Having said that, I believe that your "against the tide" is not the average tide, but more from informed reference group kinds of waves.

Yes, this is a good clarification. I'm assuming that you're going against the opinions of other people who have put significant effort in determining their opinions and have some skill in the domain in question, not merely guessing or, more likely, simply repeating the opinions of other people. As a simple example of this, we could imagine a case where 4 people copied the same answer on a test and you got a different answer than that person. You're really only comparing your answer to one "real" answer at that point, you're not really "going against the tide".

Interestingly, this also hints at a problem we encountered as we began to apply various math algorithms to our information rating software. Our first approach was to directly apply Bayes theorem to calculating probabilities using each person's opinion probability as separate evidence.

But an implicit assumption of Bayes theorem is that each new evidence is really "new" evidence that is independent of the evidence that has already been evaluated. Unfortunately, with people's opinions, often they are just repeating the opinions of someone else and no (or at least not much) new evidence is being provided. So applying Bayes theorem would incorrectly lead to high certainty probabilities very quickly because of this flawed assumption of each opinion being new evidence.