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
Evolutionary debunking and value alignment – Michael T. Dale (Hampden-Sydney College) and Bradford Saad (Global Priorities Institute, University of Oxford)
This paper examines the bearing of evolutionary debunking arguments—which use the evolutionary origins of values to challenge their epistemic credentials—on the alignment problem, i.e. the problem of ensuring that highly capable AI systems are properly aligned with values. Since evolutionary debunking arguments are among the best empirically-motivated arguments that recommend changes in values, it is unsurprising that they are relevant to the alignment problem. However, how evolutionary debunking arguments…
The Shutdown Problem: An AI Engineering Puzzle for Decision Theorists – Elliott Thornley (Global Priorities Institute, University of Oxford)
I explain and motivate the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems suggest that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do so. I end by noting that…
Misjudgment Exacerbates Collective Action Problems – Joshua Lewis (New York University) et al.
In collective action problems, suboptimal collective outcomes arise from each individual optimizing their own wellbeing. Past work assumes individuals do this because they care more about themselves than others. Yet, other factors could also contribute. We examine the role of empirical beliefs. Our results suggest people underestimate individual impact on collective problems. When collective action seems worthwhile, individual action often does not, even if the expected ratio of costs to benefits is the same. …