Nice article Kaj -- this is a phenomena I've come up against myself several times, so it's really nice to see a carefully worked analysis of this situation. In a probabilistic sense, perhaps intuitive differences are priors that arise from evidence that a person no longer recalls directly, so although the the person may have rationally based their belief on evidence, they are unable to convince another person since they do not have the original evidence at hand. I'm particularly thinking of cases where "evidence" comprises many small experiences over a prolonged period, making it particularly difficult to replay to another person. A carpenter's intuition about the strength of a piece arises from their experiences working with wood, but no single piece of evidence could be easily recalled to transfer that intuition to someone else.