Linda is single, outspoken and deeply engaged with social issues. Which of the following is more likely? That Linda is a bank manager or that Linda is a bank manager who is an active feminist?
This is one of the best-known problems in behavioural economics. Many people say that the second option is more likely. Yet, the standard response goes, this cannot be. The rules of probability tell us the probability that both A and B are true cannot exceed the probability that either A or B is true. It is less likely that someone is a female Jamaican Olympic gold medallist than that a person is female, or that a person is Jamaican, or that a person is a gold medallist. Yet even people trained in probability make a mistake with the Linda problem.
Or is it a mistake? Little introspection is required to understand what is going on. Respondents do not interpret the question as one about probability. They think it is a question about believability. The description of Linda that ends with the statement “Linda is a bank manager” is designed to be incongruous. The addition – “who is an active feminist” begins to restore coherence. The story becomes more believable, even if less probable. No one gets the Jamaican problem wrong because every part of the story makes sense.
We do not often, or easily, think in terms of probabilities, because there are not many situations in which this style of thinking is useful. Probability theory is a marvellous tool for games of chance – such as spinning a roulette wheel. The structure of the problem is comprehensively defined by the rules of the game. The set of outcomes is well defined and bounded, and we will soon know which outcome has occurred. But most of the problems we face in the business and financial worlds – or in our personal lives – are not like that. The rules are ill-defined, the range of outcomes is wider than we can easily imagine and often we do not fully comprehend what has happened even after the event. The real world is characterised by radical uncertainty – the things we do not know that we do not know.
We deal with that world by constructing simplifying narratives. We do this not because we are stupid, or irrational, or have forgotten probability 101, but because storytelling is the best means of making sense of complexity. The test of these narratives is whether they are believable.
When jurors convict a defendant after a long trial, it is not because they think there is a 95 per cent probability that the prosecution’s account is true – the rules of compound probability tell us that there is almost no chance of its story being correct in every detail. Nor because the jury thinks there is a 95 per cent probability that the defendant is guilty: no one would suggest that a husband should be convicted of his wife’s murder because it is a statistical fact that most married women who are murdered are killed by their husband. The jury convicts because it finds the prosecution’s account of events believable.
The rise of quantitative finance has led people to squeeze many things into the framework of probability. The invention of subjective or personal probabilities proved to be a means of applying a well-established branch of mathematics to a new range of problems. This approach had the appearance of science, and enabled young turks to marginalise the war stories of innumerate old fogies. The old fogies may have known something after all, however.
Still, reliance on narration is problematic. We are predisposed to find evidence that confirms our existing beliefs. That leads some people to become obsessed by narratives that offer theories of everything: communism, libertarianism, religious and environmental fundamentalism; more mundane fantasies such as the inevitability of house price appreciation; or the magical properties of securitisation.
The mark of a first-rate intelligence, said the writer F. Scott Fitzgerald, is the ability to hold conflicting ideas in the mind at the same time and still function. But to do so is hard. I have never described alternative scenarios to an audience without someone asking me: “So what do you think is really going to happen?”