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Mitchell_Porter comments on Which Basis Is More Fundamental? - Less Wrong
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The evolving basis of mangled worlds is meant to explain the Born probabilities, by producing worlds in the correct multiplicities to reproduce observed frequencies. If you ignore this, you're discarding the very rationale of mangled worlds.
I didn't express myself clearly when I wrote, "So what's to stop them from disregarding the role of Hanson's evolving projection operator's basis?". I didn't mean that "positionists" would disregard the role that Hanson's bases might have in explaining the Born probabilities. I just meant that positionists would deny that this role confers the "ontological fundamentalness" that they reserve for the position basis.
Normally, if a basis is regarded as ontologically fundamental, it is because all one's worlds are basis vectors in that basis. "Alive plus epsilon dead" and "dead plus epsilon alive" are definitely not basis vectors from the position basis.
Anyway, the important fact is that for Robin's scheme to work, each individual world must have small amplitudes of other configurations shadowing the dominant configuration. It's a sign that it's a contrivance, that it doesn't work. Do the small-amplitude copies of me in other states that shadow me in this individual world also have experiences? If so, doesn't that screw up the reproduction of the Born probabilities? Because that is all about just counting the dominant configuration.