I think we should reason in terms of decisions and not use anthropic updates or probabilities at all. This is what is argued for in Armstrong’s Anthropic Decision Theory, which itself is a form of updateless decision theory.
In my mind, this resolves a lot of confusion around anthropic problems when they’re reframed as decision problems.
If I had to pick a traditional anthropic theory...
I’d pick, in this order,
Minimal reference class SSA
SIA
Non-minimal reference class SSA
I choose this ordering because both minimal reference class SSA and SIA can give the ‘best’ decisions (ex-ante optimal ones) in anthropic problems,[1] when paired with the right decision theory.
Minimal reference class SSA needs pairing with an evidential-like decision theory, or one that supposes you are making choices for all your copies. SIA needs pairing with a causal-like decision theory (or one that does not suppose your actions give evidence for, or directly control, the actions of your copies). Since I prefer the former set of decision theories, I prefer minimal reference class SSA to SIA.
Non-minimal reference class SSA, meanwhile, cannot be paired with any (standard) decision theory to get ex-ante optimal decisions in anthropic problems.
How I think we should do anthropics
I think we should reason in terms of decisions and not use anthropic updates or probabilities at all. This is what is argued for in Armstrong’s Anthropic Decision Theory, which itself is a form of updateless decision theory.
In my mind, this resolves a lot of confusion around anthropic problems when they’re reframed as decision problems.
If I had to pick a traditional anthropic theory...
I’d pick, in this order,
Minimal reference class SSA
SIA
Non-minimal reference class SSA
I choose this ordering because both minimal reference class SSA and SIA can give the ‘best’ decisions (ex-ante optimal ones) in anthropic problems,[1] when paired with the right decision theory.
Minimal reference class SSA needs pairing with an evidential-like decision theory, or one that supposes you are making choices for all your copies. SIA needs pairing with a causal-like decision theory (or one that does not suppose your actions give evidence for, or directly control, the actions of your copies). Since I prefer the former set of decision theories, I prefer minimal reference class SSA to SIA.
Non-minimal reference class SSA, meanwhile, cannot be paired with any (standard) decision theory to get ex-ante optimal decisions in anthropic problems.
For more on this, I highly recommend Oesterheld & Conitzer’s Can de se choice be ex ante reasonable in games of imperfect recall?
For example, the sleeping beauty problem or the absent-minded driver problem