[Joker_vD]

> the MWI has to somehow define a formal notion of an observer/a classical world

Yes: in MWI, those things don't exist. The world is quantum all the way up and all the way down, observers are simply (other) quantum system that get to interact with the quantum system under the consideration. An observation, then, is simply an interaction between two quantum systems and follows all the usual rules so instead of the wave-function collapse leaving you with the observed system in pure state X and the observer is in pure state Y, you get a huge superposition of "the observed system in pure state Xi, the observer is in pure state Yi" states in the end. Those substates, in a sense, are multiple worlds.

[tsimionescu]

You're missing the point I was highlighting. Quantum mechanics makes very specific, very precise predictions about the probabilities of an observer seeing any of those states, which we have confirmed are correct to extraordinary precision.

The problem is explaining what is the relationship between these observed probabilities and the wave function amplitudes. If we say that all possible quantum states are realized in the universal wave function, we the need to explain why different states have different probabilities to an observer. The only way to do that in the deterministic world of MWI is to add a new postulate: one that says that for any state Xi, there are N observers in state Yi, where N = |psi(Xi)|, so that we can compute regular frequentist probabilities of an observer seeing a particular state over the amount of observers.

This is perfectly reasonable, but it is just as much an extra postulate as the measurement postulate.