Non-ergodic risk matrices

15/10/2016 — Leave a comment

Matrix (Image source: The Matrix film)

A reader of this blog might be aware of both the difference between ergodic and non-ergodic risks, and how the presence of non-ergodicity (i.e. the possibility of irreversible catastrophic outcomes) undermines a key assumption on which Pascalian 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 non-ergodic nature of such catastrophes. 

A while ago I put together a classical risk matrix (1) that treated risk in accordance with De Moivre’s formulation. To address the problem of non-ergodic risks I’ve tinkered with it 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 underestimates the risk. 

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).


The results of this modification, along with revised likelihood and severity definitions, can be found in hazard matrix V1.1. 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. 🙂


1. Mainly to provide a canonical example for didactic purposes 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 is a calibration point that’s used when soliciting subjective assessments of likelihood from SME.

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