The Better Angels of Our Nature: A History of Violence and Humanity

by Steven Pinker

The probability of a conjunction of events (A and B both occurring) cannot be greater than the probability of either of them occurring alone. The probability that you will draw a red jack has to be lower than the probability that you will draw a jack, because some jacks you might draw are not red. Yet Tversky and Kahneman have shown that most people, including statisticians and medical researchers, commonly make the error.263 Consider the case of Bill, a thirty-four-year-old man who is intelligent but also unimaginative, compulsive, and rather dull. In school he was strong in mathematics but undistinguished in the arts and humanities. What are the chances that Bill plays jazz saxophone? What are the chances that he is an accountant who plays jazz saxophone? Many people give higher odds to the second possibility, but the choice is nonsensical, because there are fewer saxophone-playing accountants than there are saxophone players. In judging probabilities, people rely on the vividness of their imaginations rather than thinking through the laws. Bill fits the stereotype of an accountant but not of a saxophonist, and our intuitions go with the stereotype. The conjunction fallacy, as psychologists call it, infects many kinds of reasoning. Juries are more likely to believe that a man with shady business dealings killed an employee to prevent him from talking to the police than to believe that he killed the employee. (Trial lawyers thrive on this fallacy, adding conjectural detai...