Related to: Some of the discussion going on here
In the LW version of Pascal's Mugging, a mugger threatens to simulate and torture people unless you hand over your wallet. Here, the problem is decision-theoretic: as long as you precommit to ignore all threats of blackmail and only accept positive-sum trades, the problem disappears.
However, in Nick Bostrom's version of the problem, the mugger claims to have magic powers and will give Pascal an enormous reward the following day if Pascal gives his money to the mugger. Because the utility promised by the mugger so large, it outweighs Pascal's probability that he is telling the truth. From Bostrom's essay:
Pascal: Gee . . . OK, don’t take this personally, but my credence that you have these magic powers whereof you speak is about one in a quadrillion.
Mugger: Wow, you are pretty confident in your own ability to tell a liar from an honest man! But no matter. Let me also ask you, what’s your probability that I not only have magic powers but that I will also use them to deliver on any promise – however extravagantly generous it may seem – that I might make to you tonight?
Pascal: Well, if you really were an Operator from the Seventh Dimension as you assert, then I suppose it’s not such a stretch to suppose that you might also be right in this additional claim. So, I’d say one in 10 quadrillion.
Mugger: Good. Now we will do some maths. Let us say that the 10 livres that you have in your wallet are worth to you the equivalent of one happy day. Let’s call this quantity of good 1 Util. So I ask you to give up 1 Util. In return, I could promise to perform the magic tomorrow that will give you an extra 10 quadrillion happy days, i.e. 10 quadrillion Utils. Since you say there is a 1 in 10 quadrillion probability that I will fulfil my promise, this would be a fair deal. The expected Utility for you would be zero. But I feel generous this evening, and I will make you a better deal: If you hand me your wallet, I will perform magic that will give you an extra 1,000 quadrillion happy days of life.
Pascal: I admit I see no flaw in your mathematics.
As a result, says Bostrom, there is nothing from rationally preventing Pascal from taking the mugger's offer even though it seems intuitively unwise. Unlike the LW version, in this version the problem is epistemic and cannot be solved as easily.
Peter Baumann suggests that this isn't really a problem because Pascal's probability that the mugger is honest should scale with the amount of utility he is being promised. However, as we see in the excerpt above, this isn't always the case because the mugger is using the same mechanism to procure the utility, and our so our belief will be based on the probability that the mugger has access to this mechanism (in this case, magic), not the amount of utility he promises to give. As a result, I believe Baumann's solution to be false.
So, my question is this: is it possible to defuse Bostrom's formulation of Pascal's Mugging? That is, can we solve Pascal's Mugging as an epistemic problem?