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dvasya comments on Common sense quantum mechanics - Less Wrong Discussion
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I'm not sure "not-MWI" is a single coherent interpretation :) Under Copenhagen, for example, the Born rule has to be postulated. The present paper
MWI also postulates it, see V_V's comment.
As for the paper's assumptions, they seem to be no different than the assumptions of normal probabilistic reasoning as laid out by Cox/Polya/Jaynes/etc., with all that ensues in regard to relevance.
(edit: formatting)
I have never seen anything other than MWI which even comes close to justifying the Born probabilities except by emulating MWI.