You’re missing VincentYu’s point, which is also a point I have made to you earlier: the utility function in the conclusion of the VNM theorem is not the same as a utility function that you came up with a completely different way, like by declaring linearity with respect to number of lives.
If you assign some subjective “value” to different outcomes, and to different things, then maximizing expected utility value, will maximize it, as the number of decisions approaches infinity. For every bet I lose at certain odds, I will gain more from others some predictable percent of the time. On average it cancels out.
This might not be the standard way of explaining expected utility, but it’s very simple and intuitive, and shows exactly where the problem is. It’s certainly sufficient for the explanation in my post.
This is an absurd strawman that has absolutely nothing to do with the motivation for EU maximization.
You’re missing VincentYu’s point, which is also a point I have made to you earlier: the utility function in the conclusion of the VNM theorem is not the same as a utility function that you came up with a completely different way, like by declaring linearity with respect to number of lives.
I discussed this in my post. I know VNM is indifferent to what utility function you use. I know the utility function doesn’t have to be linear. But I showed that no transformation of it fixes the problems or produces the behavior we want.
This is an absurd strawman that has absolutely nothing to do with the motivation for EU maximization.
It’s not a strawman! I know there are multiple ways of deriving EU. If you derive it a different way, that’s fine. It doesn’t affect any of my arguments whatsoever.
But I showed that no transformation of it fixes the problems or produces the behavior we want.
No, you only tried two: linearity, and a bound that’s way too low.
It’s not a strawman! I know there are multiple ways of deriving EU. If you derive it a different way, that’s fine. It doesn’t affect any of my arguments whatsoever.
You picked a possible defense of EU maximization that no one ever uses to defend EU maximization, because it is stupid and therefore easy for you to criticize. That’s what a strawman is. You use your argument against this strawman to criticize EU maximization without addressing the real motivations behind it, so it absolutely does affect your arguments.
You’re missing VincentYu’s point, which is also a point I have made to you earlier: the utility function in the conclusion of the VNM theorem is not the same as a utility function that you came up with a completely different way, like by declaring linearity with respect to number of lives.
This is an absurd strawman that has absolutely nothing to do with the motivation for EU maximization.
I discussed this in my post. I know VNM is indifferent to what utility function you use. I know the utility function doesn’t have to be linear. But I showed that no transformation of it fixes the problems or produces the behavior we want.
It’s not a strawman! I know there are multiple ways of deriving EU. If you derive it a different way, that’s fine. It doesn’t affect any of my arguments whatsoever.
No, you only tried two: linearity, and a bound that’s way too low.
You picked a possible defense of EU maximization that no one ever uses to defend EU maximization, because it is stupid and therefore easy for you to criticize. That’s what a strawman is. You use your argument against this strawman to criticize EU maximization without addressing the real motivations behind it, so it absolutely does affect your arguments.