Models can be tricky customers

From lockdowns to Brexit to climate change, data modelling is here to stay – but it’s far from infallible

ESCAPE FROM MODEL LAND by Erica Thompson

256pp, Basic, T £16.99 (0844 871 1514), RRP £20, ebook £11.99

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Models of Covid led to lockdowns. Models of climate change drive environmental policies. Models of Brexit impacts influenced votes in the EU Referendum. Models of economic growth identify “fiscal black holes” that say how much our taxes must go up. We all have an interest in models and cannot avoid them.

This is a book about what models are, how we use them, and how we test them against reality. Data scientist Erica Thompson sets out her playful concept of “Model Land”, in which the modeller sets the rules and all assumptions are by definition true. We “escape” from Model Land, back to the real world, by either comparing the model’s inputs or outputs or both with realworld data, or by comparing the model’s workings with expert insights.

Thompson offers a broad concept of a “model”, which doesn’t always have to be mathematical. For example, a mouse might be a “model” for a human, when investigating biological processes or reactions. Readers with a philosophical background may be reminded of the young Wittgenstein’s “picture theory of meaning” whereby a proposition is a model or picture of a fact in the world.

However, Thompson wants us to understand that models do not always have to be true (if any, indeed, are true) – and do not have to be true to be useful. Sometimes they cannot be compared directly with the world at all and their value might be a bit like that she ascribes to medieval astrology – as a stimulus to action and a framework for planning and for taking expert or wise advice.

She notes that the detailed assumptions of models are often driven by the preferences and insights of experts, and the outputs of models can be highly sensitive to even tiny perturbations in the model’s structure (which she calls the “Hawkmoth Effect”, distinguishing it from the better-known “Butterfly Effect”). Hence, often we should think of the model and the expert modeller not as two independent things, but as one system.

Sometimes the results of a model can be wrong, yet the model still told us the right answer as to how we should behave. I thought of how standard epidemiological models that said the Covid epidemic was effectively over by September 2021 turned out to be wrong – an omicron wave arrived – but the implied policy recommendation (“Don’t impose restrictions during September to November 2021”) was correct, because even though omicron came, it did not overwhelm the health system.

Thompson warns against the dangers of only evaluating models by the outputs of other models, likening that to the later Wittgenstein’s warning about someone who bought several copies of the same newspaper to assure himself that what it said was true. I was reminded of attempts to claim Brexit has been “proved” to have damaging long-term effects, by quoting models of Brexit’s longterm impacts.

Thompson notes that the process of testing models cannot rely upon a simple count of the number of

Were Covid modellers influenced by knowing their models would affect policy?

experts or models that say one thing as opposed to another. All the models or experts that say the same thing may come from the same assumptions, so we are not really getting many different opinions or models or perspectives, but merely different instances of the same opinion/model/perspective.

She warns against a “computer says no” attitude in which we treat models’ results as unchallengeable and no human as accountable, noting that artificial intelligence-based models may make such an approach even less transparent. She also considers cases in which people have over-relied upon models by focusing only on recent data and underplaying risk. She worries at some length about the role of models in finance and regulation. But she is clear that the right response isn’t not to trust models at all!

Although Thompson recognises that model predictions are often “conditional”, an area I felt underexplored was the challenges of modelling situations in which model outputs affect the world. She considers self-fulfilling prophecies and arbitrarily assumed “can-openers” that might one day remove carbon from the atmosphere, but I have a different issue in mind.

If I had a model that reliably predicted almost every volcanic eruption killing more than 5,000 people, it would probably fail ever to predict an eruption that killed more than 5,000 people – because people would move away whenever it predicted an eruption would occur. Many economic models are like that. That is part of the reason crises like the 2008 financial crisis cannot be reliably predicted. Similar issues may arise in Thompson’s own area of climate modelling. Similarly, I also felt she missed certain important points about how official Covid modellers’ choice of scenarios might have been influenced by knowing that their results could affect policies in the world.

Such cavilling aside, if you do modelling, take an interest in models or want to understand more about what modelling is and how it affects you, you may enjoy this book. I enjoyed it, was amused by its many metaphors (including cats that are most like dogs, pennies collected in front of bulldozers and dogs chasing guided drone Frisbees), and was taken with its central message of how to get the balance right in modelling (such as by reimagining them as ways to set out a range of possible futures) and her efforts to think how to apply this to her own area of climate modelling, and to use it to guide adaptation (such as flood defences).

In my day job as an economist, I say “If you can point at it, I can count it”, meaning almost anything can be modelled. But when data is sparse, the best theory is poorly understood or ethical judgements are required, I add: “How much you should believe my model…? Well, that’s another story!” Thompson would strongly agree.