Researcher at the Center on Long-Term Risk. Located in London.
Julian Stastny
Karma: 36
Disentangling four motivations for acting in accordance with UDT
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..
I found this is a somewhat confusing/counterintuitive way to explain SIA. (Because why start out with 1000:1 odds when it is stated that the two universes are equally likely a priori?)
How I’d explain it: Suppose I want to put a credence on the hypothesis T Trillion observer universe, starting from a 50% prior on each of the the two hypotheses. I now observe my index being, say, 100. According to my prior, what’s the expected fraction of observers that observe having index 100 who would be correct to believe T? It’s 50%.