Good_Burning_Plastic comments on Probabilities Small Enough To Ignore: An attack on Pascal's Mugging - Less Wrong
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Except, the VNM theorem in the form given applies to situations with finitely many possibilities. If there are infinitely many possibilities, then the generalized theorem does require bounded utility. This follows from precisely the Pascal's mugging-type arguments like the ones being considered here.
(And with finitely many possibilities, the utility function cannot possibly be unbounded, because any finite set of reals has a maximum.)