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jimmy comments on On the Anthropic Trilemma - Less Wrong
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I wrote in 2001:
Think of it as an extension of Eliezer's "make beliefs pay rent in anticipated experiences". I think beliefs should pay rent in decision making.
Katja, I'm not sure if this is something that has persuasive power for you, but it's an idea that has brought a lot of clarity to me regarding anthropic reasoning and has led to the UDT approach to anthropics, which several other LWers also seem to find promising. I believe anthropic reasoning is a specialization of yours, but you have mostly stayed out of the UDT-anthropics discussions. May I ask why?
I used to have the same viewpoint as your 2001 quote, but I think I'm giving it up. CDT,EDT, and TDT theorists agree that a coin flip is 50-50, so probability in general doesn't seem to be too dependent on decision theory.
I still agree that when you're confused, retreating to decisions helps. It can help you decide that it's okay to walk in the garage with the invisible dragon, and that it's okay for your friends to head out on a space expedition beyond the cosmological horizon. Once you've decided this, however, ideas like "there is no dragon" and "my friends still exist" kinda drop out of the analysis, and you can have your (non)existing invisibles back.
In the case of indexical probabilities, it's less obvious what it even means to say "I am this copy", but I don't think it's nonsense. I changed my mind when JGWeissman mentioned that all of the situations where you decide to say "1/2" in the sleeping beauty problem are one's where you have precisely enough evidence to shift your prior from 2/3 to 1/2.
Just because it all adds up to normalcy doesn't mean that it is irrelevant.
It is more elegant to just have a decision theory than to have a decision theory and a rule for updating, and it deals better with corner cases.