Preferences over Sets of Lotteries

The 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 objective 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. ∗I am grateful to Walter Bossert and Peter Klibanoff for their remarks and suggestions regarding related literature. The paper has been presented at Northwestern University, Princeton University, the University of Minnesota, the Canadian Economic Theory Conference in 2003, the ASSA Summer Meeting in 2003, and the Economic Theory Conference Rhodes 2003. I am grateful to the workshop and conference participants, especially Eddie Dekel and Marciano Siniscalchi, for their comments. Finally, I would like to thank the editor and two referees for valuable suggestions.