries; we provide a novel axiom that characterizes this case, linking the distortions for objective and subjective bets.