Decision Theory Without Finite Standard Expected Value

We address the question, in decision theory, of how the value of risky options (gambles) should be assessed when they have no finite standard expected value (i.e. where the sum of the probability-weighted payoffs is infinite or not well defined). We endorse, combine, and extend (1) the proposal of Easwaran (2008) to evaluate options on the basis of their weak expected value, and (2) the proposal of Colyvan (2008) to rank options on the basis of their relative expected value.Our goal is to outline a framework rather than to give a compelling defense of it. We shall motivate, through the use of examples, the plausibility of principles that go beyond standard expected value. Although the principles we endorse leave some options incomparable, we believe that they are, at least roughly speaking, the strongest plausible extensions of standard decision theory