Stochastic Dominance Under Independent Noise

The notions of first and second-order stochastic dominance play a central role in the economics of information, the analysis of choice under uncertainty, and other fields. The knowledge that two random variables of interest are comparable in terms of stochastic dominance is often an important ingredient in the analysis of economic models and in obtaining unambiguous comparative statics predictions. The purpose of this paper is to study stochastic orders when the distributions under consideration are not taken in isolation, but, as in many cases of interest, are subject to additional, statistically independent noise. The main conclusion of our analysis is that independent noise facilitates the ranking of random variables in terms of stochastic dominance.