  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 in
isolation. We study how additional independent sources of risk (e.g.
uninsurable labor risk, house price risk, etc.) can affect the ordering of
gambles. We show that, perhaps surprisingly, background risk can be strong
enough to render lotteries that are ranked by their expectation ranked in terms
of first-order stochastic dominance. We extend our results to second order
stochastic dominance, and show how they lead to a novel, and elementary,
axiomatization of mean-variance preferences.
