Q&A: Doubt and Statistics Lecture 8
Doubt and Statistics Lecture 8
Question
Hello
You argued there that the Sefer HaChinukh claims that the fact that most judges are right in most cases is a kind of a priori assumption of logic, without any real reason for it. A kind of symmetry consideration that says there is no reason to prefer the opposite.
I wonder whether this cannot be derived from the law of large numbers, once we define the certification required to judge as one that at least makes it possible for him to be correct with a higher probability in the individual case.
(And from there, a lower probability of error when there are multiple opinions.)
Answer
It amounts to the same thing. The assumption that each judge is right in most cases is itself an a priori assumption that cannot be measured. From that point on, you can do the calculation for three judges. By the way, I did it in one of the columns.
Discussion on Answer
No, because even if you do that, it’s still an absent majority. Besides, tests on questions that have simple answers are not representative of rulings on new questions.
Yes, actually the continuation of the lecture really does talk exactly about that; I asked in the middle because I was worried I’d forget…
By the way, I understand why we can’t measure it; I was trying to suggest that the certification itself would define it. For example, by measuring his proficiency on questions that have answers, and from there generalizing to the cases before us. Isn’t that a generalization from a relevant parameter?