students to reveal their own logical errors. This approach is an effective way to teach, but one that can be painful for the student as they learn the limits of their knowledge.

As we embark on learning about the science of irrationality, the unpleasant message is that all humans are built to make certain sorts of mistakes. Its all fun and games until the irrationality comes home to roost in our own brains. Then rather than learn, our instincts direct us to close the eyes, cover the ears, and deny the truth that we, too, are irrational. In all the oral stories of Homer, the only known reference to writing comes in the form of a secret message. It is in the Iliad, when Queen Antea falls in love with handsome Bellerophon who spurns her love. Enraged, Queen Antea convinces her husband, King Proteus, to kill Bellerophon (Antea does not reveal her secret and adulterous love).

Proteus wants to kill Bellerophon, but shies away from doing the dirty work himself. Instead he has Bellerophon travel to another kingdom, bearing a secret message for the ruler of the neighboring land. The content of the secret note is kill the messenger. So, one of the first mentions of writing reveals a human tendency to kill the messenger.

The reward, however, for not killing the messenger and critiquing ones own behavior can be large. After the 1997 Masters golf championship, Tiger Woods reevaluated his game. In the Masters, he had dominated the field and won by a record 12 strokes. Furthermore, in less than one year on the professional tour, Tiger won four events, earned over a million dollars, and became a worldwide celebrity.

After this initial round of fame and success, what was Tigers view of his game? He decided that he needed to fundamentally change his swing. In an interview with Time magazine (August 14, 2000), looking back on the decision, he told writer Dan Goodgame:

I knew I wasnt in the greatest positions in my swing at the [1997] Masters. But my timing was great, so I got away with it. And I made almost every putt. You can have a wonderful week like that even when your swing isnt sound. But can you still contend in tournaments with that swing when your timing isnt as good? Will it hold

up over a long period of time? The answer to those questions, with the swing I had, was no. And I wanted to change that.

Tiger went back to the drawing board. He revamped his swing, suffered through some disappointments, but ultimately emerged as the dominant player in the game. At one point, Woods lead over the second-ranked player was larger than the gap between No. 2 and No. 100.3 He went from being a great player to perhaps the greatest player of all time. The lesson is clear: Winning requires critical self-examination. If Tigers game needed improvement and benefited from some objective review, the rest of us surely can profit from honing our investment skills.

The Science of Individual Irrationality

The debate about irrationality has two components. First, do individuals make good decisions? Second, are market prices correct? While there is still a debate about the efficiency of market prices (well cover this topic in the next chapter), the first question has been answered. Over the last 30 years, a significant body of research has clearly illustrated our human shortcomings.

In the late 1970s, Professors Daniel Kahneman and Amos Tversky began the rigorous documentation of human decision-making problems. One of Kahneman and Tverskys famous experiments concerns the hypothetical woman named Linda. Heres what they asked in the experiment:4

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.

Which of these two alternatives is more probable?

1. Linda is a bank teller.

2. Linda is a bank teller and is active in the feminist movement.

Take a moment to answer the question (well get to the correct answer shortly). First, know that most people provide the wrong answer, and there is an intellectual debate over how to interpret the errors. Old-school economists have said that the errors were caused by poor experimental design. Their first response was to deny the evidence that humans make the mistakes shown by behavioral economists.

Behavioral economists refined their techniques and provided proof that people make mistakes in many important areas, going far beyond the Linda problem. Mainstream economists no longer refute this evidence, but still insist that models of robotic, cool-headed decision making are appropriate. In contrast, behavioral economists believe that conventional theories about rational behavior need to be fundamentally revised.

Back to Linda. What was your answer? The correct answer is: Linda is a bank teller. Of all the bank tellers in the world, only some of them are active in the feminist movement. This is true for any two attributes. Consider 100 college athletes. How many of them are women? How many are women and over 6 feet tall? Without knowing anything about the group of 100, the number of tall women cannot exceed the number of women. Similarly, there have to be more bank tellers than there are bank tellers who are also feminists.

People who answer number two in the Linda-the-bank-teller problem suffer from what Kahneman and Tversky label the conjunction fallacy : The conjoined probability of two statements must be lower than for either of the individual statements. Of the people in Kahneman and Tver-skys experiments, 85% gave the wrong answer. Why do we do so poorly on such simple tests?

Rocket Scientists Who Cant Figure

Part of the cause of our individual irrationality is that we arent very good at doing calculations.

In one of my Harvard Business School classes we investigate the causes behind corporate waste. We examine situations in which executives