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:
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.