Comment by krackers

no in fact that's the proof that adding Bob doesn't help. If Alice & Bob disagree, then since both are correct with same probability it doesn't matter if you pick alice or bob. So WLOG you choose to trust Alice. But now when Alice and Bob agree, that means that you also trust Alice's output [as in you're only right if Alice is right (which is same as when Bob's right since Bob and Alice match)]. So in both cases you are right when Alice is right, i.e. you trust Alice and that means you don't even care about Bob's output.

I think why it feels odd is that most people intuitively answer a different question. If you had to bet on an outcome then Alice and bob agreeing gives you more information. But here you're not dealing with that question, you're either right and wrong; and whether or not Alice & Bob agree, you're effectively "wagering the same" in both cases (where your wager is 0.8, the probability [or expectation] that one is correct).