The first bartender states his estimate for the best drink.
The second bartender has her own estimate, but knows that the first bartender is also qualified to make a good estimation. Her estimate of the quality of the martini thus increases. She compares her earlier estimate of the quality of the gin and tonic to the updated estimate for the martini, and finds the gin and tonic to still be the better drink.
The first bartender hears this, and increases his estimate of the gin and tonic's quality - not only does the second bartender think the gin and tonic is better, she thinks it's better even though he recommended the martini. He compares his new estimate of the quality of the gin and tonic to his estimate of the quality of the martini and finds the martini to still be superior.
Etc. etc. etc. (http://en.wikipedia.org/wiki/Aumann%27s_agreement_theorem).
Haven't you got more iterations than is necessary for Aumann's?
This is one of two autobiographies (along with Ben Franklin's) to actually change my life. I've seen it quoted often on LessWrong, as Feynman has a point of view on life that fits well with the ideas we explore here. In addition to his rationalist side, Feynman also exhibited a wonderfully free sense of humor. Even when working at the Manhattan Project, he joked around and never took himself too seriously. I think our community would benefit if the rationalism here were likewise leavened by some self-deprecating humor.
I will mail the autobiography, at my expense, to whomever posts the best corny rationalist joke in the comments below, as judged by karma voting. Anything goes. Here's a little inspirational prompting:
Edit (April 12th): The winner of the corny rationalist joke contest is this one-liner by SilasBarta, which collected 17 net up-votes:
The runner-up (and my personal favorite) is this exchange by Bo102010, which collected 14 net up-votes. The full comment thread for this one has an explanation and suggested refinements.
Thanks to everybody who contributed and voted on corny jokes.