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prase comments on Popperian Decision making - Less Wrong
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There is a correct P(T0|X) where X is your entire state of information. Probabilities aren't strictly speaking subjective, they're subjectively objective.
"Subjectively objective" just means that trying to do the best you can doesn't leave any room for choice. You can argue that you aren't really talking about probabilities if you knowingly do worse than you could, but that's just a matter of semantics.