Well, it's been two-and-a-quarter years since that post, but I'll comment anyway.
Isn't the anti-mugging axiom inadequate as stated? Basically, you're saying the expected utility is bounded, but bounded by what? If the bound is, for example, equivalent to 20 happy years of life, you're going to get mugged until you can barely keep from starving. If it's less than 20 happy years of life, you probably won't bother saving for retirement (assuming I'm interpreting this correctly).
Another way of looking at it, is that, let's say the bound is b, then U(E|X) < b/P(E|X) ∀ X, ∀ E. So an event you're sure will happen can have maximum utility b, but an event that you're much less confident about can have vastly higher maximum utilities. This seems unintuitive (which is not as much of an issue as the one stated above).
Perhaps a stronger version is necessary. How about this: P(E|X) U(E|X) should tend to zero as U(E|X) tends to infinity. Or to put that with more mathematical clarity:
For any sequence of hypothetical events E_i, i=0, 1, ..., if the sequence of utilities U(E_i|X) tends to infinity then the sequence of expectations P(E_i|X) U(E_i|X) must tend to zero.
Or perhaps an even stronger "uniform" version: For every e > 0 there exists a utility u such that for every event E with U(E|X) > u, its expected utility P(E|X) U(E|X) is less than e.
I called this an axiom, but it would be more accurate to call it a principle, something that any purported decision theory should satisfy as a theorem.
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?