The crucial point is that on H1 our existence (say, E) is much more likely than on Hϵ. That is, P(E|H1)>P(E|Hϵ). If our prior is P(H1)=P(Hϵ), then P(H1|E)>P(Hϵ|E). That is, our existence implies that H1 is more likely.
As a sanity check, this also doesn’t reliably lead us to wrong conclusions: If we have two possible universes, one where H1 is true and one where Hϵ is true, and in both possible universes the civilizations reason as above and regard H1 as more likely, much more civilizations will reach the true rather than the false conclusion, since the possible universe where H1 is true has much more civilizations (or a much higher density etc).
Now I see, yes you are right. If you want the beliefs to be accurate at the civilisation level, that is the correct way of looking at it. This corresponds to the 1⁄3 conclusion in the sleeping beauty problem.
I was thinking of it on the universe level, were we are a way for the universe to understand itself. If we want the universe to form accurate beliefs about itself, then we should not include our own civilisation when counting the number of the civilisations in the galaxy. However, when deciding if we should be surprised that we don’t see other civilisations, you are right that should include ourselves in the statistics.
The crucial point is that on H1 our existence (say, E) is much more likely than on Hϵ. That is, P(E|H1)>P(E|Hϵ). If our prior is P(H1)=P(Hϵ), then P(H1|E)>P(Hϵ|E). That is, our existence implies that H1 is more likely.
As a sanity check, this also doesn’t reliably lead us to wrong conclusions: If we have two possible universes, one where H1 is true and one where Hϵ is true, and in both possible universes the civilizations reason as above and regard H1 as more likely, much more civilizations will reach the true rather than the false conclusion, since the possible universe where H1 is true has much more civilizations (or a much higher density etc).
Now I see, yes you are right. If you want the beliefs to be accurate at the civilisation level, that is the correct way of looking at it. This corresponds to the 1⁄3 conclusion in the sleeping beauty problem.
I was thinking of it on the universe level, were we are a way for the universe to understand itself. If we want the universe to form accurate beliefs about itself, then we should not include our own civilisation when counting the number of the civilisations in the galaxy. However, when deciding if we should be surprised that we don’t see other civilisations, you are right that should include ourselves in the statistics.