I think we are all in agreement with this (modulo the fact that all of the expected values end up being infinite and so we can't compare in the normal way; if you e.g. proposed a cap of 3^^^^^^^3 on utilities, then you certainly wouldn't pay the mugger).

Sorry, I didn't mean to suggest otherwise. The "different perspective" part was supposed to be about the "in contrast" part.

It seems very likely to me that ordinary people are best modeled as having bounded utility functions, which would explain the puzzle.

I agree with yli that this has other unfortunate consequences. And, like Holden, I find it unfortunate to have to say that saving N lives with probability 1/N is worse than saving 1 life with probability 1. I also recognize that the things I would like to say about this collection of cases are inconsistent with each other. It's a puzzle. I have written about this puzzle at reasonable length in my dissertation. I tend to think that bounded utility functions are the best consistent solution I know of, but that continuing to operate with inconsistent preferences (in a tasteful way) may be better in practice.