**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Wed Aug 31 2005 - 11:11:38 MDT

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Phil Goetz wrote:

*> --- Michael Vassar <michaelvassar@hotmail.com> wrote:
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*>
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*>> do as well as we can). Account must be taken of it when designing
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*>> an FAI, but this only requires an incremental development beyond
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*>> that needed to protect it from Pascal's Wagers.
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*>
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*> Actually, I meant to ask that question. How does a Bayesian deal
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*> with Pascal's wager, assuming that they assign a non-zero probability
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*> to Christianity's claims regarding heaven and hell being true, and an
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*> infinite positive reward with eternal heaven and an infinite negative
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*> reward with eternal damnation? Assume there are no other religions
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*> being proposed.
*

Ah, but that assumption is the whole key to the fallacy, isn't it? I

think the Bayesian solution arises from unbounded other religions being

possible and assigned roughly equal non-zero probabilities. For every

possible religion which claims that believing in the Flying Spaghetti

Monster gets you 'infinite' reward, there exists a possible religion

which claims that believing in the Flying Spaghetti Monster gets you

'infinite' punishment. This hypothesis has equal Kolmogorov complexity

and hence equal infinitesimal prior probability. The sum cancels out,

like the contribution to my real-world expectations of the hypothesis

that the blue people will make the coin land heads and the hypothesis

that the blue people will make the coin land tails.

'Infinite' is in quote marks because, having never observed an infinity,

I currently disallow it in my utility function. Utility functions map

outcomes onto real numbers and 'infinity' is not a real number. The

behaviors of infinities interacting with real numbers also violate the

axioms of expected utility.

-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence

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