The problem, as stated, seems to me like it can be solved by precommitting not to negotiate with terrorists--this seems like a textbook case.
That can work when the mugger is a terrorist. Unfortunately most muggers aren't. They're businessmen. Since the 'threat' issue isn't intended to be the salient feature of the question we can perhaps specify that the mugger would be paid $3 to run the simulation and is just talking to you in a hope of getting a better offer. You do negotiate under those circumstances.
For my part I don't like the specification of the problem as found on the wiki at all:
Now suppose someone comes to me and says, "Give me five dollars, or I'll use my magic powers from outside the Matrix to run a Turing machine that simulates and kills 3^^^^3 people."
Quite aside from the 'threat' issue I just don't care what some schmuck simulates on a Turing machine outside the matrix. That is a distraction.
For background, see here.
In a comment on the original Pascal's mugging post, Nick Tarleton writes:
Coming across this again recently, it occurred to me that there might be a way to generalize Vassar's suggestion in such a way as to deal with Tarleton's more abstract formulation of the problem. I'm curious about the extent to which folks have thought about this. (Looking further through the comments on the original post, I found essentially the same idea in a comment by g, but it wasn't discussed further.)
The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3. That is, the utility function should grow only according to the complexity of the scenario being evaluated, and not (say) linearly in the number of people involved. Furthermore, the domain of the utility function should consist of low-level descriptions of the state of the world, which won't refer directly to words uttered by muggers, in such a way that a mere discussion of "3^^^^3 units of disutility" by a mugger will not typically be (anywhere near) enough evidence to promote an actual "3^^^^3-disutilon" hypothesis to attention.
This seems to imply that the intuition responsible for the problem is a kind of fake simplicity, ignoring the complexity of value (negative value in this case). A confusion of levels also appears implicated (talking about utility does not itself significantly affect utility; you don't suddenly make 3^^^^3-disutilon scenarios probable by talking about "3^^^^3 disutilons").
What do folks think of this? Any obvious problems?