Good_Burning_Plastic comments on Probabilities Small Enough To Ignore: An attack on Pascal's Mugging - Less Wrong

20 Post author: Kaj_Sotala 16 September 2015 10:45AM

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Comment author: VoiceOfRa 20 September 2015 08:40:02PM 1 point [-]

Because here the default utility is the one specified by the Von Neumann-Morgenstern theorem and there is no requirement (or indication) that it is bounded.

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.

Comment author: Good_Burning_Plastic 24 September 2015 10:31:01AM 2 points [-]

(And with finitely many possibilities, the utility function cannot possibly be unbounded, because any finite set of reals has a maximum.)