The risk in risk matrices

Not only did the consultant-led risk workshop start with a limp, it also ended with one.
For all practical purposes, it drew to its conclusion with the obfuscation of using a matrix to locate risks in a two dimensional space with dimensions 'likelihood' and 'severity'.

The problem with this was in neglecting to deal with the simple measurement error it gave us a result that was misleading; potentially so misleading it was no better than no result at all. The risk cells between different risk intensities have a natural error. That is, while they are bounded by lines, they should in fact be bounded by indeterminate zones where we cannot know the location of a risk.

This means that in a typical 4 x 4 matrix, it is not possible to distinguish between cells that touch at a corner.  But it gets worse: depending on the uncertainty between risk zones, it might be impossible to distinguish between cells one row or column apart in adjoining columns or rows. That makes the exercise pointless, and can lead to gross over- or under-allocation of resources to risk response.

Cox has examined this problem in detail, as discussed by Awati. Alleman also discusses uncertainty in projects.

As Gerd Gigerenza says (Helping Doctors and Patients Make Sense of Health Statistics), the first step in statistical literacy is understanding uncertainty. In risk analysis, above all, there should be some recursive application of uncertainty to that process that is established to deal with uncertainty. Physician, heal thyself!