Hi Harrison. I think I agree strongly with (2) and (3) here. I’d argue Infinite expected values that depend on (very) large numbers of trials / bankrolls etc. can and should be ignored. With the Petersburg Paradox as state in the link you included, making any vaguely reasonable assumption about the wealth of the casino, or lifetime of the player, the expected value falls to something much less appealing! This is kind of related to my “saving lives” example in my question—if you only get to play once, the expected value becomes basically irrelevant because the good outcome just actually doesn’t happen. It only starts to be worthwhile when you get to play many times. And hey, maybe you do. If there are 10,000 EAs all doing totally (probabilistically) independent things that each have a 1 in a million chance of some huge payoff, we start to get into realms worth thinking about.

Actually, I think it’s worth being a bit more careful about treating low-likelihood outcomes as irrelevant simply because you aren’t able to attempt to get that outcome more often: your intuition might be right, but you would likely be wrong in then concluding “expected utility/value theory is bunk.” Rather than throw out EV, you should figure out whether your intuition is recognizing something that your EV model is ignoring, and if so, figure out what that is. I listed a few example points above, to give another illustration: Suppose you have a case where you have the chance to push button X or button Y once: if you push button X, there is a ^{1}⁄_{10,000} chance that you will save 10,000,000 people from certain death (but a ^{9,999}⁄_{10,000} chance that they will all still die); if you push button Y there is a 100% chance that 1 person will be saved (but 9,999,999 people will die). There are definitely some selfish reasons to choose button Y (e.g., you won’t feel guilty like if you pressed button X and everyone still died), and there may also be some aspect of non-linearity in the impact of how many people are dying (refer back to (1) in my original answer). However, if we assume away those other details (e.g., you won’t feel guilty, the deaths to utility loss is relatively linear) -- if we just assume the situation is “press button X for a ^{1}⁄_{10,000} chance of 10,000,000 utils; press button Y for a 100% chance of 1 util” the answer is perhaps counterintuitive but still reasonable: without having a crystal ball that perfectly tells the future, the optimal strategy is to press button X.

Hi Harrison. I think I agree strongly with (2) and (3) here. I’d argue Infinite expected values that depend on (very) large numbers of trials / bankrolls etc. can and should be ignored. With the Petersburg Paradox as state in the link you included, making any vaguely reasonable assumption about the wealth of the casino, or lifetime of the player, the expected value falls to something much less appealing! This is kind of related to my “saving lives” example in my question—if you only get to play once, the expected value becomes basically irrelevant because the good outcome just actually doesn’t happen. It only starts to be worthwhile when you get to play many times. And hey, maybe you do. If there are 10,000 EAs all doing totally (probabilistically) independent things that each have a 1 in a million chance of some huge payoff, we start to get into realms worth thinking about.

Actually, I think it’s worth being a bit more careful about treating low-likelihood outcomes as irrelevant simply because you aren’t able to attempt to get that outcome more often: your intuition might be right, but you would likely be wrong in then concluding “expected utility/value theory is bunk.” Rather than throw out EV, you should figure out whether your intuition is recognizing something that your EV model is ignoring, and if so, figure out what that is. I listed a few example points above, to give another illustration:

Suppose you have a case where you have the chance to push button X or button Y once: if you push button X, there is a

^{1}⁄_{10,000}chance that you will save 10,000,000 people from certain death (but a^{9,999}⁄_{10,000}chance that they will all still die); if you push button Y there is a 100% chance that 1 person will be saved (but 9,999,999 people will die). There are definitely some selfish reasons to choose button Y (e.g., you won’t feel guilty like if you pressed button X and everyone still died), and there may also be some aspect of non-linearity in the impact of how many people are dying (refer back to (1) in my original answer). However, if we assume away those other details (e.g., you won’t feel guilty, the deaths to utility loss is relatively linear) -- if we just assume the situation is “press button X for a^{1}⁄_{10,000}chance of 10,000,000 utils; press button Y for a 100% chance of 1 util” the answer is perhaps counterintuitive but still reasonable: without having a crystal ball that perfectly tells the future, the optimal strategy is to press button X.