[W]e all know that arguments from authority carry little weight: what should sway you is not the mere fact of some other person stating their opinion, but the actual arguments and evidence that they’re able to bring. Except that as we’ve seen, for Bayesians with common priors this isn’t true at all! Instead, merely hearing your friend’s opinion serves as a powerful summary of what your friend knows. And if you learn that your rational friend disagrees with you, then even without knowing why, you should take that as seriously as if you discovered a contradiction in your own thought processes. This is related to an even broader point: there’s a normative rule of rationality that you should judge ideas only on their merits—yet if you’re a Bayesian, of course you’re going to take into account where the ideas come from, and how many other people hold them! Likewise, if you’re a Bayesian police officer or a Bayesian airport screener or a Bayesian job interviewer, of course you’re going to profile people by their superficial characteristics, however unfair that might be to individuals—so all those studies proving that people evaluate the same resume differently if you change the name at the top are no great surprise. It seems to me that the tension between these two different views of rationality, the normative and the Bayesian, generates a lot of the most intractable debates of the modern world.
Scott Aaronson, ‘Common Knowledge and Aumann’s Agreement Theorem’, Shtetl-Optimized, August 14, 2015