t's not the only way to do so, though; you can also require that the prior probabilities of statements (without corresponding opposite-utility statements) shrink at least as fast as utilities grow.
My favored solution. Incidentally, if your prior shrinks faster, then you can still be vulnerable. The mugger can simply split his offer up into a billion smaller offers, which will avoid the penalty of big offers disproportionately being discounted. So unless you would reject every single mugging offer of any magnitude (in which case isn't that kind of arbitrary?), the faster shrinking doesn't buy you anything.
Incidentally, if your prior shrinks faster, then you can still be vulnerable. The mugger can simply split his offer up into a billion smaller offers, which will avoid the penalty of big offers disproportionately being discounted. So unless you would reject every single mugging offer of any magnitude (in which case isn't that kind of arbitrary?), the faster shrinking doesn't buy you anything.
I believe a set of smaller offers would imply the existence of a statement which aggregates them and violates this formalization of the anti-mugging axiom.
On the oth...
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?