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twanvl comments on The Empty White Room: Surreal Utilities - Less Wrong
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Could utilities be multi-dimensional? Real vector spaces are much nicer to work with than to surreal numbers.
For example, the utility for frank being alive would be (1,0), while the utility for a seat cushion is (0,1). Using lexicographic ordering, (1,0) > (0,3^^^3).
Vector valued utility functions violate the VNM axiom of continuity, but who cares.
Surreal valued ones do too. Violating the VNM axiom of continuity is the whole point of the exercise. We don't want a secular value to be worth any non-zero probability of a sacred value, but we do want it to be better than nothing.