Probabilistic thinking requires us to recognise both that something might happen and that it is unlikely that it will. Because this is difficult, we are always surprised, shocked, and inadequately prepared for extreme events.
Occasionally, a conversation changes the way you think. More than 20 years ago, a Lloyd’s underwriter told me: “The threat to this market is not a Japanese earthquake. We know that will happen. The threat comes from the risks we never imagined.” That was my introduction to the idea that Nassim Taleb would successfully popularise as the “black swan”. The distinction between “known unknowns”, the things we know we don’t know, and “unknown unknowns”, the things we don’t know we don’t know, has been part of my thinking ever since.
The Japanese earthquake is a catastrophe, a personal tragedy, a blow to the Japanese economy and the world insurance industry. But there is good historical data on the incidence and location of earthquakes. We know the relative frequencies of quakes of different magnitude. We do not know, and probably will never know, when and where a particular earthquake occurs. This is exactly the sort of problem for which probability theory is designed.
This year’s headlines have been filled with sensational events – the floods in Australia, the earth tremors in New Zealand, the coups in northern Africa and the civil war in Libya. But all of these possibilities should have been on the screens of anyone scanning the future, and each type of event occurs with a degree of regularity. They are all unexpected only in a probabilistic sense, just as the roulette wheel spinning to any particular slot is unexpected. “What is the likelihood of an 9.0 scale earthquake in Japan?” is a question you can sensibly discuss in terms of probabilities.
But others are not. The underwriter was talking about phenomena of a different nature. At a recent talk, someone asked me to identify the four or five black swans most likely to materialise over the next five years. No question could have demonstrated more clearly that he had missed the point (or that I had failed to make it effectively). The problem that had brought the insurance market close to collapse was liability for asbestos-related injuries under policies written decades before. No one suspected that even momentary exposure to asbestos might cause mesothelioma.
But the example that stuck most vividly in my mind was the cost to my friend’s syndicate of errors and omissions insurance taken out by directors and officers of US thrift institutions. Who could have anticipated that the dullest corner of the financial sector would have become an open hunting ground for fraudsters? Or that generations of craftsmen who built precision watches would be superseded by quartz technology, which costs a few pence but keeps more accurate time? The scientists who discovered radium did not know that it would kill them. These are truly unknown unknowns.
Yet many unknown events are neither known or unknown. We have general, but not very specific, ideas about what might happen. The result may not be clear even after it has happened. What will be the outcome of the Iraq or Afghan wars? What will be the influence of the Tea Party on American politics? How will the eurozone crisis be resolved?
For half a century or more, the prevailing doctrine has been that such issues can be pressed into a probabilistic framework. If you frame appropriate questions – “What odds would you take that Germany and Greece will have a common currency in 2020?” – and press respondents hard, polite people will usually give answers.
But such answers are often inconsistent – a finding that is often interpreted as demonstrating that the respondents are irrational. What it really tells us is that probabilistic mathematics does not correspond to the way most people think. We consider scenarios rather than probabilities, we review narratives rather than contemplate quantitative outcomes. Perhaps this is because it is the only way we can deal with a world of unknowns.
The mark of a first-rate intelligence, Scott Fitzgerald wrote, is the ability to hold contradictory ideas in the mind at the same time and still function. Probabilistic thinking requires us to recognise both that something might happen and that it is unlikely that it will. Because this is difficult, we are always surprised, shocked, and inadequately prepared for extreme events.