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PhilGoetz comments on [LINK] The Wrong Objections to the Many-Worlds Interpretation of Quantum Mechanics - Less Wrong Discussion
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The probability of the postulates all being true goes down as you add postulates. The probability of the theory being correct given the postulates may go up.
This assumes the postulates are interdependent such that the theory may be true with all postulates, but false with all postulates save one. In this case, the theories are the same except for the collapse postulate, which may or may not have any real-world consequences, depending on whether you believe decoherence accounts for the appearance of collapse all by itself.