Question: In your paper on Anthropic Decision Theory, you wrote "If the philosopher is selfish, ADT reduces to the SSA and the philosopher will bet at 1:1 odds" in reference to Presumptuous Philosopher problem. I don't quite see how that follows - it seems to assume that the philosopher automatically exists in both universes. But if we assume there are more philosophers in the larger universe, then there must be at least some philosophers who lack a counterpart in the smaller universe. So it seems that ADT only reduces to SSA when the philosopher identifies with only his physical self in the current universe AND (his physical self in the alternate universe OR exactly one other self if he doesn't exist in the smaller universe).

I'll pre-emptively note that obviously he can never observe himself not existing. The point is that in order for the token to be worth $0.50 in the dollar, there must be a version of him to buy a losing token in the counterfactual. We can't get from "If the actual universe is small, I exist" to "If actual universe is large, I would also exist in the counterfactual". Probably the easiest way to understand this is to pretend you have a button that will do nothing in the small universe, but shrink the universe killing everyone in the large universe who wouldn't have existed if the universe were small instead. There's no way to know that pressing the button won't kill you. On the other hand, if you do have this knowledge, then you have more knowledge than everyone else who doesn't know that is true about them.

I agree about this when you are reasoning about scenarios with uncertainty about the number of copies, but FNIC is about scenarios with certainty about the number of copies e.g. the variation on Sleeping Beauty where you know it's Monday.