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Stuart_Armstrong comments on Anthropic decision theory I: Sleeping beauty and selflessness - Less Wrong Discussion
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In practice, everyone's motivation is a mixture of all sorts of stuff, and very little is even a utility function...
But in theory, this is how I would define a selfish utility: one that is defined entirely in terms of an index "me". If you have two people with exactly the same selfish utility function, completely identical (except that the "me" is different), then those two utilities are independent of each other.