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
On the desire to make a difference – Hilary Greaves, William MacAskill, Andreas Mogensen and Teruji Thomas (Global Priorities Institute, University of Oxford)
True benevolence is, most fundamentally, a desire that the world be better. It is natural and common, however, to frame thinking about benevolence indirectly, in terms of a desire to make a difference to how good the world is. This would be an innocuous shift if desires to make a difference were extensionally equivalent to desires that the world be better. This paper shows that at least on some common ways of making a “desire to make a difference” precise, this extensional equivalence fails.
Dynamic public good provision under time preference heterogeneity – Philip Trammell (Global Priorities Institute and Department of Economics, University of Oxford)
I explore the implications of time preference heterogeneity for the private funding of public goods. The assumption that players use a common discount rate is knife-edge: relaxing it yields substantially different equilibria, for two reasons. First, time preference heterogeneity motivates intertemporal polarization, analogous to the polarization seen in a static public good game. In the simplest settings, more patient players spend nothing early in time and less patient players spending nothing later. Second…
Minimal and Expansive Longtermism – Hilary Greaves (University of Oxford) and Christian Tarsney (Population Wellbeing Initiative, University of Texas at Austin)
The standard case for longtermism focuses on a small set of risks to the far future, and argues that in a small set of choice situations, the present marginal value of mitigating those risks is very great. But many longtermists are attracted to, and many critics of longtermism worried by, a farther-reaching form of longtermism. According to this farther-reaching form, there are many ways of improving the far future, which determine the value of our options in all or nearly all choice situations…