# Kay and King’s Coronavirus

John Kay and Mervyn King The radical uncertainties of coronavirus Prospect March 30, 2020

Radical uncertainty arises when we know something, but not enough to enable us to act with confidence. And that is a situation we all too frequently encounter.

The language and mathematics of probability is a compelling way of analysing games of chance. And similar models have proved useful in some branches of physics. …

But most of the problems we face in politics, business (including finance) and society are not like that. We do not have, and never will have, the kind of understanding of human behaviour which emulates the understanding of physical behaviour which yields equations of planetary motion. Worse, human behaviour changes over time in a way that the equations of planetary motion do not. And Venus continues in its orbit unaffected by our opinions about it, while human beliefs about viruses and anything else, whether true or false, will often have a major influence on human behaviour.

Discourse about uncertainty has fallen victim to a pseudo-science. When no meaningful quantification is possible, algebra can provide only spurious precision, while at the same time the language becomes casual and sloppy.The terms risk, uncertainty and volatility are treated as equivalent; the words likelihood, confidence and probability are also used as if they had the same meaning. But risk is not the same as uncertainty, although it arises from it, and the confidence with which a statement is made is at best weakly related to the probability that it is true.

A key function of a good model is to direct attention to the usually small number of parameters that really matter.

Models should be treated not as forecasting tools but as ways of organising our thinking. Their construction and interpretation require judgment.

Few people—even actuaries and statisticians—use probabilities to run their own lives. We cope with a world that contains mysteries rather than puzzles by telling stories, constructing a “reference narrative” that incorporates our realistic expectations. When uncertainty encroaches on that narrative, it may be good or bad—the frisson of uncertainty that attracts punters to gambling venues and the uncertainty attached to visiting new places, meeting new people, and enjoying new experiences that adds much to the pleasure of life. And it is uncertainty that creates opportunities for entrepreneurship and profit, and is the dynamic of a market economy. But for human beings to thrive in a world of unknowns, you need to develop the capacity to manage uncertainty, and even embrace it. …

Charting a happy course through a world where much is unknown means ensuring that one’s reference narrative—personal, financial, commercial or political—is robust and resilient to events we cannot fully anticipate. …

Robustness and resilience in complex systems are achieved by ensuring that the system is organised in a way that ensures a failure of part of it need not jeopardise the whole. …

The vicissitudes of our uncertain world have not only subjected our society to a brief if nasty disease, but also exposed our economy’s susceptibility to, in the parlance of the hour, a serious underlying condition.

## My Comments

I have tried to pick out the parts of broad significance. I recommend the article for those interested in pandemics or financial crises.

My main comment is that there is a lot more to the mathematics of uncertainty than the mathematics of quantifiable uncertainty. For example, statisticians such as Savage have noted the limitations of ‘small world’ models. The notion that uncertainty needs to be considered in the context of decision-making is also uncontroversial. That is, there is no such thing as ‘the’ probability or even ‘the’ uncertainty: only an appreciation (or ‘model’) of uncertainty that may be fit for a particular purpose.

On the other hand, that “The language and mathematics of probability is a compelling way of analysing games of chance” seems to make little sense. Casinos have ostensible rules for their ‘games of chance’. If we took these at face value then we might well apply probability theory, e.g. to roulette or cards. But what could give us the confidence to take the game at face value? Reputation? A school text book on probability? Game-theory would seem a more obvious basis than probability theory or blind trust. One would try to establish the nature of the game and the incentives of the various players. For example, who is their motivation to cheat? How do they see the hazards of cheating? How might they cheat? Can we be sure that they might not have some ways of cheating that we do not? If a stranger offers us a bet at ‘very attractive’ odds, do we not ‘smell a rat’?

It seems to me that unquantifiable uncertainty is everywhere. Dodgson is credited with the observation that a finite number of observations can only be used to reduce the dimensionality of the uncertainty by a finite amount. So to reduce uncertainty to a single dimension (e.g. ‘probability’) we would need to start with a finitistic model of uncertainty. But how would we put bounds on the creativity of a Casino, its staff and clientele? Even from a probability theory point of view (such as Boole‘s) the notion that ‘games of chance’ can ever be reduced to a single-dimensional probability is hard to believe.

Boole also suggests a more fundamental issue with the idea that “Radical uncertainty arises when we know something, but not enough to enable us to act with confidence.” This could easily be interpreted that there is some threshold of ‘confidence’ beyond which we are ‘enabled to act’. But what could this be? If we set it too high we may never act. If we set it too low we may act in a way that we later realise was mistaken. How then can we continue to act ‘with confidence’ on that threshold. Even if there were some ideal threshold, how would we assess it?

We might think consider thinking in terms of ‘degrees of confidence’, in which case radical uncertainty would correspond to some low degree of confidence. But where would that get us?

And yet Kay and King have something important to say. We may be suffering from many ‘serious underlying conditions’, and lack of confidence may be one of them. But I think confusion about uncertainty is certainly one of them. To me ‘radical uncertainty’ arises when we make our decisions based on an inadequate understanding of uncertainty. The problem is not so much our lack of confidence as our over-confidence in our ability to assess uncertainty. The more we develop our tools, be better we shall do, but we can never eradicate genuine uncertainty.

How then should we act?

TBC