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paulfchristiano comments on The Absolute Self-Selection Assumption - Less Wrong
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So you're going with "randomly generated". Which is fine, but it needs to be spelled out.
You need to be very careful pulling intuitions about randomness from the finite case and applying it to the infinite case. In particular, it is no longer true that just because something happened, it has a positive probability. Any given real number has probability zero of being picked from the uniform distribution on [0,1) yet one certainly will be picked. And we can pick an infinite number of times and never encounter a duplicate.
I'm not attacking this assumption in order to attack your final conclusion, I'm just attacking this assumption.
I believe there are probably only countably many distinguishable observer moments, in which case this can't happen by countable additivity.
But you are certainly correct, that a lot goes into this assumption. I should be more clear about this; in particular, I should probably add a bunch of "may"'s.