EW JOURNAL

A military psychologist’s file on an officer candidate in Israel’s new army, sometime in the early 1950s, might have read: displays natural authority, keeps his head under pressure, strongly recommended for command. The number eventually attached to recommendations of exactly that kind, once anyone checked them against how the candidates actually performed months later in the field, turned out barely better than a coin flip would have managed without interviewing anybody at all. The psychologist’s name was Daniel Kahneman, and the gap he had just found, between how right a judgement feels and how right it actually is, he later gave a name precise enough to outlast the argument that produced it: the illusion of validity.

The exercise behind that file was a deliberately stressful one: a group of candidates, told to get a telephone pole over a wall without anyone touching the wall, while a panel of psychologists watched for who took charge, who buckled, and who kept his composure. Kahneman and his colleagues came out of each session with vivid, specific, mutually agreed impressions of who had officer material and who did not. The feedback, when it eventually arrived from the training schools downstream, showed almost no relationship between those confident impressions and how the candidates actually went on to perform. The next morning’s group produced exactly the same vivid confidence, undiminished by yesterday’s figures, as though the statistics belonged to some entirely different exercise from the one being watched with such conviction.

He later named the deeper mechanism What You See Is All There Is: the mind builds its confident story entirely out of whatever evidence happens to be in the room, and never thinks to discount that confidence for the evidence it was never shown. An assessor watching a candidate carry a telephone pole has no instinct for wondering what the same candidate might have revealed under a test he was never given. It was, by his own later account, one of the formative irritations behind the decades of research with Amos Tversky that eventually won him a Nobel memorial prize in economics, an odd destination for a man who had never taken an economics course in his life.

This is the detail Kahneman kept returning to for the rest of his career: he told the story himself, decades later, in Thinking, Fast and Slow, still visibly amused by how little his own certainty had been worth.

Confidence of this kind, he eventually concluded, tracks the coherence of a story, not the accuracy of a prediction built from it. A judgement feels right when its pieces fit together smoothly and nothing in the room contradicts it, on exactly the same terms whether the pieces happen to be true or not. A roomful of equally confident analysts can divide on a single call, each one sincere by his own lights, and only the outcome will ever reveal who was right. Philip Tetlock ran a much larger, more public version of the same test decades later, tracking several hundred experts, pundits and academics across two decades and tens of thousands of individual predictions about politics and economics, work he eventually published as Expert Political Judgment. The average expert, it turned out, forecast little better than random guessing would have, and confidence ran in almost the opposite direction from accuracy. The most frequently quoted, most certain-sounding forecasters tended to be the least reliable: hedgehogs, in the term Tetlock borrowed from Isaiah Berlin, wedded to one big idea they fitted every new fact around regardless of what the fact actually was. The more modest forecasters, the foxes, who changed their minds in small increments as evidence arrived and described their own confidence as a range, did measurably better. Fame and airtime rewarded almost exactly the wrong temperament.

Numbers exploit the same feeling more efficiently than words ever manage. A forecast offered as around a third invites a reasonable scepticism, the kind any sensible listener should bring to a guess. Rewrite the identical forecast as 33.4 percent, and the number suddenly carries an authority the underlying knowledge never supplied, merely by changing its costume. The world the two versions describe is identical; only the telling has changed.

Probability, stated honestly, collides badly with an audience untrained in reading it. Statistical forecasters gave Donald Trump something approaching a three-in-ten chance of winning the 2016 American presidential election, a number low enough to be read, by most people who saw it, as a confident prediction that he would lose. When he won, a great many of those same people concluded the forecasters had been wrong, when a three-in-ten event is merely an event that happens a little under a third of the time, and happens all the same with some regularity. The forecast had been honest about its own uncertainty in a way a flat prediction never is. Almost nobody reading it that November was equipped to hear the honesty for what it was.

Those extra digits mostly stand as a certificate for the precision of the arithmetic alone, a different thing entirely from the precision of whatever estimate was fed into it in the first place. A spreadsheet will carry a guess out to as many decimal places as the formula allows, flawlessly, and the flawlessness belongs entirely to the multiplication, a separate matter from the number that started the chain.

Equity research runs the identical trick at industrial scale, a routine most analysts perform daily for every company they cover. They build a discounted cash flow model from a revenue growth assumption, a margin assumption, a discount rate and a terminal growth rate, every one of them a judgement call dressed as an input, and the machine returns a single number: a price target of, say, 47.32 dollars a share, carried out to the cent. Change the discount rate by half a percentage point, a difference well within the model-builder’s own honest uncertainty about which rate is correct, and the output can move by a tenth of the share price or more. The cent in 47.32 marks only where the arithmetic happened to stop.

Imagine a surveyor measuring the height of a cliff face to the nearest millimetre on the one afternoon a landslide has just taken two metres off the top, before anyone has thought to report it. His instrument performs perfectly; his answer is worthless, because precision was never the part of the job that could fail that day. He packs up his tripod satisfied, logs the reading to four decimal places, and drives home unaware that the number he just certified describes a cliff that no longer exists. A cracked premise fails at the fourth decimal exactly as completely as it fails at the first, indifferent to how many decimal places follow it.

All of this argues for honesty about which part of a claim is solid and which part is scaffolding borrowed from hope. A wide range stated plainly, with the uncertainty left visible, is a more useful and a more professional object than a single confident figure that hides exactly where its confidence actually comes from, even though the range will never look as impressive on a slide. Saying so costs something real in a meeting, which is exactly why it happens so rarely.

Professional forecasting runs this exact test every quarter. A sell-side analyst’s earnings estimate arrives to the cent, carrying an authority that one single-point number cannot possibly support, given how many assumptions sit underneath it unstated. Central banks, oddly, have moved the other way. Since the 1990s the Bank of England has published its growth and inflation forecasts as fan charts in its quarterly Inflation Report, bands of shaded probability widening across the years ahead, nothing like a single confident line, built specifically so that a reader cannot mistake the forecast for a fact. One of these two habits is honest about what a forecast actually is. The other sells a certainty it does not have, at a price its customers rarely notice they are paying.

An individual investor meets the identical trap watching a market strategist name a year-end target to the exact index point on television, in the same confident register regardless of whether last year’s target was ever right, or the one before that. The confidence mostly reflects a practised understanding of what sounds authoritative on screen, a different skill from forecasting entirely.

Kahneman himself said, decades afterward, that knowing all this changed remarkably little about how confident his own next snap judgement would feel. The feeling of validity is simply a sensation, produced just as reliably by a tidy story as by a true one, persisting at full strength even once you know better, exactly as it did for the man who first named it, and exactly as it is doing to you on this very page.