Teams of friends visit a shooting range. All the shots of team B are below and to the left of the bullseye. The shots of team C are scattered all over the target. Team B demonstrates bias. Team C illustrates noise.

With this metaphor, Daniel Kahneman, Olivier Sibony and Cass Sunstein (KSS) begin their new, much anticipated, book. Kahneman’s Thinking Fast and Slow, and Sunstein’s Nudge (written with Richard Thaler) have both been bestsellers.

The central argument of Noise is that the metaphor of the target at the shooting range has wide application. The world is one of bullseyes waiting to be hit. Decision problems have correct answers, but fallible humans do not reach them. Their actions suffer from bias and noise.

Thus Noise is a logical extension of Kahneman’s approach to behavioural economics. That subject began in the 1950s as a critique – led by the French Nobel Prize winner Maurice Allais – of economists’ models of rational behaviour. Under the leadership of Kahneman and  his late colleague Amos Tversky, behavioural economics became a critique of people for failing to conform to the axioms which had been deemed to define ‘rationality’. If the models did not describe the world, the deficiencies lay not in the models but in the world.

The precepts of the new school of behavioural economics were supported by multiple experiments in which students earned a few dollars by participating in experiments conducted in the basement of prestigious universities. The students failed to give the answers predicted by the models that the professors had taught them; the professors, in turn, generated publications by discovering this failure. That failure was, of course, the fault of the students. Even the cream of American youth suffered from ‘biases’.

Now we learn that their bias is aggravated by noise. Worse still, it is not only students whose decisions are ‘noisy’. Judges, insurance underwriters, teachers, doctors, recruiters – all of their decisions are blighted by noise. How, one might wonder, can such inadequate beings have reached the moon, built cities, and flown around the world? To pose that question takes us to the heart of the matter – the bullseye, perhaps. At the shooting range, we know immediately whether we have hit the target. In the real world, few problems have identifiably correct answers – and mostly we do not know what the correct answer was even after firing our gun. We didn’t fail to reach the moon before 1969 because earlier generations had aimed at it and missed. Reaching the moon was the result of an extended process of accumulating scientific and engineering knowledge, much of it through small scale trial and error.

The limitations of the metaphor of the bullseye emerge in the two signature examples employed by KSS – judicial decision making and insurance underwriting. There is no right answer to the question ‘what prison term should be imposed on convicted criminal X?’ The goals of sentencing are multiple – deterrence, retribution, reform, and denying X the opportunity to offend again. Different societies, the same society at different times, and – yes – different judges will attach different weights to each of these factors.

The resulting divergences are not simply ones of taste –  I prefer raspberry jam while you like strawberry. Value pluralism necessarily entails different and wholly legitimate balances of judgment more profound than differences of preference. The existence of such divergences does not demonstrate that Judge A made a mistake in imposing on X a sentence different from the one Judge B might have determined. Nor is there reason to attach any special weight to the average sentence of all judges who might have determined the case of X.  Despite a rather strange but lengthy passage in which KSS appear not to recognise that the mean minimises the error in noisy judgments only because they have chosen to define error as the mean square error of deviations from the mean.

Of course, it is intolerable for judges to be more severe before lunch than after it, although the story of harsh, hungry judges did not survive further scrutiny.^[1] Most judges are careful, conscientious people who have achieved office by persuading their peers that their views are worthy of respect. Judges receive training and exchange views and experiences, and senior members of the judiciary participate in the construction of sentencing guidelines. This does not mean they reach the ‘right’ answer in any particular case although everywhere there is provision for reviewing answers that are egregiously wrong. The common law of Anglo-American jurisdictions, which emphasises precedent while accommodating evolution, is an exemplar of what the anthropologist Joe Henrich has described as ‘the secret of our success’^[2] – the collective intelligence which is the product of accumulated social learning. We no longer burn witches because of a developed moral sensitivity that regard it as wrong to burn any offenders, whatever their crime, and a better scientific understanding that teaches us that social evils are not the result of witchcraft. After making grave errors in the course of finding these things out.

