So would it be accurate to say that a preference over lotteries (where each lottery involves only real-valued probabilities) satisfies the axioms of the VNM theorem (except for the Archimedean property) if and only if that preference is equivalent to maximizing the expectation value of a surreal-valued utility function?
Re the parent example, I agree that changing in an expectable way is problematic to rational optimizing, but I think “what kind of agent am I happy about being?” is a distinct question from “what kinds of agents exist among minds in the world?”.
So would it be accurate to say that a preference over lotteries (where each lottery involves only real-valued probabilities) satisfies the axioms of the VNM theorem (except for the Archimedean property) if and only if that preference is equivalent to maximizing the expectation value of a surreal-valued utility function?
Re the parent example, I agree that changing in an expectable way is problematic to rational optimizing, but I think “what kind of agent am I happy about being?” is a distinct question from “what kinds of agents exist among minds in the world?”.