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,

Many countries base college admissions on a centrally administered test. Students invest a great deal of resources to improve their performance on the test, and there is growing concern about the high costs associated with these activities. We consider modifying the test by introducing performance-disclosure policies that pool intervals of performance rankings. Pooling affects the equilibrium allocation of students to colleges, which hurts some students and benefits others, but also affects students’ effort. We investigate how such policies can improve students’ welfare in a Pareto sense, study the Pareto frontier of pooling policies, and identify improvements that are robust to the distribution of college seats. We illustrate the potential applicability of our results with an empirical estimation that uses data on college admissions in Turkey. We find that a policy that pools a large fraction of the lowest-performing students leads to a Pareto improvement in a contest based on the estimated parameters. A laboratory experiment based on the estimated parameters generally supports our theoretical predictions.