‘The wisdom of crowds’ has become a modern cliché.  And a strange one – the crowds which attended the Nuremberg Rallies, or cheered the tumbrels of the Reign of Terror, were anything but wise.  Many adjectives might be applied to the assemblies which 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 the question. How can large numbers of people, not so different from 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 – often exploited by unscrupulous or mentally unbalanced leaders. Groups of people with similar opinions reinforce each other’s views and thus render the expression of their opinions more extreme.  The answer to the question ‘what were they thinking?’ is that mostly they were not thinking very much 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, citing  Francis Galton’s observation at an ox weighing competition.(actually Galton was concerned with the median rather than the mean  estimate, but let that technical detail pass)   

        But the number of practical situations in which this statistical property is useful is severely limited.  It is usually better to direct effort to reducing the error of estimates rather than increasing the number of erroneous estimates.  That is why we prefer to entrust the navigation of a plane to a skilled pilot instead of using the average of the opinions of the passengers.

The wisdom of crowds becomes a pathology when the estimates of the members of the crowd cease to be independent of each other, and this is likely when the crowd is large, or ill-informed, or both. It is entirely rational to adopt the common opinion on a subject about which one knows little; I believe the earth is round because that is the balance of informed opinion, and would a millennium ago have believed it to be  flat, for the same reason.

         It is in the nature of a crowd to turn on anyone who dissents from what is already the average opinion.  This is equally true on the streets of revolutionary Paris, the squares of Pyongyang, and the terraces of Chelsea Football Club.

         Or on the trading floor of an investment bank.  The supposed wisdom of crowds is used as justification for claims of market efficiency.  Crudely, in slogans such as ‘the market knows best’ and ’you can’t buck the market’.   At a sophisticated level, the idea provides rationale for a regulatory philosophy which attempts to reproduce the conditions required for the validity of Galton’s result – the existence of many independent estimates of the same unobservable variable.

So we aim to promote a trading environment characterised by many conflicting assessments of the value of a security based on identical– and therefore necessarily limited – information about the value of securities.  The belief that an aggregate of casual opinions provides a better process of value discovery than a flow of informed judgment through close engagement by investors is an article of faith rather than a matter of empirical evidence.  The distinguished mathematician, Francis Galton, wrote of the wisdom of crowds.  The still more distinguished mathematician Isaac Newton wrote, perhaps more wisely, of their madness.