On the question of how to modify your prior over possible universe+index combinations based on observer counts, the way that I like to think of the SSA vs SIA methods is that with SSA you are first apportioning probability mass to each possible universe, then dividing that up among possible observers within each universe, while with SIA you are directly apportioning among possible observers, irrespective of which possible universes they are in.
The numbers come out the same as considering it in the way you write in the post, but this way feels more intuitive to me (as a natural way of doing things, rather than “and then we add an arbitrary weighing to make the numbers come out right”) and maybe to others.
That’s a nice way of looking at it. It’s still not very clear to me why the SIA approach of apportioning among possible observers is something you should want to do. But it definitely feels useful to know that that’s one way of interpreting what SIA is saying.
From the SIA viewpoint the anthropic update process is essentially just a prior and an update. You start with a prior on each hypothesis (possible universe) and then update by weighting each by how many observers in your epistemic situation each universe has.
This perspective sees the equalization of “anthropic probability mass” between possible universes prior to apportionment as an unnecessary distortion of the process: after all, “why would you give a hypothesis an artificial boost in likelihood just because it posits fewer observers than other hypotheses”.
Of course, this is just the flip side of what SSA sees as an unnecessary distortion in the other direction. “Why would you give a hypothesis an artificial boost due to positing more observers” it says. And here we get back to deep-seated differences in what people consider the intuitive way of doing things that underlie the whole disagreement over different anthropic methods.
On the question of how to modify your prior over possible universe+index combinations based on observer counts, the way that I like to think of the SSA vs SIA methods is that with SSA you are first apportioning probability mass to each possible universe, then dividing that up among possible observers within each universe, while with SIA you are directly apportioning among possible observers, irrespective of which possible universes they are in.
The numbers come out the same as considering it in the way you write in the post, but this way feels more intuitive to me (as a natural way of doing things, rather than “and then we add an arbitrary weighing to make the numbers come out right”) and maybe to others.
That’s a nice way of looking at it. It’s still not very clear to me why the SIA approach of apportioning among possible observers is something you should want to do. But it definitely feels useful to know that that’s one way of interpreting what SIA is saying.
From the SIA viewpoint the anthropic update process is essentially just a prior and an update. You start with a prior on each hypothesis (possible universe) and then update by weighting each by how many observers in your epistemic situation each universe has.
This perspective sees the equalization of “anthropic probability mass” between possible universes prior to apportionment as an unnecessary distortion of the process: after all, “why would you give a hypothesis an artificial boost in likelihood just because it posits fewer observers than other hypotheses”.
Of course, this is just the flip side of what SSA sees as an unnecessary distortion in the other direction. “Why would you give a hypothesis an artificial boost due to positing more observers” it says. And here we get back to deep-seated differences in what people consider the intuitive way of doing things that underlie the whole disagreement over different anthropic methods.