Even really, really smart people make mistakes

Keith Landsburg has a neat post on the Allais Paradox:

Question 1: Which would you rather have:

1. A million dollars for certain
2. A lottery ticket that gives you an 89% chance to win a million dollars, a 10% chance to win five million dollars, and a 1% chance to win nothing.

Question 2: Which would you rather have:

1. A lottery ticket that gives you an 11% chance at a million dollars (and an 89% chance of nothing)
2. A lottery ticket that gives you a 10% chance at five million dollars (and a 90% chance of nothing)
...
Allais proceeded to demonstrate that while the Savage axioms allow rational people to choose 1A and allow other rational people to choose 2B, they don’t allow any one rational person to choose both 1A and 2B. Therefore, he triumphantly announced, Savage must either abandon his axioms or confess to his own irrationality.