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Stuart_Armstrong comments on Expected utility without the independence axiom - Less Wrong
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Thanks for bringing this up, and I've change my post to reflect your comments. Unfortunately, I have to decree a utility function ahead of time for this to make any sense, as I can change the mean and SD of any distribution by just changing my utility function.
I have a new post up that argues that where small sums are concerned, you have to have a utility function linear in cash.