The Mousetrap and the Economist: How a Discipline Began with a Footnote

Chapter 1: The Mousetrap and the Economist: How a Discipline Began with a Footnote

In the spring of 1969, a young Israeli psychologist named Daniel Kahneman boarded a bus in Jerusalem and rode toward the coast. He was on his way to the army base near Tel Aviv, where he had spent the previous year helping the Israeli Defense Forces build a new system for evaluating officer candidates. He had worked for the Ministry of Defense, he had interviewed hundreds of tired young men in uniform, and he had learned, in the most concrete way a researcher can learn anything, that the human mind does not behave the way the textbooks say it should. The textbooks said that people integrate information according to Bayes' theorem. The young men on the bench in front of him integrated information by gestalt, by gut, by the look in their cousin's eye, by the answer they had rehearsed in the waiting room. Kahneman had walked into the project a credentialed psychologist trained in the mathematical theory of perception. He walked out a man with a different set of questions.

The bus ride itself is not the famous part of the story. The famous part is what happened when he arrived. At a kibbutz south of Haifa, by the Mediterranean shore, Kahneman gave a talk about what he had seen in the interview room. In the audience sat a younger man named Amos Tversky, then a junior faculty member at Hebrew University, who had built his reputation on a startling and slightly irritating paper about how people make decisions when they are uncertain. Tversky was, by Kahneman's later description, brilliant, combative, and almost pathologically skeptical of any claim about human reasoning that could not be tested with numbers. He listened to Kahneman's talk. Then he stood up and said, in effect, that the talk was interesting but unscientific, that the impressions Kahneman had collected were impressions and not data, and that if Kahneman really wanted to understand how people made decisions under uncertainty he ought to come up with a proper experiment.

The two men began to argue. They argued through lunch. They argued through dinner. They argued on the beach, where, by the historian Michael Lewis's later and only partly tongue-in-cheek account, they walked back and forth, gesticulating, while the gulls circled and the Mediterranean went about its business. Within a year, Kahneman would leave his post in Israel and join Tversky at Hebrew University. Within three years they would publish the first of nine papers that would, by 1980, all but dismantle a particular picture of the human mind that economics had carried for two hundred years. And the footnote — the footnote is coming, do not worry — would turn out to be not a footnote at all but the cornerstone of a new science.

But we are getting ahead of the story. Before we can understand what Kahneman and Tversky were trying to break, we have to understand what was already in place. Before we can understand why an entire discipline had to be reinvented to account for the ordinary decisions of ordinary people, we have to understand why an older discipline had worked so well for so long.

The Dream of Rational Man

The story of modern economic thought is, in one telling, the story of a question: what would a person do if she had unlimited time, unlimited information, and unlimited mental capacity? The answer that emerged between the eighteenth and twentieth centuries was so elegant, and so useful, that it survived almost any amount of contrary evidence. We call the answer *the rational-agent model*, and it has roughly the following form.

A person — call her *Eve* — stands in front of a set of possible choices. Each choice has consequences, and the consequences have probabilities. Eve assigns a number, called *utility*, to each possible consequence, in such a way that the numbers reflect the strength of her preferences. She then chooses the act whose expected utility is highest. That is, she multiplies each consequence by its probability, adds up the products, and picks the biggest sum. If Eve is acting on the stock market, the consequences are dollar amounts. If she is acting on the marriage market, the consequences are people. If she is acting on the operating table, the consequences are years of life. The math is the same. Eve's mind, in this picture, is a kind of calculator — fast, accurate, indifferent to framing, immune to mood, and unaffected by the order in which the options are presented. It is a beautiful picture, and it is, of course, entirely fictional.

But it did not begin as fiction. It began as an attempt to solve a real puzzle. The puzzle was first set out by a Swiss mathematician named Daniel Bernoulli in 1738, and it has been called the St. Petersburg paradox ever since. Imagine that a casino offers you the following game. A fair coin is flipped repeatedly until it lands on tails. If the first tails comes on the first flip, you win two dollars. If it comes on the second, you win four. If on the third, eight. And so on, doubling each time. How much would you be willing to pay to play the game?

You can do the math. The expected value of the game is infinite. There is a one-half chance of winning two dollars, a one-quarter chance of winning four, a one-eighth chance of winning eight, and so on. Multiply and add:

$$E = \sum_{k=1}^{\infty} \frac{1}{2^k} \cdot 2^k = \sum_{k=1}^{\infty} 1 = \infty$$

An infinite expected value. A risk-neutral calculator, playing this game over and over, should happily pay any finite sum — a dollar, a thousand dollars, the gross domestic product of a small country — to participate. And yet, when Bernoulli asked sensible people what they would actually pay, they gave answers like two dollars, five dollars, perhaps twenty. There was a yawning gulf between the math and the mind, and Bernoulli's response to the gulf was to propose something radical. He proposed that people do not evaluate outcomes by their dollar amounts at all. They evaluate them by their *utility*, by the subjective satisfaction the dollar amounts produce. And subjective satisfaction, he suggested, is concave: the more dollars you already have, the less an additional dollar matters to you.

A doubling of wealth from one to two million feels good. A doubling from one to two thousand feels like a small miracle. Bernoulli's insight was that utility is *not* proportional to money; it rises more slowly than money. The square root of wealth, he guessed, might be a reasonable approximation of the utility of wealth. Under that assumption, the St. Petersburg paradox dissolves. The expected utility of the game is finite, even though the expected dollar value is infinite, because the marginal utility of each doubling is shrinking fast enough to tame the series.

The idea that people maximize *expected utility* rather than expected dollars became, over the next two centuries, the foundation stone of decision theory. It was developed and formalized by John von Neumann and Oskar Morgenstern in their 1944 masterpiece *Theory of Games and Economic Behavior*. They proved a remarkable theorem. If a person's preferences satisfy a small number of reasonable axioms — completeness (you can compare any two options), transitivity (if you prefer A to B and B to C, you prefer A to C), independence (mixing in a third option does not flip the ranking between two others), and continuity (you are not pathologically indifferent between some pairs and infinitely fussy about others) — then there exists a utility function such that the person chooses, with perfect consistency, the option with the highest expected utility. The person behaves as if she were the calculator in our earlier paragraph. The axioms are the calculator's user manual. And since reasonable people tend to satisfy the axioms, the conclusion is that reasonable people tend to be calculators.

This was a stunning intellectual achievement. It gave economics a vocabulary for talking about choice t