The wisdom of crowds” has become a modern cliché. And a strange one — the crowds that attended the Nuremberg Rallies, or cheered the tumbrils of the Reign of Terror, were anything but wise. Many adjectives might be applied to the assemblies that gather to applaud Dear Leader Kim Jong Un or cheer Chelsea Football Club — but “wise” is not one. Anyone standing back from these events must ask themselves a question: how could large numbers of people, so similar to ourselves, behave like that? What on earth were they thinking?

There is considerable research on the factors that influence the behaviour of crowds. We experience a need to affirm group or tribal identities — a fact that is often exploited by unscrupulous or mentally unbalanced leaders. Groups of people with similar opinions reinforce each other’s positions, encouraging one another to adopt ever moreextreme views. The answer to the question “what were they thinking?” is that, mostly, they were not thinking at all. That is often the nature of social behaviour.

So how did the phrase “wisdom of crowds” come into being? It is an expression of the mathematical property that an average of many independent estimates of the same variable has a lower expected error than the individual estimates themselves. That was the context of the example which James Surowecki used to introduce the idea in his widely read book of the same name, citing the distinguished mathematician Francis Galton’s observations at an ox weighing competition (actually, Galton was concerned with the median rather than the mean estimate, but let that technical detail pass).