What is the Public Understanding of Risk?

What is the Public Understanding of Risk?
Risky Business: Risk and Reward Assessment in Business Decision Making
D. Simmons FIMA , MD Analytics, Willes RE

Science in Parliament, Spring 2012, Reprinted in the IMA’s Mathematics Today, Vol. 48 No. 3 June 2012

This says very little about the public understanding of risk, and is more about the understanding within insurance and reinsurance companies. It discusses the potential use of probability in legal cases, and says:

There is no reason why such [probabilistic / statistical ] tools should not be used in government.

This contrasts oddly with an article in the previous issue:

T. Johnson, Heralding a New Era in Financial Mathematics, April 2012 

This starts by referring to Keynes and goes on:

The Bank of England believes that recent developments in financial mathematics have focused on microeconomic issues, such as pricing derivatives. Their concern is whether there is the mathematics to support macroeconomic risk analysis; how the whole system works. While probability theory has an important role to play in addressing these questions, other mathematical disciplines, not usually associated with finance, could prove useful. For example, the Bank’s interest in complexity in networks and dynamical systems has been well documented.

… As well as the Bank of England’s interest in models of market failure and systemic risk, more esoteric topics such as non-ergodic dynamical systems and models of learning in markets would be interesting. Topics associated with mainstream financial mathematics could include control in the presence of liquidity constraints, Knightian uncertainty and behavioural issues and credit modelling.

Thus, there seems to be at least one area where Keynes’ notion that uncertainty cannot always be represented by a single number, probability, is still relevant. Simmons’ contention inevitably lies outside the proper scope of mathematics, and is contentious.

Simmons does say:

All assumptions behind a decision can be seen, discussed, challenged and stressed.

This is a common claim of Bayesians and other probabilists, and has great merit, particularly if one is comparing it with a status quo of relying on gut-feel. But the decision to use a probabilistic approach is not unimportant and we should consider, as Keynes does, the implicit assumptions behind it.

There are actually many different axiomatizations of probability. They all assume that the system under consideration is in some sense regular, and that one is concerned with averages. These conditions seem to apply to insurance and re-insurance, but not always to legal matters or government policy.

My own involvement in reinsurance was in the government’s covering of the market’s failure to cope with the non-stochastic risk presented by terrorism. If it were true that government could address risk in the same way as the reinsurers, what would the point of government cover be? Similarly, in finance, what is the regulatory role of governmental institutions if the probabilistic view of risk is correct? My career has largely been spent in explaining to decision-makers why the people who ultimately carry the risk have to take a different approach to limited liability companies, who can treat risk as if it were a gamble. (I tend to find the tools of Keynes, Turing and Good appropriate to ‘wider risk’.)

Hopefully the IMA president’s up-coming address will enlighten us all.

See also

Other debates, my blog, bibliography.


Dave Marsay 


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

6 Responses to What is the Public Understanding of Risk?

  1. Thanks Dave, very interesting and, thankfully for a non-mathematician such as myself, not a challenging as some of your recent posts!

    I am aware of some of the excellent papers and presentations from Andy Haldane (and Lord May) re complexity and learning from biological systems but do you know if there is anyone at B of E actually charged with investigating/testing possible solutions in current use?


  2. Tim Johnson says:

    I don’t think my article contrasts too much with Simmons, in fact as a probabilist I’d be daft to argue that the government should not make more use of probability theory, and have just spent a day in Whitehall talking about it.

    The point, perhaps not well made, in the Maths Today article was that for the past 20 years or so, research in mathematical finance has been dominated by stochastic analysis. The point of the article is that there are opportunities for mathematicians not steeped in martingale theory or Levy processes to become involved in finance and economics. In addition the BoE is interested in initiating research into macro issues, rather than the problems of pricing derivatives, as one none-financial mathematician put it, moving maths out of the dark side, and on to the side of the regulator.

    I strongly recommend Franklin’s “The Science of Conjecture” for an account of how mathematical probability emerged out of legal/theological issues.

  3. Dave Marsay says:

    Tim, thanks for the comments.

    My reading of Simmons is (as quoted) he was proposing that government should be using the same kind of tools as insurance and re-insurance, whereas you (as quoted, and as in your comment) seemed to be giving a list of reasons why Simmons’ tools are inappropriate, or at least not obviously appropriate.

    Your article referred to Keynes. I agree that government ought to be using probability theory in the sense in which he understood it. If Bayesian probability is associated with the ‘dark side’, where is the theory for the ‘good guys’? If it is still Bayesian, how does one prevent the misuse of the theory?

    Thanks for the Franklin ref.

  4. geopolicraticus says:

    Hi Dave,

    I think that the different axiomatizations of probably flow from different, and sometimes conflicting, intuitions about risk. There are our “gut” feelings about risk, to which you refer, and then we have more educated intuitions, and these will vary according to interest and inclination.

    Ultimately, these different intuitions about risk can be followed backward to entire Weltanschauungen — almost incommensurable Kuhnian paradisms.

    I am skeptical, then, that, “All assumptions behind a decision can be seen, discussed, challenged and stressed,” though certainly some of them can be discussed, etc.

    The attempt to quantify risk in a narrowly technical context will always make some pretty significant metaphysical assumptions about the nature of the world, and the sort of people who write about narrowly technical conceptions of risk are not likely to be comfortable giving a short sketch of their metaphysical background, which is what they properly ought to do, so that we know where they are coming from, intellectually speaking.

    Best wishes,


  5. Dave Marsay says:


    I have been reading Russell’s Human Knowledge (rough notes at https://djmarsay.wordpress.com/bibliography/rationality-and-uncertainty/logic/russells-human-knowledge/ ). It seems very pertinent.

    Russell points out that our understanding of concepts like uncertainty depend on our experience, so presumably those with little experience of what economists call radical uncertainty can’t really discuss it, and those who do ‘get’ uncertainty can’t really challenge the view of those who don’t, except logically.

    My limited experience of people who are confident that probability is just about numbers is that it is just a belief. They may attempt to give a logical justification but when that is challenged will move on to another. Either that, or they have a different conception of logic to me (and Keynes, and Russell).

    More often, people will acknowledge that radical uncertainty does exist, and will even take account of it in their private lives, but will suppose it ‘beyond their pay grade’ to consider in more formal settings, and perhaps not something that can be admitted in many institutions, unless it destroy vital confidence in those institutions. Thus, in the UK, politics and governance used to be all about uncertainty, whereas now although politics is still all about uncertainty, the government seems constrained to act ‘rationally’, perhaps constrained by the public’s misperceptions about risk. As with earlier generations, mathematicians and scientists could provide critical advice here – as long as they actually understood risk, in all its aspects, themselves.

    The president of the IMA is going to talk on this subject. Hopefully he will address Keynes’ issues and identify some credible axioms for a proper theory.

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