Rather than assigning 0 probability to infinities or infinite impacts, if you’re set on sticking to unbounded utility, I’d endorse just allowing (not necessarily requiring) yourself to ignore probabilities up to some small threshold for any option, including tiny probability differences for outcomes that aren’t very unlikely.
I wouldn’t want to keep ignoring the possibility of infinities if I believed I could make an actual infinite difference with a large enough probability. Giving this up seems worse to me than deviating slightly (more) from the ideal of vNM or Savage rationality. That ideal was also never realistic to meet, anyway.
This solution also works for St. Petersburg lotteries and Pascal’s muggings, although you might also have independent reasons to pick a very skeptical prior.
Rather than assigning 0 probability to infinities or infinite impacts, if you’re set on sticking to unbounded utility, I’d endorse just allowing (not necessarily requiring) yourself to ignore probabilities up to some small threshold for any option, including tiny probability differences for outcomes that aren’t very unlikely.
I wouldn’t want to keep ignoring the possibility of infinities if I believed I could make an actual infinite difference with a large enough probability. Giving this up seems worse to me than deviating slightly (more) from the ideal of vNM or Savage rationality. That ideal was also never realistic to meet, anyway.
This solution also works for St. Petersburg lotteries and Pascal’s muggings, although you might also have independent reasons to pick a very skeptical prior.
Related: Monton, How to Avoid Maximizing Expected Utility.