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Comments (176)
So, um:
Which axiom does this violate?
Continuity and independence.
Continuity: Consider the scenario where each of the [LMN] bets refer to one (guaranteed) outcome, which we'll also call L, M and N for simplicity.
Let U(L) = 0, U(M) = 1, U(N) = 10**100
For a simple EU maximizer, you can then satisfy continuity by picking p=(1-1/10**100). A PESTI agent, OTOH, may just discard a (1-p) of 1/10**100, which leaves no other options to satisfy it.
The 10**100 value is chosen without loss of generality. For PESTI agents that still track probabilities of this magnitude, increase it until they don't.
Independence: Set p to a number small enough that it's Small Enough To Ignore. At that point, the terms for getting L and M by that probability become zero, and you get equality between both sides.
Theoretically, that's the question he's asking about Pascal's Mugging, since accepting the mugger's argument would tell you that expected utility never converges. And since we could rephrase the problem in terms of (say) diamond creation for a diamond maximizer, it does look like an issue of probability rather than goals.
Of course, and the paper cited in http://wiki.lesswrong.com/wiki/Pascal's_mugging makes that argument rigorous.
It's a problem of expected utility, not necessarily probability. And I still would like to know which axiom it ends up violating. I suspect Continuity.
We can replace Continuity with the Archimedean property (or, 'You would accept some chance of a bad outcome from crossing the street.') By my reading, this ELU idea trivially follows Archimedes by ignoring the part of a compound 'lottery' that involves a sufficiently small probability. In which case it would violate Independence, and would do so by treating the two sides as effectively equal when the differing outcomes have small enough probability.