If only the non-mathematical approaches were just a more convenient, more approximate version of the mathematical. Sadly, they are not.
The conceptual bases of the mathematical and non-mathematical approaches differ radically. It is not a matter of whether the approach uses numbers or not. The fundamental beliefs implied by the different approaches are so different that people in the different camps nd it hard to agree on much.
Before I present a detailed comparison of the two, here is an example to show how differently the two approaches go about understanding and managing risk in the same situation.
Imagine that we are working in a government-funded organization whose goal is to reduce teenage smoking using advertising methods.
In the mathematically based approach modelling begins immediately because it is tackling the whole problem, not just the uncertainty. We want to think through what causes smoking and what can be done about it. At its simplest the key variable in the model could just be the percentage of teenagers who smoke, but more elaborate versions might look at the number and percentage of smokers of different ages, and perhaps also represent how often they smoke. There might even be distinctions between heavy, daily smokers and people who only smoke occasionally, such as at parties. Perhaps different persuasive methods would work with these different groups.
To the model might then be added likely causal in uences on teenage smoking, such as attitudes towards smoking, parental behaviour, legal restrictions, the cost of cigarettes, smoking behaviour earlier in life, alcohol abuse, and the example set by friends. These would be represented by other variables and linked to the level of smoking by relationships whose properties are likely to be uncertain.
Since the job of the organization is to reduce teenage smoking by using advertising methods, the model also needs variables to represent things like the amount and quality of advertising, the number of teenagers and pre-teens exposed to it, and the number of times they see it. Again, the links between these variables and other related variables, mainly attitudes towards smoking, would need to be considered and made part of the model.
Nobody expects perfect predictions. The goal of modelling in this way is to clarify beliefs and compute their implications, including the implications of our various uncertainties.
Consequently, modelling would typically represent links between variables, and future levels of each variable, using probability distributions of various kinds.
This is where uncertainty comes in. Various measures of risk/uncertainty have been devised.
Models that include uncertainty explicitly do not have to be complex or hard to understand, though sometimes they are.
More work would go into estimating the strength and any timing delays in the relationships between variables in this model so that the effect of investments
in different forms and extents of advertising using different messages could be estimated. This would lead, almost inevitably, to the idea of doing experiments with potential advertisements to study attitude changes (if any) on a small scale and so improve the reliability of the model.
In summary, in this approach the uncertainties about future levels of smoking and the effectiveness of various advertising approaches are the ‘risks’ that need to be managed, but are rarely given that name. There is an explicit model that links variables and informs all planning, not just planning to do with risk; the modelling starts before a plan exists.
What would a non-mathematically inspired approach look like by contrast?
At rst there would be no serious consideration of risks or uncertainty. After some debate a plan of action would emerge and only then would risk-thinking kick in. A workshop might be held at which people begin by restating the objective, which of course is to cut teenage smoking by using advertising methods. The group would then suggest things that could happen that might mean they fail to cut teenage smoking, such as ‘Advertisements have an ineffective message’, ‘Advertisements are not seen by enough teenagers’, and ‘Advertisements back re’. These suggestions would often be generated by looking at each step in the initial plan of action and thinking about what could stop it being done or stop it producing the desired results.
These ideas would be described as ‘risks’ and listed. Most risks would be expressed relative to some desired outcome. For example, ‘Insuf cient viewing of advertising’ rather than the more neutral ‘Level of viewing of advertising’ which the mathematical approach would usually prefer.
Against the risks the team would then try to write actions they could take to manage those risks, such as testing advertisements before they are used widely.
Table 2.1 compares the two approaches side by side, picking out some of the less obvious but fundamental conceptual differences implied by their language and preferred practices. Of course to do this I’ve ignored some occasional exceptions.
Sometimes mathematicians try to use ideas from the non-mathematical world, like targets for example, and already some progressive risk managers are making more use of mathematical concepts. However, the differences in practice are still real and stark.
With hundreds of years of development and science behind it the conceptual basis of the mathematically in uenced work is far more rigorous, accurate, consistent, realistic, better researched, less commercially manipulated, and more reliable than the non-mathematical work. The non-mathematical approach is based on some conceptual errors that have led to serious practical problems. However, this doesn’t mean that the mathematical approach is always more useful.
The mathematical approaches have done well where data are plentiful and there are people, such as scientists, engineers, and nancial ‘quants’ to do the clever stuff and use the results. The non-mathematical approaches have developed among groups who typically lack, or at least do not reward, mathematical skill and where data are hard to come by. When nearly all risk assessments feel like guesswork people seem to think they don’t matter and are less concerned about getting the thinking right.
Mathematical Non-mathematical
Often does not use the word ‘risk’. Almost always uses the word ‘risk’.
Part of the same thought process that generates the plan of action.
Usually begins once a basic plan of action is already in mind.
The models used are explicit. The models used are implicit.
Risk is seen as a lack of knowledge (perhaps arising from unpredictable variability) that makes it hard or impossible to know the future exactly.
Risks are treated as real things that exist outside our minds.
The thinker is responsible for de ning the models.
Often no effort is made to de ne models used.
Variables need to be de ned, especially if they are to be measured.
Also, events in probability theory are seen as sets of atomic outcomes. These sets need to be de ned.
Risks and events are named and given descriptions, but not usually with the intention of de ning them.
Models have variables in them whose values are uncertain and usually represented using probabilities or probability densities.
These variables represent the behaviour of a system and are usually closest in intent to measures of performance. ‘Risks’ are usually just uncertainties about future values of performance/behaviour measures.
Risks are separate things that rub shoulders with objectives, critical success factors, measures of performance, and so on, but are different from them.
Most models are concerned with all possible outcomes.
Risk thinking is almost always concerned only with bad potential outcomes.
Risk and uncertainty change as information arrives, which it can at any time.
Risks are often seen as things that can be completely understood with suf cient effort and, once this is done, there is nothing more to be learned from experience.
Variables in a model are linked by mathematical relationships representing causal or statistical connections.
In practice, risks are usually treated as if unconnected even though people often know this is not the case.
Decision-making usually focuses on nding optimal decisions within the model given a way to value different outcomes e.g. in money terms or with an explicit objective function.
Decision-making usually focuses on reaching targets that are considered givens.
Comparisons of ‘better’ and ‘worse’
are made between explicitly identi ed alternatives.
‘Good’ and ‘bad’ are rarely de ned explicitly but play a big role in thinking because, usually, only bad potential outcomes are considered.
Numerical measurement using real numbers (i.e. not just whole numbers) is preferred.
Categories with verbal descriptions or de ned by number ranges are usually preferred.
Table 2.1 Mathematical and non-mathematical approaches to risk management
The non-mathematical approaches typically do not provide a true analysis of risk; instead they provide a worry-driven ‘to do’ list; but such a list is useful. Very often people feel that a session discussing the risks they have listed has been a helpful one, even if technically the output is indefensible.
Risk workshops are sometimes a much needed opportunity for people to speak more openly about their concerns and provide a helpful mandate for risk responses that otherwise people might view as unnecessary or time wasting. As explained in Chapter 4, the psychological impact of risk control activities is crucial.