c © 2007 The Review of Economic Studies Limited Preferences Over Sets of Lotteries1

This paper studies a model in which in period 1, a decision-maker chooses a set of lotteries and in period 2, Nature chooses a lottery from the set chosen by the decision-maker and the decision-maker consumes the lottery chosen by Nature. Larger sets are interpreted as representing more ambiguous ob-jective information about the lottery that will be consumed. The axioms imposed on preferences over sets of lotteries generalize those often imposed on preferences over single lotteries in the existing literature. A decision-maker who satisfies these axioms evaluates sets of lotteries according to a weighted average of the expected utilities of the best and the worst lottery in a set, with the weights interpreted as a measure of (comparative) attitude to objective ambiguity. 1