Based on your explanation in this comment, it seems to me that St. Petersburg-like prospects don’t actually invalidate utilitarian ethics as it would have been understood by e.g. Bentham, but it does contradict the existence of a real-valued utility function. It can still be true that welfare is the only thing that matters, and that the value of welfare aggregates linearly. It’s not clear how to choose when a decision has multiple options with infinite expected utility (or an option that has infinite positive EV plus infinite negative EV), but I don’t think these theorems imply that there cannot be any decision criterion that’s consistent with the principles of utilitarianism. (At the same time, I don’t know what the decision criterion would actually be.) Perhaps you could have a version of Bentham-esque utilitarianism that uses a real-valued utility function for finite values, and uses some other decision procedure for infinite values.
Ya, I don’t think utilitarian ethics is invalidated, it’s just that we don’t really have much reason to be utilitarian specifically anymore (not that there are necessarily much more compelling reasons for other views). Why sum welfare and not combine them some other way? I guess there’s still direct intuition: two of a good thing is twice as good as just one of them. But I don’t see how we could defend that or utilitarianism in general any further in a way that isn’t question-begging and doesn’t depend on arguments that undermine utilitarianism when generalized.
You could just take your utility function to be σ(∑Ni=1ui) where σ is any bounded increasing function, say arctan, and maximize the expected value of that. This doesn’t work with actual infinities, but it can handle arbitrary prospects over finite populations. Or, you could just rank prospects by stochastic dominance with respect to the sum of utilities, like Tarsney, 2020.
You can’t extend it the naive way, though, i.e. just maximize E[∑iUi] whenever that’s finite and then do something else when it’s infinite or undefined, though. One of the following would happen: the money pump argument goes through again, you give up stochastic dominance or you give up transitivity, each of which seems irrational. This was my 4th response to Infinities are generally too problematic.
Based on your explanation in this comment, it seems to me that St. Petersburg-like prospects don’t actually invalidate utilitarian ethics as it would have been understood by e.g. Bentham, but it does contradict the existence of a real-valued utility function. It can still be true that welfare is the only thing that matters, and that the value of welfare aggregates linearly. It’s not clear how to choose when a decision has multiple options with infinite expected utility (or an option that has infinite positive EV plus infinite negative EV), but I don’t think these theorems imply that there cannot be any decision criterion that’s consistent with the principles of utilitarianism. (At the same time, I don’t know what the decision criterion would actually be.) Perhaps you could have a version of Bentham-esque utilitarianism that uses a real-valued utility function for finite values, and uses some other decision procedure for infinite values.
Ya, I don’t think utilitarian ethics is invalidated, it’s just that we don’t really have much reason to be utilitarian specifically anymore (not that there are necessarily much more compelling reasons for other views). Why sum welfare and not combine them some other way? I guess there’s still direct intuition: two of a good thing is twice as good as just one of them. But I don’t see how we could defend that or utilitarianism in general any further in a way that isn’t question-begging and doesn’t depend on arguments that undermine utilitarianism when generalized.
You could just take your utility function to be σ(∑Ni=1ui) where σ is any bounded increasing function, say arctan, and maximize the expected value of that. This doesn’t work with actual infinities, but it can handle arbitrary prospects over finite populations. Or, you could just rank prospects by stochastic dominance with respect to the sum of utilities, like Tarsney, 2020.
You can’t extend it the naive way, though, i.e. just maximize E[∑iUi] whenever that’s finite and then do something else when it’s infinite or undefined, though. One of the following would happen: the money pump argument goes through again, you give up stochastic dominance or you give up transitivity, each of which seems irrational. This was my 4th response to Infinities are generally too problematic.