Author Archives: Utilitarian

Where Does Pascal’s Wager Fail?

The topic of Pascal’s wager has been mentioned several times before on Overcoming Bias, most notably in Eliezer’s post on Pascal’s mugging. I’m interested in discussing the question with specific reference to its original context: religion. My assumption is that almost all readers agree that the wager fails in this context — but where exactly?

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Are More Complicated Revelations Less Probable?

Consider two possible situations, A and B. In situation A, we come across a person–call him "A"–who makes the following claim: "I was abducted by aliens from the planet Alpha; they had green skin." In situation B, we come across a different person–call him "B"–who tells us, "I was abducted by aliens from the planet Beta; they had blue skin, they liked to play ping-pong, they rode around on unicycles, and their favorite number was 7." In either situation, we are likely to assign low subjective probability to the abduction claim that we hear. But should we assign higher subjective probability to the claim in one situation more than in the other?

Mindful of Occam’s razor, and careful to avoid the type of reasoning that leads to the conjunction fallacy, we might agree that A’s claim is, in itself, more probable, because it is less specific. However, we have to condition our probability assessment on the evidence that A or B actually made his claim. While B’s claim is less intrinsically likely, the hypothesis that B’s claim is true has strong explanatory power to account for why B made the specific statements he did. Thus, in the end it may not be so obvious whether we should believe A’s claim more in situation A than we believe B’s claim in situation B.

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