압도, 기대효용 최대화, 포함, 그리고 무한 효용

Abstract

I argue that the following three decision-theoretic principles are inconsistent with the assumption that there are options with infinite expected utility: (1) the principle of expected utility maximization that given a collection of options, you should choose the one with maximum expected utility; (2) the principle of dominance that if an option X produces at least as good an outcome as an option Y in every possible state of the world and a strictly better outcome in at least one possible state of the world with non-zero probability, then X is strictly preferable to Y; and (3) the principle of inclusion that if an option X contains a suboption x (i.e., if you take X, then you are given suboptions one of which is x) such that taking X and then x always yields the same outcome as taking an option Y, then X is at least as desirable as Y. Consequently, relative expectation theory proposed by Mark Colyvan (2008), which combines the principle of dominance with the principle of expected utility maximization and is designed to apply to options with infinite expected utility, is inconsistent with the principle of inclusion. To avoid inconsistency, I suggest, either applications of the principle of dominance should be restricted to options with finite expected utilities, or a rational agent should not assign infinite expected utility to options.