In the dialog you give, Pascal assigns a probability that the mugger will fulfill his promise without hearing what that promise is, then fails to update it when the promise is revealed. But after hearing the number "1000 quadrillion", Pascal would then be justified in updating his probability to something less than 1 in 1000 quadrillion.
Other known defenses against Pascal's mugging are bounded utility functions, and rounding probabilities below some noise floor to zero. Another strategy that might be less likely to carry adverse side effects would be to combine a sub-linear utility function with a prior that assigns statements involving a number N probability at most 1/N (and the Occamian prior does indeed do this).
In the dialog you give, Pascal assigns a probability that the mugger will fulfill his promise without hearing what that promise is, then fails to update it when the promise is revealed. But after hearing the number "1000 quadrillion", Pascal would then be justified in updating his probability to something less than 1 in 1000 quadrillion.
I think this might be it, but I'm not sure. Here is the key piece of the puzzle:
...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,
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:
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?