And so there are two reasons why judges will not be replaced by algorithms. KSS quote thoughtful Supreme Court Justice Stephen Breyer on the difficulty of setting sentencing guidelines other than on the basis of past judgments. ‘Why didn’t the commission sit down and really go and rationalise this thing and not just take history? The short answer to that is: we couldn’t. We couldn’t because there are such good arguments all over the place pointing in opposite directions.’^[3]

Thus there is no agreement, and no reason why there should be agreement, on the content of the sentencing algorithm. It is plainly useful for judges to know what other judges have done in similar  circumstances, but also necessary to modify and develop  the historic consensus in the light of fresh experience, changing social norms, and the particular circumstances of a case. A strictly algorithmic judge, deprived of discretion, would still be implementing the law of Hammurabi. 

The second weakness of the judicial algorithm is that the robotically delivered verdict of an impersonal computer does not accord with general conceptions of justice. Our society’s respect for human dignity requires that everyone is treated as an individual. In the words of the American legal scholar Laurence Tribe, ‘tolerating a system in which perhaps one innocent man in a hundred is erroneously convicted despite each jury’s attempt to make as few mistakes as possible is in this respect vastly different from instructing a jury to aim at a 1% rate (or even a 0.1% rate) of mistaken convictions’.^[4]  When the covid pandemic prompted England’s examining boards to replace human assessment with algorithms, the noise of an angry public forced the Education Secretary to abandon the scheme within days of the announcement of the results and effectively ended his political career.                     

While sentencing offenders is a public sector monopoly, insurance is provided by private companies in a competitive market, and the dynamics of the evolution of collective intelligence reflect that difference. We do not know the ‘correct’ premium for any idiosyncratic risk, even at the maturity of the policy. Different underwriters will arrive at different judgments. Customers will shop around so that there is a potential ‘winner’s curse’ – the business you get is likely to be the business you have underpriced. Thus even if you thought you knew all the relevant outcomes and their probabilities, you would be unwise to base your premium on that information alone. You need to understand your competitors and your clients as well as the range of insurable events. It is not an accident that insurers are clustered – ‘the room’ at Lloyds is at the centre of the City of London’s insurance market and there is similar physical proximity and information exchange in reinsurance centres such as Munich and Zurich – and other financial markets.

Good underwriters outperform bad underwriters, and insurance companies that select, train and promote good underwriters outperform their competitors. In this way, market pressures contribute to the development of the collective intelligence in risk assessment that has grown over the centuries since English gentlemen gathered in Thomas Lloyd’s coffee house to gamble on the fate of ships.

And social learning and markets will continue to advance such collective intelligence – unless KSS arrive with their noise audits, checklists and algorithms. The major financial crisis of our times occurred, in part, because bankers and their regulators wrongly believed that the judgment of experienced bankers should be replaced by scientific risk models derived from historic data which had been rendered irrelevant by the banking practices that the models had supposedly validated.

Much of what KSS describe as ‘decision hygiene’ – structure your assessments, seek different independent views – is sensible if hardly path-breaking. But just as much behavioural economics fails to recognise that what are described as ‘biases’ are often adaptive responses to radical uncertainty, KSS fail to recognise that the differences in subjective judgments of complex situations -’ noise’ – are not only inevitable but are desirable means of advancing our collective knowledge and intelligence. The Darwinian insight that an element of randomness is the means by which evolution allows people and cultures to adapt to changing, complex environments illuminates almost every aspect of life. Perhaps noise is not ‘a flaw in human judgment’ but ‘the secret of our success’.

^[1] https://www.pnas.org/content/108/42/E833.full

^[2] Henrich, Joseph. The Secret of Our Success: How Culture Is Driving Human Evolution, Domesticating Our Species, and Making Us Smarter, Princeton University Press, 2016.

^[3] Breyer quoted in Jeffrey Rosen, New Republic, July 11 1994

^[4] Tribe, L. H., ‘Trial by Mathematics: Precision and Ritual in the Legal Process’, Harvard Law Review, Vol. 84, No. 6 (1971), 1329–93