Reckoning With Risk: learning to live with uncertainty, by Gerd Gigerenzer

What do David Blunkett's plan to overhaul cannabis laws and Alan Milburn's initiative to detain people with severe personality disorders have in common? Both were justified on the basis of their capacity to reduce harm and fought over by parties wielding conflicting assessments of the risks involved. More than ever, citizens need to know how to evaluate risk.

Enter Gerd Gigerenzer, a German psychology professor with a simple brief: to help us to avoid coming unstuck when confronted with seemingly impermeable representations of risk. With admirable patience, he sets about explaining "mind tools" that we can use to interrogate faulty statistical methods and to iron out ambiguities in the presentation of statistical evidence.

Gigerenzer's first rule of thumb is to beware statistics that leave ambiguous the class to which they refer. When a German magazine informed readers that 10 per cent of women will develop breast cancer, it neglected to mention that women are much more vulnerable to breast cancer later in life, that its data referred to the chances of cancer developing by the age of 85 and that most women who contract it at this age are likely to die of some other cause.

The solution to such statistical mirages, Gigerenzer advises, is to express probabilities in terms of their "natural frequency" within a period of time or a particular group, rather than in blunt percentage points – only four women in a thousand will develop breast cancer by the age of 40.

The second bugbear is just as menacing, and concerns the presentation of data in relative rather than absolute form. Journalists in the UK reported that women using the contraceptive pill were twice as likely to develop deep-vein thrombosis as non-users. The ensuing panic led to a temporary increase in abortions and unwanted pregnancies. If women had told that the chances of deep-vein thrombosis increase from only 1 in 14,000 to 2 in 14,000 when they use the pill, they would have concluded that the risk was relatively high compared to non-users – but still absolutely tiny.

The author is clearly an academic in love with his subject. His case studies, both real and hypothetical, are consistently fascinating: the tale of a group of prisoners on death row, attempting to work out the odds that each will be pardoned by a benevolent king; a survey of the wildly differing ways in which Aids counsellors express the risk of contracting the disease; or how prosecutors manipulated mathematical probability in an attempt to convict OJ Simpson.

If there is a fault, it is that Gigerenzer has little to say about why our ignorance of the rules of uncertainty has become an epidemic. He blames interest groups for manipulating figures but fails to explain why scare stories find such a rapt audience. In a society predisposed to fearing the worst, however, Reckoning With Risk may help to slow the ghost train. The book should be pressed into the palms of politicians, journalists, health professionals – and anyone who has ever read an alarming statistic.