I'm thinking about cases where you receive advice from two people who are (i) independent, and (ii) supposed to be competent on getting questions within this domain correct to a probability of >.5
Suppose, for example, that they are each .8 competent at getting questions right.
Person 1 tells you: P!
Then, Person 2 tells you: P!
Intuitively, you should become .8 confident in P after hearing from person 1. (Suppose you were entirely agnostic beforehand, with no particular view).
And, intuitively, you should become MORE confident in P after hearing from person 2.
But if you try to incorporate these two pieces of evidence by multiplying them together -- as in (0.8)*(0.8) -- then you get a LOWER confidence in proposition P than when you only had evidence from one advisor.
What gives?