Probabilities: Keynesian Legal Versus Bayesian Mathematical
by Philip Pilkington
Lars Syll has (once again) directed me to a fascinating piece, this time by John Kay. Kay starts the piece by noting that in a recent legal case in Britain the judge was asked to define the term “beyond reasonable doubt” and, as is typical in such cases, refused to do so.
The question, however, as Kay notes, was not a silly one: in English law criminal cases are decided only if the evidence is “beyond reasonable doubt” while civil cases are decided based on the “the balance of probabilities”.
Kay also notes, however, that these terms are not being used in the manner a trained statistician might use them. He writes:
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.
Clearly this is not in line with, say, a Bayesian interpretation of these terms. Rather such reasoning is much closer, as Syll notes in his post, to Keynes’ theories of probability which involve the weighting of an argument based on degrees of belief that are ultimately not subject to quantitative measurement.
Kay says in his post, correctly I think, that when those trained in statistics are confronted with the manner in which our legal institutions function they immediately think that the jurors are simply not educated sufficiently in modern mathematical methods. But, Kay says, to think this would be wrong. Rather we must understand that these legal institutions have evolved over centuries and have come to regard their approach to the weighting of evidence to be superior to any other. They have come to realise what some who are trained in statistics often simply will not concede: when faced with the extremely nuanced and complex aspects of a legal case quantitative probability estimates simply do not cut it.
Personally I remember thinking this when I used to hang around courts while training as a journalist. The court system is by no means perfect and one can often detect bias, but it is an extremely functional institution that I have always been impressed by. Having known a little bit about economic theory I remember sitting in the courts thinking “what if we replaced the judge with a computer?”. I did not think this as just some sci-fi fantasy but because I had seen mandatory minimum sentences in action and, not only did I think them grotesquely unfair, but I also noted that judges tended to issue them with a sigh.
At some level many judges knew that such methods of sentencing — relying as they do wholly on rigid rules that they had very little discretion in enforcing — were often unjust. It was in this context that I thought about the computer replacing the judge. In such a circumstance pretty much all sentences would be mandatory sentences because computers lack the nuances that humans possess. The legal system thereby produced would be nothing short of grotesque — perhaps reminding some of the Star Trek episode in which a computer allocated medical resources.
Now, here’s where the economics comes in: in my judgement economics is, in fact, more correctly thought of an extension of legal theory rather than a science — something that has not gone unnoticed by legal scholars. It is, in fact, a sort of Art of Governance and legal institutions are one of the founding pillars in our systems of governance. I think that Keynes was getting at something similar when he said that economics was a distinctly moral science. Here perhaps it is worth quoting his letter to Harrod of the 4th of July 1938 in the original:
It seems to me that economics is a branch of logic, a way of thinking; and that you [i.e. Harrod] do not repel sufficiently firmly attempts à la Schultz to turn it into a pseudo-natural-science… economics is essentially a moral science and not a natural science. That is to say, it employs introspection and judgments of value.
I think that this goes back to Keynes’ work on probability. His probability theories were, I think, supposed to be understood as how we should weigh up arguments in everyday life and come to a decision — as would a judge. He also thought that economics should be done along the same lines.
This seems to me the best way to apply economics. In fact, it seems to me, that the attempts to apply various statistical methods — I refer to econometrics and the like — to economic reasoning is not unlike replacing judges with computers. All critical economists should know the arbitrary policies that can be enforced through reliance on such methods and they should equally realise that, at the end of the day, the econometric studies chosen are chosen on the basis of their political usefulness and not vice versa. (Think, for example, of the IMF changing its multiplier estimates after the countries most closely associated with running it were hit with economic crises while having ignored such crises in the developing world for years).
Indeed, it would seem that economics really is subject to political judgements regardless of whether most economists use mathematical methods or not. We would all be a lot better off if we simply admitted what economics really is and what it is really used for. Then we can have a proper discussion of how it should be applied rather than people bickering over the supposed objectivity of their particular study.
The goal of a training in economics would then have to change too. Rather than attempting to turn economists into engineer-like functionaries as is currently the case, the goal would be to try to teach economics as part of a general Art of Governance. In this it would be closer to a training in law rather than a training in engineering. Much of the opacity and irrelevance of the discipline, I think, would then fall away. This is, of course, unlikely to happen because the engineer-like functionaries currently run the profession. But one can dream, right?