How do you do Bayesian belief revision when one of your alternative hypotheses uses the anthropic principle? Can you give a strong preference to the hypothesis that does not require it? Because I know that I would.
Your existence can never be Bayesian evidence for you either way due to conservation of expected evidence. Your non-existence can never be Bayesian evidence the other way for you.
In a wider sense it seems far from obvious that a claim like "most observers are instances of probable observers" is true, and even if it is true it's not clear that you are allowed to draw inferences from that as though being a particular instance of you was a random sample, that may be just a malfunction of human reasoning caused by the particular way we evolved. Updateless reasoning suggests that you should not distinguish between yourself and other instances of you in that way.
That's not the question I'm asking. If you have two hypotheses to explain something, and one of them uses anthropic reasoning, and the other does not, how much can you favor the one that does not?
If anthropic reasoning is used to get around a prior of 10^-11, can I favor the hypothesis not requiring anthropic reasoning by a factor of 100? If I favor the latter hypothesis at all, shouldn't that show up in the priors; and shouldn't anthropic reasoning therefore lose out to, eg., the God hypothesis?
I believe that life on Earth arose spontaneously. I also believe the galaxy around me is largely devoid of life. I reconcile these things using the anthropic principle.
I also believe that fundamental cosmological constants have values convenient for the development of life. I don't know if it makes sense to pretend that those constants could have had other values - it seems to me like arguing that e could have been 2.716. But it's certainly done. And again, the anthropic principle is sometimes invoked, as an alternative to, say, God.
Suppose somebody came up with a new theory of cosmological constants, that claimed that only certain values are allowable, and that a large percentage of the allowable sets would make life possible. Then you wouldn't have to use the anthropic principle. Wouldn't you be more comfortable with that?
But if that's so, doesn't it mean that you really attach a low prior to the anthropic principle? And that you don't truly accept the anthropic principle?
How do you do Bayesian belief revision when one of your alternative hypotheses uses the anthropic principle? Can you give a strong preference to the hypothesis that does not require it? Because I know that I would.