Christian Tarnsey (Oxford): “Exceeding Expectations: Stochastic Dominance as a General Decision Theory”

Abstract: The principle that rational agents should maximize expectations is intuitively plausible with respect to many ordinary cases of decision-making under uncertainty. But it becomes increasingly implausible as we consider cases of more extreme, low-probability risk (like Pascal’s Mugging), and intolerably paradoxical in cases like the St. Petersburg Lottery and the Pasadena Game. In this paper I show that, under certain assumptions, stochastic dominance reasoning can capture many of the plausible implications of expectational reasoning while avoiding its implausible implications. More specifically, when an agent starts from a condition of background uncertainty about the choiceworthiness of her options representable by a probability distribution over possible degrees of choiceworthiness with exponential or heavier tails and a sufficiently large scale parameter, many expectation-maximizing gambles that would not stochastically dominate their alternatives “in a vacuum” turn out to do so in virtue of this background uncertainty. Nonetheless, even under these conditions, stochastic dominance will generally not require agents to accept extreme gambles like Pascal’s Mugging or the St. Petersburg Lottery. I argue that the sort of background uncertainty on which these results depend is appropriate for any agent who assigns normative weight to aggregative consequentialist considerations, i.e., who measures the choiceworthiness of an option 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.