So, if asked to assign a probability to an arbitrary A, you’d say p = 0.5. But if you were given evidence in the form of some constraints on p, say that p ≥ 0.8, you’d set p = 0.8, as that was the new entropy-maximising level. Constraints are restricted to Affine constraints. I found this somewhat counter-intuitive already, but I do follow what he means.
This bit doesn’t make sense either, what kind of evidence imposes a condition on your personal (subjective) probability?
I think you’re misunderstanding me, but I can’t think of a way to better phrase what I said, sorry.
Maybe if I put it thus: I can’t think of a situation where some evidence E will make my posterior probability P(A|E) greater than 0.8 regardless of my prior P(A).
Yeah, re-reading the quote, I see what you mean. He seems to have confused a frequency with a probability distribution over possible values of the frequency. Maybe that’s why he made the other error that the post discusses.
This bit doesn’t make sense either, what kind of evidence imposes a condition on your personal (subjective) probability?
A subjective probability is not arbitrary. It is the most accurate estimate possible given the evidence to the subject. See http://lesswrong.com/lw/s6/probability_is_subjectively_objective .
I think you’re misunderstanding me, but I can’t think of a way to better phrase what I said, sorry.
Maybe if I put it thus: I can’t think of a situation where some evidence E will make my posterior probability P(A|E) greater than 0.8 regardless of my prior P(A).
Yeah, re-reading the quote, I see what you mean. He seems to have confused a frequency with a probability distribution over possible values of the frequency. Maybe that’s why he made the other error that the post discusses.