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.
So switch it to Pascal's Philanthropist, who says "I offer you a choice: either you may take this $5 bill in my hand, or I will use my magic powers outside the universe to grant you 3^^^^3 units of utility."
But I'm actually not intuitively bothered by the thought of refusing the $5 in that case. It's an eccentric thing to do, but it may be rational. Can anybody give me a formulation of the problem where taking the magic powers claim seriously is obviously crazy?
The two situations are not necessarily equivalent.
See my most recent response in the Pascal's Mugging thread - taking into account the Mugger's intentions & motives is relevant to the probability calculation.
Having said that, probably the two situations ARE equivalent - in both cases an increasingly high number indicates a higher probability that you are being manipulated.
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?