If there are a million universes with a population of 1000 each, and one universe with a population of 1000000, you ought to find yourself in one of the universes with a population of 1000.
We agree there (I just meant more likely to be in the 1000000 one than any given 1000 one). If there are any that have infinitely many people (eg go on forever), you are almost certainly in one of those.
That still depends on an assumption about the demographics of universes. If there are finitely many universes that are infinitely populated, but infinitely many that are finitely populated, the latter still have a chance to outweigh the former. I concede that if you can have an infinitely populated universe at all, you ought to have infinitely many variations on it, and so infinity ought to win.
Actually I think there is some confusion or ambiguity about the meaning of SIA here. In his article Stuart speaks of a non-intuitive and an intuitive formulation of SIA. The intuitive one is that you should consider yourself a random sample. The non-intuitive one is that you should prefer many-observer hypotheses. Stuart’s “intuitive” form of SIA, I am used to thinking of as SSA, the self-sampling assumption. I normally assume SSA but our radical ignorance about the actual population of the universe/multiverse makes it problematic to apply. The “non-intuitive SIA” seems to be a principle for choosing among theories about multiverse demographics but I’m not convinced of its validity.
Intuitive SIA = consider yourself a random sample out of all possible people
SSA = consider yourself a random sample from people in each given universe separately
e.g. if there are ten people and half might be you in one universe, and one person who might be you in another,
SIA: a greater proportion of those who might be you are in the first
SSA: a greater proportion of the people in the second might be you
If you are in a universe SIA tells you it is most likely the most populated one.
If there are a million universes with a population of 1000 each, and one universe with a population of 1000000, you ought to find yourself in one of the universes with a population of 1000.
We agree there (I just meant more likely to be in the 1000000 one than any given 1000 one). If there are any that have infinitely many people (eg go on forever), you are almost certainly in one of those.
That still depends on an assumption about the demographics of universes. If there are finitely many universes that are infinitely populated, but infinitely many that are finitely populated, the latter still have a chance to outweigh the former. I concede that if you can have an infinitely populated universe at all, you ought to have infinitely many variations on it, and so infinity ought to win.
Actually I think there is some confusion or ambiguity about the meaning of SIA here. In his article Stuart speaks of a non-intuitive and an intuitive formulation of SIA. The intuitive one is that you should consider yourself a random sample. The non-intuitive one is that you should prefer many-observer hypotheses. Stuart’s “intuitive” form of SIA, I am used to thinking of as SSA, the self-sampling assumption. I normally assume SSA but our radical ignorance about the actual population of the universe/multiverse makes it problematic to apply. The “non-intuitive SIA” seems to be a principle for choosing among theories about multiverse demographics but I’m not convinced of its validity.
Intuitive SIA = consider yourself a random sample out of all possible people
SSA = consider yourself a random sample from people in each given universe separately
e.g. if there are ten people and half might be you in one universe, and one person who might be you in another, SIA: a greater proportion of those who might be you are in the first SSA: a greater proportion of the people in the second might be you