Prostate cancer is another disease for which we have good data. In the U.S. and European countries doctors advise men aged 40 to 50 to take a PSA test. This is a prostate cancer test that is very simple, requiring just a bit of blood, and so many people do it. The interesting thing is that most of the men I've talked to have no idea of the benefits and costs of this test. It's an example of decision-making based on trusting your doctor or on rumors. But interestingly, if you read about the test on the Internet in independent medical societies like Cochran.com, or read the reports of various physicians' agencies who give recommendations for screening, then you find out that the benefits and costs of prostate cancer screening are roughly the following: Mortality reduction is the usual goal of medical testing, yet there's no proof that prostate cancer screening reduces mortality. On the other hand there is proof that, if we distinguish between people who do not have prostate cancer and those who do, there is a good likelihood that it will do harm. The test produces a number of false positives. If you do it often enough there's a good chance of getting a high level on the test, a so-called positive result, even though you don't have cancer. It's like a car alarm that goes off all the time.

For those who actually have cancer, surgery can result in incontinence or impotence, which are serious consequences that stay with you for the rest of your life. For that reason, the U.S. Preventive Services task force says very clearly in a report that men should not participate in PSA screening because there is no proof in mortality reduction, only likely harm.

It is very puzzling that in a country where a 12-year-old knows baseball statistics, adults don't know the simplest statistics about tests, diseases, and the consequences that may cause them serious damage. Why is this? One reason, of course, is that the cost benefit computations for doctors are not the same as for patients. One cannot simply accuse doctors of knowing things or not caring about patients, but a doctor has to face the possibility that if he or she doesn't advise someone to participate in the PSA test and that person gets prostate cancer, then the patient may turn up at his doorstep with a lawyer. The second thing is that doctors are members of a community with professional pride, and for many of them not detecting a cancer is something they don't want to have on their records. Third, there are groups of doctors who have very clear financial incentives to perform certain procedures. A good doctor would explain this to a patient but leave the decision to the patient. Many patients don't see this situation in which doctors find themselves, but most doctors will recommend the test.

But who knows? Autopsy studies show that one out of three or one out of four men who die a natural death have prostate cancer. Everyone has some cancer cells. If everyone underwent PSA testing and cancer were detected, then these poor guys would spend the last years or decades of their lives living with severe bodily injury. These are very simple facts.

Thus, dealing with probabilities also relates to the issue of understanding the psychology of how we make rational decisions. According to decision theory, rational decisions are made according to the so-called expected utility calculus, or some variant thereof. In economics, for instance, the idea is that if you make an important decision — whom to marry or what stock to buy, for example — you look at all the consequences of each decision, attach a probability to these consequences, attach a value, and sum them up, choosing the optimal, highest expected value or expected utility. This theory, which is very widespread, maintains that people behave in this way when they make their decisions. The problem is that we know from experimental studies that people don't behave this way.

There is a nice story that illustrates the whole conflict: A famous decision theorist who once taught at Columbia got an offer from a rival university and was struggling with the question of whether to stay where he was or accept the new post. His friend, a philosopher, took him aside and said, "What's the problem? Just do what you write about and what you teach your students. Maximize your expected utility." The decision theorist, exasperated, responded, "Come on, get serious!"