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Peter_de_Blanc comments on Expected utility without the independence axiom - Less Wrong
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? This is just the standard definition. The mean of the random variable, when it is expressed in terms of utils.
Should this be specified in the post, or is it common knowledge on this list?
You started out by assuming a preference relation on lotteries with various properties. The completeness, transitivity, and continuity axioms talk about this preference relation. Your "standard deviation bound" axiom, however, talks about a utility function. What utility function?