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

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: Lumifer 21 September 2015 03:13:00PM 0 points [-]

If there are infinitely many possibilities, then the generalized theorem does require bounded utility.

I am not sure I understand. Link?

Comment author: entirelyuseless 21 September 2015 07:54:05PM 0 points [-]

http://arxiv.org/pdf/0907.5598.pdf

Comment author: Lumifer 21 September 2015 08:09:51PM 0 points [-]

Our main result implies that if you have an unbounded, perception determined, computable utility function, and you use a Solomonoff-like prior (Solomonoff, 1964), then you have no way to choose between policies using expected utility.

So, it's within the AIXI context and you feed your utility function infinite (!) sequences of "perceptions".

We're not in VNM land any more.

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