I present a new puzzle about choice under uncertainty for agents whose preferences are sensitive to multiple dimensions of outcomes in such a way as to be incomplete. In response, I develop a new theory of choice under uncertainty for incomplete preferences. I connect the puzzle to central questions in epistemology about the nature of rational requirements, and ask whether it shows that preferences are rationally required to be complete.

Longtermists claim that what we ought to do is mainly determined by how our actions might affect the very long-run future. A natural objection to longtermism is that these effects may be nearly impossible to predict — perhaps so close to impossible that, despite the astronomical importance of the far future, the expected value of our present actions is mainly determined by near-term considerations. This paper aims to precisify and evaluate one version of this epistemic objection to longtermism. To that (...) end, I develop two simple models for comparing ‘longtermist’ and ‘neartermist’ interventions, incorporating the idea that it is harder to make a predictable difference to the further future. These models yield mixed conclusions: if we simply aim to maximize expected value, and don’t mind premising our choices on minuscule probabilities of astronomical payoffs, the case for longtermism looks robust. But on some prima facie plausible empirical worldviews, the expectational superiority of longtermist interventions depends heavily on these ‘Pascalian’ probabilities. So the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories (...) of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (shrink)

Longtermists claim that what we ought to do is mainly determined by how our actions might affect the very long-run future. A natural objection to longtermism is that these effects may be nearly impossible to predict -- perhaps so close to impossible that, despite the astronomical importance of the far future, the expected value of our present actions is mainly determined by near-term considerations. This paper aims to precisify and evaluate one version of this epistemic objection to longtermism. To that (...) end, I develop two simple models for comparing "longtermist" and "neartermist" interventions, incorporating the idea that it is harder to make a predictable difference to the further future. These models yield mixed conclusions: if we simply aim to maximize expected value, and don't mind premising our choices on minuscule probabilities of astronomical payoffs, the case for longtermism looks robust. But on some prima facie plausible empirical worldviews, the expectational superiority of longtermist interventions depends heavily on these "Pascalian" probabilities. So the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism. (shrink)

Various decision theories share a troubling implication. They imply that, for any finite amount of value, it would be better to wager it all for a vanishingly small probability of some greater value. Counterintuitive as it might be, this _fanaticism_ has seemingly compelling independent arguments in its favour. In this paper, I consider perhaps the most _prima facie_ compelling such argument: an _Egyptology argument_ (an analogue of the Egyptology argument from population ethics). I show that, despite recent objections from Russell (...) (Noûs, 2023) and Goodsell (Analysis 81(3):420–426, 2021), the argument’s premises can be justified and defended, and the argument itself remains compelling. (shrink)