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endoself comments on Anthropics in a Tegmark Multiverse - Less Wrong
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I don't recall the suggestion of using the Born probabilities as a test ever having been discussed.
I agree that this could potentially supply strong evidence one way or another, but I do not see any way of deriving the Born probabilities and it seems unlikely that it would be easy to prove that deducing the Born probabilities is impossible, because the derivation might depend on some unknown aspect of physics or consciousness.