Really appreciate you taking the time to go through this!
To establish some language for what I want to talk about, I want to say your setup has two world sets (each with a prior of 50%) and six worlds (3 in each world set). A possible error I was making was just thinking in terms of one world set (or, one hypothesis: C), and not thinking about the competing hypotheses.
I think in your SSA, you treat all observers in the conditioned-on world set as “actually existing”. But shouldn’t you treat only the observers in a single world as “actually existing”? That is, you notice you’re in a world where everyone survives. If C is true, the probability of this, given that you survived, is (0.7/0.9)/(0.7/0.9 + 0.2/0.9) = 7⁄9.
And then what I wanted to do with SIA is to use a similar structure to the not-C branch of your SSA argument to say “Look, we have 10⁄11 of being in an everyone survived world even given not-C. So it isn’t strong evidence for C to find ourselves in an everyone survived world”.
It’s not yet clear to me (possibly because I am confused) that I definitely shouldn’t do this kind of reasoning. It’s tempting to say something like “I think the multiverse might be such that measure is assigned in one of these two ways to these three worlds. I don’t know which, but there’s not an anthropic effect about which way they’re assigned, while there is an anthropic effect within any particular assignment”. Perhaps this is more like ASSA than SIA?
Really appreciate you taking the time to go through this!
To establish some language for what I want to talk about, I want to say your setup has two world sets (each with a prior of 50%) and six worlds (3 in each world set). A possible error I was making was just thinking in terms of one world set (or, one hypothesis: C), and not thinking about the competing hypotheses.
I think in your SSA, you treat all observers in the conditioned-on world set as “actually existing”. But shouldn’t you treat only the observers in a single world as “actually existing”? That is, you notice you’re in a world where everyone survives. If C is true, the probability of this, given that you survived, is (0.7/0.9)/(0.7/0.9 + 0.2/0.9) = 7⁄9.
And then what I wanted to do with SIA is to use a similar structure to the not-C branch of your SSA argument to say “Look, we have 10⁄11 of being in an everyone survived world even given not-C. So it isn’t strong evidence for C to find ourselves in an everyone survived world”.
It’s not yet clear to me (possibly because I am confused) that I definitely shouldn’t do this kind of reasoning. It’s tempting to say something like “I think the multiverse might be such that measure is assigned in one of these two ways to these three worlds. I don’t know which, but there’s not an anthropic effect about which way they’re assigned, while there is an anthropic effect within any particular assignment”. Perhaps this is more like ASSA than SIA?