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potato comments on Naming the Highest Virtue of Epistemic Rationality - Less Wrong Discussion
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No wait, of course not sorry. If P(A) = 1, then P(~A) = 0, and A is false, then your score goes down to negative infinity (kind of, I think).
That only works if the agent's beliefs have that kind of consistency. If it is taken for granted that this scoring only applies for agents with completely consistent beliefs (including complete satisfaction of Bayes' theorem), then I don't think this scoring can be applied to any human.
Hmm, idk bout that. P(a) + P(~a) = 1 seems like something humans do alright with. But of course humans don't really use numbers in the first place. but that does not matter. bayes has been formalized with simple degrees of confidence like: lots, all, not very much, none.
But if you're right then we I'll give up the point and simply penalize for false claims.
But take note that if humans don't have the consistency to satisfy P(a) + P(~a) = 1 they most certainly don't have the consistency to satisfy P(a) = 1 either. So no you could not get a perfect score by setting all your beliefs to 1 because you can't set all your beliefs to 1.
I don't follow the argument. Perhaps we mean different things by 'consistency'? By consistent beliefs, I meant a set of beliefs that cannot be used to derive a contradiction with the usual probability axioms. I was not making a claim about how humans come to believe things.
ETA: About this:
I think you place too much trust in the consistency of human beliefs. In fact, I wouldn't trust myself with that. Suppose you ask me to assign subjective probabilities to 50 statements. Immediately afterwards, you give me a list of the negations of these 50 statements. I'm pretty sure I'll violate P(a) + P(~a) = 1 at least once.
But you'll probably violate it within some reasonable error range. I doubt you would ever get anything as high as 150% given to (a or ~a) if you actually performed this test. And still 1/50 isn't bad.