Beauty contests and when crowds go wrong
As the authors acknowledged, the idea behind composite photos was hardly new.
In the 1870s, Sir Francis Galton, creator of statistical regression and correlation, came across a set of what we would today call police "mug shots". Galton, who also later pioneered the use of fingerprints in criminal investigations, hoped to identify physical traits that might predict unlawful behavior. He had been toying with the idea of creating composite portraits by superimposing photographic exposures, and the mug shots were perfectly suited for this project. After examining some early results, Galton noted, "All composites are better looking than their components, because the averaged portrait of many persons is free from the irregularities that variously blemish the looks of each of them." Galton went on to publish a number of articles on "composite portraiture", which included a reconstruction of Alexander the Great's likeness based on six different ancient coins, a report on pedigree horses, and even an attempt at "analytical photography" in which a special process would be used to exaggerate the distinct features of a face. Clearly, there is some eugenic motivation behind much of this enquiry, and indeed the political correctness of the late 20th century has (understandably) robbed Galton of some notoriety.
Prediction market enthusiasts will probably be familiar with Galton's ox-weight guessing contest as described by James Surowiecki. The logic behind the wisdom of the crowd as exemplified there is eerily similar to the averaging of portraits. Pertaining to group judgment, individual errors and biases tend to cancel each other out as sought-after information is distilled in some aggregate measure of belief. Pertaining to beauty, asymmetries in facial structure and complexion likewise cancel-out, yielding pleasing symmetrical and robust features.
So where do crowds go wrong? When biases lack diversity, and here we can reference Keynes' "beauty contest", in which judges suppress their own opinions and vote according to their predictions of how other judges will vote, or by even higher-order predictions. This loss of independence can cause initial biases to wildly exaggerate themselves instead of neutralizing one another. Keynes suggested the beauty contest dynamic as a metaphor for the stock market, and this is sometimes apt. At least, there is pervasive feedback and momentum trading in established markets, and these markets deal in objects much less tangible than oxen and jelly-bean jars. Insofar as returns on a given scale don't seem to fit a normal distribution, these dynamics might well play a role. Though, like many fiercely independent critics, they might overstate their case, Taleb and Mandelbrot warn, "One can safely disregard the odds of running into someone several miles tall, or someone who weighs several million kilogrammes, but similar excessive observations can never be ruled out in other areas of life."