loqi comments on Average utilitarianism must be correct? - Less Wrong
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If that is true, then that means their utility is a function of the distribution of others' utility, and they will maximize their expected utility by maximizing the expected equity of others' utility.
Is this the case? I don't know how you reached this conclusion. Even if it is the case, I also don't see how this is necessarily inconsistent unless one also makes the claim that they make no value distinction between future selves and other people.