pines-demon said:
Most of these observers get results that map correctly to the predictions of quantum mechanics.
"Most" is subjective. So is "map correctly", since we are talking about statistical comparisons.
But leaving that aside, if you are going to say that "probability" in the MWI means "relative frequencies of observed outcomes in a particular world (i.e., decoherent branch of the wave function)", then you are defining "probability" so that you can adopt the Born Rule as an additional postulate and using a version of the "MWI" that includes that additional postulate. But MWI proponents don't do that. They claim they can
derive the Born Rule in the MWI without having to assume it as an additional postulate. And they can't do that by
defining "probability" to mean "relative frequencies of observed outcomes in a particular world", because then their claimed "derivation" of the Born Rule would be circular. They have to come up with some
independent formulation of the concept of "probability" in the MWI that doesn't depend on relative frequencies of observed outcomes in a particular world, and
then use that to derive the Born Rule.
pines-demon said:
If they are "the same" themselves (whatever that means) as before the branching is not very relevant here.
If it's not very relevant, why did you go to the trouble of making a claim about it?
That said, I agree the question of whether observers are "the same" before and after branching is indeed irrelevant to formulating a concept of probability in the MWI. But in the posts I was responding to (by others, not by you), claims were made about "random selection" of which outcome an observer observes. Getting clear about exactly what "an observer"
means (and doesn't mean) in this context
is relevant to rebutting those claims, which is what I was doing. You, as far as I can tell, have not made those claims, so you might not be making the same conceptual mistakes the other posters I was responding to were making.