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orthonormal comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong
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LCPW isn't even necessary: do you really think that it wouldn't make a difference that you'd care about?
LCPW cuts two ways here, because there are two universal quantifiers in your claim. You need to look at every possible bounded utility function, not just every possible scenario. At least, if I understand you correctly, you're claiming that no bounded utility function reflects your preferences accurately.