If, between your actions, you can carve out the undefined/infinite welfare parts so that they’re (physically) subjectively identically distributed, then you can just ignore them, as an extension of expected value maximizing total utilitarianism, essentially using a kind of additivity/separability axiom. For example, if you’re choosing between two actions A and B, and their payoffs are distributed like
A: X + Z, and
B: Y + Z,
then you can just ignore Z and compare the expected values of X and Y, even if Z is undefined or infinite, or its expectation is undefined or infinite. I would only do this if Z actually represents essentially the same distribution of local events in spacetime for each of A and B, though, since otherwise you can include more or less into X and Y arbitrarily and independently, and the reduction isn’t unique.
Unfortunately, I think complex cluelessness should usually prevent us from being able to carve out matching problematic parts so cleanly. This seems pretty catastrophic for any attempts to generalize expected utility theory, including using stochastic dominance.
EDIT: Hmm, might be saved in general even if A’s and B’s Zs are not identical, but similar enough so that their expected difference is dominated by the expected difference between X and Y. You’d be allowed to the two Zs dependence on each other to match as closely as possible, as long as you preserve their individual distributions.
If, between your actions, you can carve out the undefined/infinite welfare parts so that they’re (physically) subjectively identically distributed, then you can just ignore them, as an extension of expected value maximizing total utilitarianism, essentially using a kind of additivity/separability axiom. For example, if you’re choosing between two actions A and B, and their payoffs are distributed like
A: X + Z, and
B: Y + Z,
then you can just ignore Z and compare the expected values of X and Y, even if Z is undefined or infinite, or its expectation is undefined or infinite. I would only do this if Z actually represents essentially the same distribution of local events in spacetime for each of A and B, though, since otherwise you can include more or less into X and Y arbitrarily and independently, and the reduction isn’t unique.
Unfortunately, I think complex cluelessness should usually prevent us from being able to carve out matching problematic parts so cleanly. This seems pretty catastrophic for any attempts to generalize expected utility theory, including using stochastic dominance.
EDIT: Hmm, might be saved in general even if A’s and B’s Zs are not identical, but similar enough so that their expected difference is dominated by the expected difference between X and Y. You’d be allowed to the two Zs dependence on each other to match as closely as possible, as long as you preserve their individual distributions.