Clearly you understand me now, and I think that I understand you.
A “bit of evidence” does not unambiguously tell someone whether you mean probability-bit or odds-ratio-bit, and Eliezer does not distinguish between them properly.
OK, if what is at issue here is whether Eliezer was sufficiently clear, then I’ll bow out. Obviously, he was not sufficiently clear from your viewpoint. I will say, though, that your comment is the first time I have seen the word “evidence” used by a Bayesian for anything other than a log odds ratio.
Log odds evidence has the virtue that it is additive (when independent). On the other hand, your idea of a log probability meaning of ‘evidence’ has the virtue that a question can be decided by a finite amount of evidence.
Ok, I think you are misinterpreting, but I see what you mean. When EY writes:
...I have transmitted three bits of information to you, because I informed you of an outcome whose probability was 1⁄8.
I take this as illustrating the definition of bits in general, rather than bits of ‘evidence’. But, yes, I agree with you now that placing that explanation in a paragraph with that lead sentence promising a definition of ‘evidence’ - well it definitely could have been written more clearly.
Clearly you understand me now, and I think that I understand you.
OK, if what is at issue here is whether Eliezer was sufficiently clear, then I’ll bow out. Obviously, he was not sufficiently clear from your viewpoint. I will say, though, that your comment is the first time I have seen the word “evidence” used by a Bayesian for anything other than a log odds ratio.
Log odds evidence has the virtue that it is additive (when independent). On the other hand, your idea of a log probability meaning of ‘evidence’ has the virtue that a question can be decided by a finite amount of evidence.
Eliezer used it to mean log probability in the section that I quoted. That was what I was complaining about.
Ok, I think you are misinterpreting, but I see what you mean. When EY writes:
I take this as illustrating the definition of bits in general, rather than bits of ‘evidence’. But, yes, I agree with you now that placing that explanation in a paragraph with that lead sentence promising a definition of ‘evidence’ - well it definitely could have been written more clearly.