Accidents of potentially catastrophic potential pose a particular challenge to classical utilitarian theories of managing risk. A reader of this blog might be aware of how the presence of possibility of irreversible catastrophic outcomes (i.e. non-ergodicity) undermines a key assumption on which classical risk assessment is based. But what to do about it? Well one thing we can practically do is to ensure that when we assess risk we take into account the irreversible (non-ergodic) nature of such catastrophes and there are good reasons that we should do so, as the law does not look kindly on organisations (or people) who make decisions about risk of death purely on the basis of frequency gambling.

A while ago I put together a classical risk matrix (1) that treated risk in accordance with De Moivre’s formulation and I’ve modified this matrix to explicitly address non-ergodicity. The modification is to the extreme (catastrophic) severity column where I’ve shifted the boundary of unacceptable risk downwards to reflect that the (classical) iso-risk contour in that catastrophic case under-estimates the risk posed by catastrophic irreversible outcomes. The matrix now also imposes claim limits on risk where a SPOF may exist that could result in a catastrophic loss (2). We end up with something that looks a bit like the matrix below (3).

From a decision making perspective you’ll note that not only is the threshold for unacceptable risk reduced but that for catastrophic severity (one or more deaths) there is no longer a ‘acceptable’ threshold. This is an important consideration reflecting as it does the laws position that you cannot in gamble away your duty of care, e.g justify not taking an action purely the basis of a risk threshold (4). The final outcome of this work, along with revised likelihood and severity definitions, can be found in hazard matrix V1.1 (5). I’m still thinking about how you might introduce more consideration of epistemic and ontological risks into the matrix, it’s a work in progress.

**Notes**

1. Mainly to provide a canonical example of what a well constructed matrix should look like as there are an awful lot of bad ones floating around.

2. You have to either eliminate the SPOF or reduce the severity. There’s an implied treatment of epistemic uncertainty in such a claim limit that I find appealing.

3. The star represents a calibration point that’s used when soliciting subjective assessments of likelihood from SME.

4. By the way you’re not going to find these sort of considerations in ISO 31000.

5. **Important note**. like all risk matrices it needs to be calibrated to the actual circumstances and risk appetite of the organisation. No warranty given and YMMV.