Kenny Easwaran on Infinite Ethics and Decision Theory

“Infinite Ethics Meets Decision Theory”

ABSTRACT: 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.

Kenny Easwaran is an Associate Professor at Texas A & M. He is well-known for a broad range of contributions to formal philosophy related to, among other things, decision theory and epistemology.