Kenny Easwaran, Texas A&M University
"Infinite Ethics Meets Decision Theory"
Some classic forms of utilitarianism presume that the goodness of a state of affairs can be determined by adding up numerical representations of the welfare of each of the people. When a population is infinite, however, this doesn't yield useful results. But there have been suggestions for how to say when such states of affairs are better or worse, even without assigning numerical scores to them, particularly in a series of papers by Vallentyne and Kagan.
Nick Bostrom notes that to evaluate acts, rather than states, we need to also deal with uncertainty. If state A is better than B, and C is worse, that doesn't yet settle whether it is better to bring about B for sure, or a risky gamble between A and C. Bostrom proposes a method to assign numerical scores to infinite states of affairs that can then be combined by traditional decision-theoretic means of expected value. Frank Arntzenius, however, suggests evaluating the expected outcome of an act for each person, and then using Vallentyne and Kagan's methods to aggregate them into an overall ordering.
I propose that, following some ideas of Harsanyi and Rawls, we treat the uncertainty over outcomes of an act, and the way it affects different persons, in a symmetric fashion, rather than treating one of the two first. I extend some ideas from my 2014 paper, "Decision Theory without Representation Theorems" to cases with infinitely many persons and show that it can solve the problems that Bostrom and Arntzenius raise, while preserving many of the results of Vallentyne and Kagan.
Regardless of the status of the particular proposals I make, and the possibility of infinite populations, I suggest that the methods I use can help explain why addition seems relevant in finite populations, and expected value seems relevant in single-person decision problems, even though both are abstract mathematical operations with no obvious intrinsic connection to the practical questions of better and worse.