  The principle that rational agents should maximize expected utility or
choiceworthiness is intuitively plausible in many ordinary cases of
decision-making under uncertainty. But it is less plausible in cases of
extreme, low-probability risk (like Pascal's Mugging), and intolerably
paradoxical in cases like the St. Petersburg and Pasadena games. In this paper
I show that, under certain conditions, stochastic dominance reasoning can
capture most of the plausible implications of expectational reasoning while
avoiding most of its pitfalls. Specifically, given sufficient background
uncertainty about the choiceworthiness of one's options, many
expectation-maximizing gambles that do not stochastically dominate their
alternatives "in a vacuum" become stochastically dominant in virtue of that
background uncertainty. But, even under these conditions, stochastic dominance
will not require agents to accept options whose expectational superiority
depends on sufficiently small probabilities of extreme payoffs. The sort of
background uncertainty on which these results depend looks unavoidable for any
agent who measures the choiceworthiness of her options in part by the total
amount of value in the resulting world. At least for such agents, then,
stochastic dominance offers a plausible general principle of choice under
uncertainty that can explain more of the apparent rational constraints on such
choices than has previously been recognized.
