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
In Defence of Moderation – Jacob Barrett (Vanderbilt University)
A decision theory is fanatical if it says that, for any sure thing of getting some finite amount of value, it would always be better to almost certainly get nothing while having some tiny probability (no matter how small) of getting sufficiently more finite value. Fanaticism is extremely counterintuitive; common sense requires a more moderate view. However, a recent slew of arguments purport to vindicate it, claiming that moderate alternatives to fanaticism are sometimes similarly counterintuitive, face a powerful continuum argument…
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…
Numbers Tell, Words Sell – Michael Thaler (University College London), Mattie Toma (University of Warwick) and Victor Yaneng Wang (Massachusetts Institute of Technology)
When communicating numeric estimates with policymakers, journalists, or the general public, experts must choose between using numbers or natural language. We run two experiments to study whether experts strategically use language to communicate numeric estimates in order to persuade receivers. In Study 1, senders communicate probabilities of abstract events to receivers on Prolific, and in Study 2 academic researchers communicate the effect sizes in research papers to government policymakers. When…