Exceeding expectations: stochastic dominance as a general decision theory
Christian Tarsney (Global Priorities Institute, Oxford University)
GPI Working Paper No. 3-2020
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.
Other working papers
The scope of longtermism – David Thorstad (Global Priorities Institute, University of Oxford)
Longtermism holds roughly that in many decision situations, the best thing we can do is what is best for the long-term future. The scope question for longtermism asks: how large is the class of decision situations for which longtermism holds? Although longtermism was initially developed to describe the situation of…
A bargaining-theoretic approach to moral uncertainty – Owen Cotton-Barratt (Future of Humanity Institute, Oxford University), Hilary Greaves (Global Priorities Institute, Oxford University)
This paper explores a new approach to the problem of decision under relevant moral uncertainty. We treat the case of an agent making decisions in the face of moral uncertainty on the model of bargaining theory, as if the decision-making process were one of bargaining among different internal parts of the agent, with different parts committed to different moral theories. The resulting approach contrasts interestingly with the extant “maximise expected choiceworthiness”…
The unexpected value of the future – Hayden Wilkinson (Global Priorities Institute, University of Oxford)
Various philosophers accept moral views that are impartial, additive, and risk-neutral with respect to betterness. But, if that risk neutrality is spelt out according to expected value theory alone, such views face a dire reductio ad absurdum. If the expected sum of value in humanity’s future is undefined—if, e.g., the probability distribution over possible values of the future resembles the Pasadena game, or a Cauchy distribution—then those views say that no real-world option is ever better than any other. And, as I argue…