I recently got around to reading Scott Aaronson's Complexity of Agreement: http://www.scottaaronson.com/papers/agree-econ.pdf
One of the predictions of this paper is that rational Bayesians sharing information will a) rapidly converge to agreement and b) after making arguments, will often switch sides. An individual's position in an argument will look like a convergent random walk rather than a gradual concession in a negotiation. Of course, real life arguments rarely go this way [1].
But when reading this, I was struck by the fact that in some rare cases I have engaged in arguments that move this way. In every case I can think of, the other participant in the conversation was either a mathematician, a philosophers or a lesswrong reader.
[1] One rare exception to this is real life arguments about what a stock price should be. Yay for market transmission of information!