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EHeller comments on Open thread, August 5-11, 2013 - Less Wrong Discussion
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Well, you still need a host of ideas about how to actually interpret a diagonal density matrix. Because you don't have Born probabilities as a postulate, you have this structure but no method for connecting it back to lab-measured values.
While it seems straightforward, its because many-world's advocates are doing slight of hand. They use probabilities to build a theory (because lab experiments appear to be only describable probabilistically), and later they kick away that ladder but they want to keep all the structure that comes with it (density matrices,etc).
I know of many good expositions that start with the probabilities and use that to develop the form of the Schroedinger equation from Galilean relativity and cluster decomposition (Ballentine, parts of Weinberg).
I don't know any good expositions that go the other way. There are reasons that Deutsch, Wallace,etc have spent so much time trying to develop Born probabilities in a many world's context- because its an important problem.
Hold on a moment. What ladder is being kicked away here?
We've got observed probabilities. They're the experimental results, the basis of the theory. The theory then explains this in terms of indexical ignorance (thanks, RobbBB). I don't see a kicked ladder. Not every observed phenomenon needs a special law of nature to make it so.
Instead of specially postulating the Born Probabilities, elevating them to the status of a law of nature, we use it to label parts of the universe in much the same way as we notice, say, hydrogen or iron atoms - 'oh, look, there's that thing again'. In this case, it's the way that sometimes, components of the wavefunction propagate such that different segments won't be interfering with each other coherently (or in any sane basis, at all).
Also, about density matrices - what's the problem? We're still allowed to not know things and have subjective probabilities, even in MWI. Nothing in it suggests otherwise.