Tom_McCabe2 suggests generalizing EY's rebuttal of Pascal's Wager to Pascal's Mugging: it's not actually obvious that someone claiming they'll destroy 3^^^^3 people makes it more likely that 3^^^^3 people will die. The claim is arguably such weak evidence that it's still about equally likely that handing over the $5 will kill 3^^^^3 people, and if the two probabilities are sufficiently equal, they'll cancel out enough to make it not worth handing over the $5.

Personally, I always just figured that the probability of someone (a) threatening me with killing 3^^^^3 people, (b) having the ability to do so, and (c) not going ahead and killing the people anyway after I give them the $5, is going to be way less than 1/3^^^^3, so the expected utility of giving the mugger the $5 is almost certainly less than the $5 of utility I get by hanging on to it. In which case there is no problem to fix. EY claims that the Solomonoff-calculated probability of someone having 'magic powers from outside the Matrix' 'isn't anywhere near as small as 3^^^^3 is large,' but to me that just suggests that the Solomonoff calculation is too credulous.

(Edited to try and improve paraphrase of Tom_McCabe2.)