But I see what you’re getting at, SIA selects observers from the whole distribution over observers taken as a single bag.
That phrasing sounds right, yeah.
I wrote expected fraction in the previous comment in order to circumvent the requirement of both universes existing simultaneously. But I acknowledge that my intuition is more compelling when assuming that they all exist, or (in Sleeping Beauty or God’s extreme coin toss) that the experiment is repeated many times. Still, it seems odd to expect an inconsistency between the “it just happened once” and the “it happens many times” cases..
That phrasing sounds right, yeah.
I wrote expected fraction in the previous comment in order to circumvent the requirement of both universes existing simultaneously. But I acknowledge that my intuition is more compelling when assuming that they all exist, or (in Sleeping Beauty or God’s extreme coin toss) that the experiment is repeated many times. Still, it seems odd to expect an inconsistency between the “it just happened once” and the “it happens many times” cases..