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.
See also the post/sequence by Daniel Kokotajlo, “Tiny Probabilities of Vast Utilities”. I’m linking to the post that was most valuable to me, but by default it might make sense to start with the first one in the sequence. ^^
Thanks—that last link was one I’d come across and liked when looking for previous coverage. My sole previous blog post was about Pascal’s Wager. I’d found though when speaking about it that I was assuming too much for some of the audience I wanted to bring along; notwithstanding my sloppy writing :D So, I’m going to attempt to stay focused and incremental.
I’ve found Christian Tarsney’s “Exceeding Expectations” insightful when it comes to recognizing and maybe coping with the limits of expected value.
See also the post/sequence by Daniel Kokotajlo, “Tiny Probabilities of Vast Utilities”. I’m linking to the post that was most valuable to me, but by default it might make sense to start with the first one in the sequence. ^^
Thanks—that last link was one I’d come across and liked when looking for previous coverage. My sole previous blog post was about Pascal’s Wager. I’d found though when speaking about it that I was assuming too much for some of the audience I wanted to bring along; notwithstanding my sloppy writing :D So, I’m going to attempt to stay focused and incremental.