Ulric B. and Evelyn L. Bray Social Sciences Seminar
Abstract: We show that the presence of statistically independent noise facilitates the ranking of gambles in terms of stochastic dominance. In particular, we address the following question: Given two random variables, X and Y, under what conditions is it possible to find a random variable Z, independent from X and Y, so that X + Z first-order stochastically dominates Y + Z? We show that such a Z exists whenever X has higher expectation than Y. In addition, if X and Y have equal mean, but the first has lower variance, then Z can be chosen so that X + Z dominates Y + Z in terms of second-order stochastic dominance. We present applications to choice under risk, the axiomatization of mean-variance preferences, and mechanism design with risk averse agents.
Joint work with Philipp Strack and Omer Tamuz.