The death this week of Nobel laureate (and relativity denier!) Maurice Allais reminds me that I’ve been meaning to blog about Allais’s famous challenge to the way economists think about rational decision making.
I’m going to ask you two questions about your preferences. In neither case is there a right or a wrong answer. A perfectly rational person could answer either question either way. But I do want you to think about your answers, and to write them down before you read any further.
Question 1: Which would you rather have:
- A million dollars for certain
- 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.
Try taking this seriously. What would you actually do if you faced this choice? Don’t bother trying to figure out the “right” answer, because there is no right answer. Some perfectly rational people choose A, and other perfectly rational people choose B.
Okay, ready for the next question?
Question 2: Which would you rather have:
- A lottery ticket that gives you an 11% chance at a million dollars (and an 89% chance of nothing)
- A lottery ticket that gives you a 10% chance at five million dollars (and a 90% chance of nothing)
Once again, this is a matter of preference. There is no right or wrong answer. But decide what your answer is and write it down before you continue.
Okay, ready? As I said, there is no such thing as an irrational answer to either of these questions. But arguably, there is such a thing as an irrational pattern of answers. If you answered “A” to both questions, that’s fine. If you answered “B” to both questions, that’s also fine. But if you answered “A” to the first and “B” to the second, as many people do, then we have a problem here.
To see why, I want you to answer one more question. Imagine I’ve got an urn with 89 red balls, 10 black balls and 1 white ball. I’m going to write dollar amounts on these balls, then let you choose one at random and award you the corresponding prize. I’ve already written some dollar amounts on the red balls but I haven’t gotten around to the blacks and whites yet.
Question 3: Which would you prefer that I write?
- One million dollars on each of the 10 black balls and one million dollars on the white ball.
- Five million dollars on each of the 10 black balls and zero on the white ball.
Try writing down your answer to that one.
Now: I claim that if you are a rational person in the sense that economists traditionally understand the word, your answer to Question 3 must be the same as your answer to Question 1 — because Question 3 is the same as Question 1, provided I’ve written “one million dollars” on each of the 89 red balls.
And I also claim that if you are that rational person, your answer to Question 3 must be the same as your answer to Question 2 — because Question 3 is the same as Question 2, provided I’ve written “zero” on each of the 89 red balls.
So if you answered “A” to all three questions, congratulations — economists pronounce you rational! Likewise if you answered “B” to all three questions. But if your answers included both an “A” and a “B”, economists see a problem here — though as Allais pointed out, a lot of people give mixed answers, so you’ve got plenty of irrational company. Whether the problem is really with you or with the economists is a question I’ll come back to in a few days, once you’ve had time to ponder this.