I simply don’t believe that infinities exist, and even though 0 isn’t a probability, I reject the probabilistic argument that any possibility of infinity allows them to dominate all EV calculations.
Problems with infinity doesn’t go away just because you assume that actual infinities don’t exist. Even with just finite numbers, you can face gambles that have infinite expected value, if increasingly good possibilities have insufficiently rapidly diminishing probabilities. And this still causes a lot of problems.
(I also don’t think that’s an esoteric possibility. I think that’s the epistemic situation we’re currently in, e.g. with respect to the amount of possible lives that could be created in the future.)
Also, as far as I know (which isn’t a super strong guarantee) every nice theorem that shows that it’s good to maximize expected value assumes that possible utility is bounded in both directions (for outcomes with probability >0). So there’s no really strong reason to think that it would make sense to maximize expected welfare in an unbounded way, in the first place.
Under mainstream conceptions of physics (as I loosely understand them), the number of possible lives in the future is unfathomably large, but not actually infinite.
I’m not saying it’s infinite, just that (even assuming it’s finite) I assign non-0 probability to different possible finite numbers in a fashion such that the expected value is infinite. (Just like the expected value of an infinite st petersburg challenge is infinite, although every outcome has finite size.)
Is the expected number finite, though? If you assign nonzero probability to a distribution with infinite EV, your overall EV will be infinite. If you can’t give a hard upper bound, i.e. you can’t prove that there exists some finite number N, such that the number of possible lives in the future is at most N with probability 1, it seems hard to rule out giving any weight to such distributions with infinite EV (although I am now just invoking Cromwell’s rule).
i.e. you can’t prove that there exists some finite number N, such that the number of possible lives in the future is at most N with probability 1,
I think you probably can? Edit: assuming current physics holds up, which is of course not probability 1. But I don’t think it makes sense to treat the event that it doesn’t seriously, in a Pascal’s mugging sense.
The topic under discussion is whether pascalian scenarios are a problem for utilitarianism, so we do need to take pascalian scenarios seriously, in this discussion.
Problems with infinity doesn’t go away just because you assume that actual infinities don’t exist. Even with just finite numbers, you can face gambles that have infinite expected value, if increasingly good possibilities have insufficiently rapidly diminishing probabilities. And this still causes a lot of problems.
(I also don’t think that’s an esoteric possibility. I think that’s the epistemic situation we’re currently in, e.g. with respect to the amount of possible lives that could be created in the future.)
Also, as far as I know (which isn’t a super strong guarantee) every nice theorem that shows that it’s good to maximize expected value assumes that possible utility is bounded in both directions (for outcomes with probability >0). So there’s no really strong reason to think that it would make sense to maximize expected welfare in an unbounded way, in the first place.
See also: www.lesswrong.com/posts/hbmsW2k9DxED5Z4eJ/impossibility-results-for-unbounded-utilities
Under mainstream conceptions of physics (as I loosely understand them), the number of possible lives in the future is unfathomably large, but not actually infinite.
I’m not saying it’s infinite, just that (even assuming it’s finite) I assign non-0 probability to different possible finite numbers in a fashion such that the expected value is infinite. (Just like the expected value of an infinite st petersburg challenge is infinite, although every outcome has finite size.)
Is the expected number finite, though? If you assign nonzero probability to a distribution with infinite EV, your overall EV will be infinite. If you can’t give a hard upper bound, i.e. you can’t prove that there exists some finite number N, such that the number of possible lives in the future is at most N with probability 1, it seems hard to rule out giving any weight to such distributions with infinite EV (although I am now just invoking Cromwell’s rule).
I think you probably can? Edit: assuming current physics holds up, which is of course not probability 1. But I don’t think it makes sense to treat the event that it doesn’t seriously, in a Pascal’s mugging sense.
The topic under discussion is whether pascalian scenarios are a problem for utilitarianism, so we do need to take pascalian scenarios seriously, in this discussion.