Why the successful prefer being average to extreme

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One of the most important, and least widely understood, ideas in economics is the importance of convexity – our preference for averages over extremes.

The Democrats won Montana by 3,000 votes and Virginia by 7,000. If either of these US senate races had come out differently, the future of the Bush presidency would also be different.

In Florida 2000, a relative handful of votes handed George W. Bush rather than Al Gore victory.

Modern American politics exemplify what Malcolm Gladwell called “tipping points”. Small differences in process can lead to sharp differences in outcomes. Contrast this American experience with Germany’s close election last year, where the narrowness of Chancellor Angela Merkel’s victory forced her to reach an accommodation with the opposition Social Democrats in a grand coalition.

This contrast is no accident. US politics has become increasingly polarised and polarising. Emphasis on the spoils of office and ideology encourages political leaders to build the narrowest coalition which might command a majority. Postwar Germany acquired an electoral system designed to favour consensus and resist extremism.

School physics teaches the difference between stable and unstable equilibria. A cone can – in principle – rest on its base or point. But it cannot really rest on its point because the slightest displacement tips it over. In political, business and economic life, some systems tip and others revert.

Much hinges on understanding which is which. Markets tip when there are advantages to having the same product as others – cool fashions for teenagers. The personal computer market tipped in favour of Microsoft’s Windows. Urban regeneration projects sometimes succeed triumphantly, sometimes fail dismally. People want to be in the same neighbourhood as people like them. Scale economies favour tipping – urban transport systems polarise between Paris, with an efficient metro and street chaos, and Los Angeles, with great parking lots and no buses. Ant colonies tip – ants sometimes follow each other around in a circle of death – and so do herds of fund managers.

Once you look for tipping phenomena, as Mr Gladwell did, you see them everywhere. He used the notion to explain epidemics of crime, syphilis and the popularity of Sesame Street. But reversion to the mean – the tendency for displaced systems to move back to their normal state – is much more general. Fortunately so. One of the most important, yet least understood, ideas in economics is the importance of convexity – our preference for averages over extremes. If you take an average of two attractive faces, most people find the resulting blend more attractive still. This phenomenon is general and the existence and stability of market equilibrium depends on it.

Political parties frequently polarise – especially in opposition – but find their survival depends on moving back towards the centre. Michael Porter offered a celebrated injunction to business not to be “stuck in the middle”. But there is more that is misleading than helpful in the maxim. While market success does depend on differentiation, the trick for an innovative company, as for a political party, is to differentiate itself just enough to appeal to a mass market. Companies that survive for decades – Exxon Mobil or General Electric, or Procter & Gamble – have achieved that by sticking to the fat and lucrative middle, while visionary leaders pushing transformational change come, and mostly go.

Mean reversion explains why star fund managers tumble, fatalities fall when speed cameras are installed on dangerous roads and why subordinates tend to improve performance when criticised but not when praised. No cause and effect is necessary: these processes simply return to their normal state. Fashions in clothes, fads in management and speculative asset prices often seem to tip and then to revert. Momentum drives behaviour in the short run but mean reversion rules in the long run. There always seem to be retailers who sweep all before them – Wal-Mart and Tesco today, Sears, K-mart and J Sainsbury in an earlier generation – but mean reversion strikes back. And so, despite the polarisation of US politics and its gerrymandered electoral map, Montana and Virginia voters gave a lesson in mean reversion to the White House.

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