The rational lottery

Until recently it was assumed that people mostly thought and acted rationally - indeed all economic theories were based on the assumption that firms would maximise their profits and consumers would spend in such a way as to maximise the ratio of their benefits to costs. Work undertaken over the past 30 years or so has shown that this picture of the human mind is not merely glamourised but false. Ministries of defence continue to pursue projects they have started even after it has become obvious that the additional money will achieve nothing: they cannot accept the money already spent has been wasted. People are less likely to opt for an operation if told they have a 7 per cent chance of dying in the course of it than if told they have a 93 per cent chance of survival. And the citizens of Britain pump money into the National Lottery even though their chances of winning a £1 million would be much greater if they were to play roulette (starting with a £1 stake and betting their gains repeatedly on red or black, they would need 20 consecutive wins).

Psychologists have worked out many of the reasons for irrational thinking. For example, we tend to plump for what first comes to mind. Most people believe there are more murders than suicides: it is, of course, the other way round, but because murders are more sensational and are more often reported they are more salient. Causes are more striking than effects, with the result that many people believe that it is more likely that a mother will have a daughter with blue eyes than that a daughter will have a mother with blue eyes.

Some well-attested errors are hard to explain. Many doctors having performed a test (for example, mammography) that yields conclusive evidence of an illness (breast cancer) will perform another test (a breast biopsy) before operating, although they know they will operate even if the second test is negative. This phenomenon - seeking confirmation when one is going to proceed even if confirmation is lacking - has been repeatedly demonstrated but is hard to understand.

There are very few books on irrationality available to the public and Inevitable Illusions concentrates on one aspect - people's inability to handle probabilities. Here is a version of the sort of problem it deals with. An illness is present in one person in a thousand; there is a test for it that yields a positive result in 5 per cent of people who do not have the illness. At Harvard, 60 doctors and medical students were asked what percentage of people who tested positive would have the disease. Only 11 gave the correct answer - 2 per cent. Clearly, high intelligence does not protect against gross errors. Massimo Piatelli-Palmerini is aware that not everyone can be expected to have an elementary knowledge of probability theory, but the mistakes on such problems come from ignoring the base rate (only one in a thousand has the disease) and people could be trained to take it into account even if they do not follow formal mathematical procedures.

The material Piatelli-Palmarini presents is fascinating, but the book is hard going. He sometimes fails to say what he means or even to give the reader the information needed to understand a point. Words are used imprecisely - "casually'' for "randomly'' - it is given to slang, cliche ("79 per cent is not peanuts") and repetition, and condescends to the reader - "Think!".

The book is useful for the new material it contains, but readers would do well first to digest John Paulos's superb Innumeracy.

Finally, one wonders whether the author was wholly rational in giving way to political correctness by using throughout the book the word "she'' as the generic singular pronoun: female readers may well be displeased, since they are after all no more likely to commit the egregious errors attributed to them than are men.

Stuart Sutherland is the author of Irrationality: The Enemy Within.