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Jonathan_Graehl comments on Bayesian Utility: Representing Preference by Probability Measures - Less Wrong
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I see - by "prior" you mean "current estimate of probability", because P was defined
I've been dealing lately with learning research where "prior" means how likely a given model of probability(outcome) is before any evidence, so maybe I was a little rigid.
In any case, I suggest you consistently use "probability" and drop "prior".