In this, belief set A and belief set B are analogous to A[C] and C (or some c in C), right?
Yes.
If we replace our beliefs with A[C]’s, then how is that us trusting it “over” c or C? It seems like it’s us trusting it, full stop
So I only showed the case where info contains information about A[C]’s predictions, but info is allowed to contain information from A[C]andC (but not other agents). Even if it contains lots of information from C, we still need to trust A[C].
In contrast, if info contained information about A[A[C]]’s beliefs, then we would not trust A[C] over that.
Yes.
So I only showed the case where info contains information about A[C]’s predictions, but info is allowed to contain information from A[C] and C (but not other agents). Even if it contains lots of information from C, we still need to trust A[C].
In contrast, if info contained information about A[A[C]]’s beliefs, then we would not trust A[C] over that.