Why wait for the mugger to make his stupendous offer? Maybe he's going to give you this stupendous blessing anyway -- can you put a sufficiently low probability on that? Don't you have to give all your money to the next person you meet? But wait! Maybe instead he intends to inflict unbounded negative utility if you do that -- what must you do to be saved from that fate? Maybe the next rock you see is a superintelligent, superpowerful alien who, for its superunintelligible reasons requires you to -- well, you get the idea.

The difference between this and the standard Mugger scenario is that by making his offer, the mugger promotes to attention the hypothesis that he presents. However, for the usual Bayesian reasons, this must at the same time promote many other unlikely hypotheses, such as the mugger being an evil tempter. I don't see any reason to suppose that the mugger's claim promotes any of these hypotheses sufficiently to distinguish the two scenarios. If you're vulnerable to Pascal's Mugger, you've already been mugged by your own decision theory.

If your decision theory has you walking through the world obsessed with tiny possibilities of vast utility fluctuations, like a placid-seeming vacuum state seething with colossal energies, then your decision theory is wrong. I propose the following constraint on utility-based rational decision theories:

The Anti-Mugging Axiom: For events E and current knowledge X, let P(E|X) = probability of E given X, U(E|X) = utility of E given X. For every state of knowledge X, P(E|X) U(E|X) is bounded over all events E.

The quantifiers here are deliberately chosen. For each X there must be an upper bound, but no bound is placed on the amount of probability-weighted utility that one might discover.