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Stochastic dominance is a crucial tool for the analysis of choice under risk.It is typically analyzed as a property of two gambles that are taken inisolation. We study how additional independent sources of risk (e.g.uninsurable labor risk, house price risk, etc.) can affect the ordering ofgambles. We show that, perhaps surprisingly, background risk can be strongenough to render lotteries that are ranked by their expectation ranked in termsof first-order stochastic dominance. We extend our results to second orderstochastic dominance, and show how they lead to a novel, and elementary,axiomatization of mean-variance preferences.

Stochastic Dominance Under Independent Noise