In a high-profile legal case last week, the jury asked the judge to explain what was meant by the term “beyond reasonable doubt”. As is the custom of the English courts, the judge refused to clarify the words further.
But the jurors’ question is legitimate, and the attempt to answer it reveals much, not just about the law, but the analysis of complex problems. English law recognises two principal standards of proof. The criminal test is that a charge must be “beyond reasonable doubt”, while civil cases are decided on “the balance of probabilities”.
The meaning of these terms would seem obvious to anyone trained in basic statistics. Scientists think in terms of confidence intervals – they are inclined to accept a hypothesis if the probability that it is true exceeds 95 per cent. “Beyond reasonable doubt” appears to be a claim that there is a high probability that the hypothesis – the defendant’s guilt – is true. Perhaps criminal conviction requires a higher standard than the scientific norm – 99 per cent or even 99.9 per cent confidence is required to throw you in jail. “On the balance of probabilities” must surely mean that the probability the claim is well founded exceeds 50 per cent.
And yet a brief conversation with experienced lawyers establishes that they do not interpret the terms in these ways. One famous illustration supposes you are knocked down by a bus, which you did not see (that is why it knocked you down). Say Company A operates more than half the buses in the town. Absent other evidence, the probability that your injuries were caused by a bus belonging to Company A is more than one half. But no court would determine that Company A was liable on that basis.
A court approaches the issue in a different way. You must tell a story about yourself and the bus. Legal reasoning uses a narrative rather than a probabilistic approach, and when the courts are faced with probabilistic reasoning the result is often a damaging muddle – as, for example, the flawed testimony of Sir Roy Meadow on child deaths that led courts to wrongfully convict grieving parents of murdering their children.
The US legal system, tellingly, prefers the term “preponderance of the evidence” to “balance of probabilities”. To a statistician, it is not apparent that these terms have the same meaning. But lawyers take the view that broadly speaking they do. The reason is that the term “balance of probabilities” is not interpreted in the same way by lawyers and statisticians.
When I have raised these issues with people with scientific training, they tend to reply that lawyers are mostly innumerate and with better education would learn to think in the same way as statisticians. Probabilistic reasoning has become the dominant method of structured thinking about problems involving risk and uncertainty – to such an extent that people who do not think this way are derided as incompetent and irrational. Yet this probabilistic approach, a recent intellectual development, was heavily implicated in the 2008 financial crisis. Legal systems have evolved over hundreds if not thousands of years, applying different modes of reasoning.
It is possible – common, even – to believe something is true without being confident in that belief. Or to be sure that, say, a housing bubble will burst without being able to attach a high probability to any specific event, such as “house prices will fall 20 per cent in the next year”. A court is concerned to establish the degree of confidence in a narrative, not to measure a probability in a model.
Such narrative reasoning is the most effective means humans have developed of handling complex and ill-defined problems. A court can rarely establish a complete account of the probabilities of the events on which it is required to adjudicate. Similarly, an individual cannot know how career and relationships will evolve. A business must be steered into a future of unknown and unknowable dimensions.
So while probabilistic thinking is indispensable when dealing with recurrent events or histories that repeat themselves, it often fails when we try to apply it to idiosyncratic events and open-ended problems. We cope with these situations by telling stories, and we base decisions on their persuasiveness. Not because we are stupid, but because experience has told us it is the best way to cope. That is why novels sell better than statistics texts.