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.
There seems to be no obvious reason to assume that the probability falls exactly in proportion to the number of lives saved.
If GiveWell told me they thought that real-life intervention A could save one life with probability PA and real-life intervention B could save a hundred lives with probability PB, I'm pretty sure that dividing PB by 100 would be the wrong move to make.
It is an assumption to make asymptotically (that is, for the tails of the distribution), which is reasonable due to all the nice properties of exponential family distributions.
I'm... (read more)