Here is an attempt at an updateless answer, because the problem is too confusing for me from an individual perspective. I'm not sure in how far this contradicts my earlier answer.
Assume multiverse branches A and B with equal mesure/prior probability. A has 99 times as many instances of the agent as B. If the agent weights the consequences of the actions of each instance equally the instances of the agent will in most cases behave like individualist single world agents believing "A" to be true with 0.99 confidence. Most human level problems probably are of that type. There may be problems where the majority answer in A and B is equally important, or some other weighting where the answer in A is not 99 times as important as the one in B. In those cases the agent won't behave like agents believing in "A" with 0.99 confidence.
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.