You could’ve said it simpler: Reading a couple of essays on the subject written by a person is more informative about whether the person is reasonable about that subject than learning whether the person is a theist.
Well, that’s true, but it misses the point that not only is the “reading essays” evidence more informative than the “theist” evidence, the former radically changes how you should update on the latter. If most of the probability flow from “theist” to “wrong about other subject” flows through the bit that “reading essays” makes improbable, then to make up arbitrary exaggerated numbers with the right qualitative behavior:
You could’ve said it simpler:
Reading a couple of essays on the subject written by a person is more informative about whether the person is reasonable about that subject than learning whether the person is a theist.
Well, that’s true, but it misses the point that not only is the “reading essays” evidence more informative than the “theist” evidence, the former radically changes how you should update on the latter. If most of the probability flow from “theist” to “wrong about other subject” flows through the bit that “reading essays” makes improbable, then to make up arbitrary exaggerated numbers with the right qualitative behavior:
log(P(wrong|theist)/P(wrong|~theist)) = L(wrong|theist) = 0.1
L(wrong|reasonableessays) = −1.0
L(wrong|theist&reasonableessays) = −0.99 rather than −0.9.