Forty per cent chance of war with Iraq" proclaimed a headline in the Daily Mail on the day this review was written in January. Such numbers, devoid of any reference class, Gerd Gigerenzer argues, are meaningless, or at best nothing more than a "degree of belief" converted into a number by unverifiable hunch. What kind of reference class would make such a number meaningful? Perhaps evidence that on 40 per cent of previous occasions in which Iraq found itself in an identical situation war ensued? Or perhaps that 40 per cent of countries in circumstances identical to those experienced by Iraq ended up going to war? Such reference classes do not exist. The start of the war neither proved nor disproved the 40 per cent estimate. Any estimate of a single-event probability that is greater than zero and less than one is irrefutable by subsequent events.
Gigerenzer is a "frequentist"; in this book he focuses on the problem of making sense of information that can be quantified on the basis of frequency data. In so doing he makes a number of points that, if taken on board by experts and the public alike, would raise the level of discussion about risks. One is the importance of understanding the distinction between relative and absolute risk. The case of the contraceptive pill uproar a few years ago illustrates why it matters. A large, and highly publicised, relative increase in a small absolute risk led to a significant increase in unwanted pregnancies and abortions - both of which carried much higher absolute risks than those speculatively associated with the new pill.
Another point that he makes very convincingly is that we all - lay people and experts - find information presented in the form of natural frequencies much more intelligible than information presented as probabilities. In his discussion of HIV testing he combines this point with a discussion of the importance of being clear about the reference group to which the person being tested belongs. A brief summary of his argument goes like this. About .01 per cent of men with no known risk behaviour are HIV positive. The test is 99.9 per cent accurate. Of 10,000 low-risk men, one will be HIV positive and accurately identified as such. Of the other 9,999 one will be wrongly identified as being positive. Thus, if you belong to the low-risk reference group and test positive you have only a 50 per cent chance of actually being positive - a surprising and reassuring conclusion for anyone who tests positive and one, Gigerenzer suggests, that is not sufficiently understood by most Aids counsellors.
He applies a similar analysis to the breast cancer screening debate and concludes that one out of ten women who tests positive actually has breast cancer, and that 41 out of every 42 women in the moderate-risk group who undergo prophylactic mastectomies lose their breasts without a benefit - a conclusion to be borne in mind by readers of a Daily Mail headline on another risk story: "Testing women for breast cancer at 40 can save their lives."
With these and numerous other examples, Gigerenzer makes a compelling case for the need to improve numeracy, and provides helpful suggestions for how this improvement might be brought about. However, in the numerous cases he explores he does not always adhere to his own advice. For example, he laments that a young man is unlikely to know that "his chance of dying on a motorcycle trip is about 15 times higher than his chance of dying on a car trip of the same distance". This number is consistent with figures published by the US fatal accident recording system's comparison of death rates per mile travelled in cars and on motorcycles. But what is the relevant reference group? Young men have much higher than average accident rates whether in cars or on motorcycles. Motorcyclists tend to be young - in Britain, more than 80 per cent of motorcyclist fatalities are under 30.
And motorcyclists tend to be found at the high risk-taker end of the population spectrum, and more dangerous to themselves and others no matter what vehicles they travel in or on.
He also casts aspersions rather liberally. He notes that Washington DC is home to 1,700 trade associations that are "active in the manufacture of knowledge and ignorance". Citing an Environmental Protection Agency report on passive smoking, he is particularly critical of those who doubt that it kills 3,000 Americans a year. Having followed this highly polarised debate for years, I still find the evidence produced by both sides less than conclusive, which leads me to my final complaint. The book claims too much.
It contains much helpful advice about how to reckon with risk, but none about how to live with true uncertainty. Gigerenzer focuses on the problem of making statistical sense of issues that are accompanied by actuarial tables sufficiently large and stable as to permit useful predictions. However, there are two other, much larger, categories of risk into which he does not venture. The first consists of individuals seeking to manage directly perceptible risks - perhaps a cautious middle-aged woman riding a motorcycle on a rainy night. The multitude of risk factors at work in such situations defies actuaries and computers. It is managed instinctively and intuitively by someone who constitutes his or her own unique reference class. The second, even larger, category consists of virtual risks, risks about which science confesses ignorance, or about which reputable scientists disagree in ways that mystify the rest of us.
This is the foggy realm in which the trade associations ply their trades and do battle with their opponents. In this realm doubts are sometimes manufactured - by both sides - but more commonly genuine ignorance is exploited to fit the agenda of the lobbyist.
True uncertainty is liberating; everyone is freed to argue from belief, conviction and prejudice. For those seeking to manage individual directly perceptible risks, or virtual risks, there is little the frequentist can do to help.
John Adams is professor of geography, University College London.
Reckoning with Risk: Learning to Live with Uncertainty
Author - Gerd Gigerenzer
ISBN - 0 14 029786 3
Publisher - Allen Lane The Penguin Press
Price - £8.99
Pages - 310