Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.
I like Scott Aaronson's approach for resolving paradoxes that seemingly violate intuitions -- see if the situation makes physical sense.
Like people bring up "blockhead," a big lookup table that can hold an intelligent conversation with you for [length of time], and wonder whether this has ramifications for the Turing test. But blockhead is not really physically realizable for reasonable lengths.
Similarly for creating 10^100 happy lives, how exactly would you go about doing that in our Universe?
It's easy if they have access to running detailed simulations, and while the probability that someone secretly has that ability is very low, it's not nearly as low as the probabilities Kaj mentioned here.