Assessing and Communicating Risks and Uncertainty

David Spielgelhalter Assessing and Communicating Risks and Uncertainty Science in Parliament vol 69, no. 2, pp. 21-26. This is part of the IMA’s Mathematics Matters: A Crucial Contribution to the Country’s Economy.

This starts with a Harvard study showing that “a daily portion of red meat was associated with an increase in the annual risk of death by 13% over the period of the study”. Does this mean, as the Daily Express claimed, that “10% of all deaths could be avoided”?

David S uses ‘survival analysis’ to show that “a 40 year-old  man who eats a quarter-pound burger for his working lunch each day can expect, on average, to live to 79, while his mate who avoids the burger can expect to live to 80.” He goes on: “over a lifetime habit, each daily portion of red meat is associated with about 30 minutes off your life expectancy .. ” (my emphasis.)

As a mathematician advising politicians and other decision-makers, I would not be comfortable that policy-makers understood this, and would act appropriately. They might, for example, assume that we should all be discouraged from eating too much red meat.

Even some numerate colleagues with some exposure to statistics might, I think, suppose that their life expectancy was being reduced by eating red meat. But all that is being said is that if a random person were selected from the population as a whole then – knowing nothing about them – a statistician would ‘expect’ them to have a shorter life if they eat red meat. But every actual individual ‘you’ has a family history and many by 40 will have had cholesterol tests. It is not clear what the relevance to them is of the statistician’s ‘averaged’ figures.

Generally speaking, statistics gathered for one set of factors cannot be used to draw precise conclusions about  other sets of factors, much less about individuals. David S’s previous advice at Don’t Know, Can’t Know applies. In my experience, it is not safe to assume that the audience will appreciate these finer points. All that I would take from the Harvard study is that if you eat red meat most days it might be a good idea to consult your doctor. I would also hope that there was research going on into the factors in the apparent dangers.

See Also

I would appreciate a link to the original study.

Dave Marsay


About Dave Marsay
Mathematician with an interest in 'good' reasoning.

3 Responses to Assessing and Communicating Risks and Uncertainty

  1. Blue Aurora says:

    As someone who enjoys to eat red meat, I would agree that one should consult your doctor.

    But there is no need for “libertarian paternalism” of the type Richard Thaler or Cass Sunstein have advocated in their book, Nudge. Have you read that book? While I do support the welfare state, I don’t believe that people need to be micro-managed to the point that their consumption habits are dictated by an external authority.

    On another note, Dr. Marsay, have you ever heard of Itzhak Gilboa and David Schmeidler?

    If you have not they are two highly mathematical scholars who have developed “Choquet integration” to explain the Ellsberg paradox and other anomalies that affect Subjective Expected Utility.

    • Dave Marsay says:

      Blue, my general approach to these issues is that in the first place government should make sure that significant risks are assessed and communicated. Thus, for example, if share-holders had understood the risks that banks were taking in 2005/6 the world’s economies might be in better shape. Medical risks seem no different. As a taxpayer I might approve of nudging if it worked and an information campaign hadn’t. Maybe one should even tax fat, just as tobacco and alcohol are taxed. But one would want to get the facts straight.

      I haven’t read Nudge. I have read G&S, but not understood ‘what they are on about’. If one takes Wittgenstein’s theory, one naturally gets outer and inner measures that correspond to Keynes’ upper and lower bounds, but are less general. (Keynes supported Wittgenstein.) I am not sure what G&S add. In the case of burgers the measureability issue does not seem so important. Maybe I just haven’t understood G&S, but it seems to me that they illustrate one source of anomalies rather than fully explaining them.

      • Blue Aurora says:

        I would agree with you that risks need to be communicated effectively by policy-makers, but I’m not the only person who has made the criticism of a certain “paternalistic” bent in behavioural economics. Others have made that criticism before.

        Regarding Gilboa and Schmeidler, yes, I believe Dr. Michael Emmett Brady has made the same point. Brady feels that Gilboa and Schmeidler are actually “reinventing the wheel” that Boole and Keynes had already done.

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