My apologies, my statement that it was equivalent to epsilon=0 was incorrect.
The description given is that of lexicographic preferences, which in this case cannot be represented with real-valued utility functions at all. There are consistent ways to deal with such preferences, by they do do tend have unusual properties.
Such as, for example, preferring that everyone in the universe is tortured forever rather than accepting 0.00000000000001 extra probability that a single person somewhere might die.
I suspect one problem is that really “death” depends crucially upon “personal identity”, and it’s a fuzzy enough concept at the extreme boundaries that lexicographic preferences over it make no sense.
My apologies, my statement that it was equivalent to epsilon=0 was incorrect.
The description given is that of lexicographic preferences, which in this case cannot be represented with real-valued utility functions at all. There are consistent ways to deal with such preferences, by they do do tend have unusual properties.
Such as, for example, preferring that everyone in the universe is tortured forever rather than accepting 0.00000000000001 extra probability that a single person somewhere might die.
I suspect one problem is that really “death” depends crucially upon “personal identity”, and it’s a fuzzy enough concept at the extreme boundaries that lexicographic preferences over it make no sense.