The wisdom of crowds is the consistent finding that the averaged judgements of a diverse group of independent people will nearly always be more accurate than any single person's judgement, no matter how expert that individual is. Note the emboldened words. The group must be diverse, with members having unique insights into the problem at hand. Group members must also be independent, in the sense that their own judgement is not contaminated or swayed by the opinions of others. In these conditions, the combined, diverse knowledge of a group of people can be effectively brought to bear on a problem. Judgements biased in one direction will be cancelled out by judgements biased in the other direction, as the group's combined verdict homes in on the truth.
As described by James Surowiecki in his excellent book, stock exchanges provide an ideal, though imperfect, medium for the collective pooling of wisdom as many thousands of individuals place their judgements on future outcomes. Stock exchanges often arrive at highly accurate judgements, both trivial as in the Hollywood Stock Exchange, and more serious, as in the share market's prediction of who was to blame for the Challenger space disaster.
There's also a fascinating literature on why crowds often work badly, rather than fulfilling their potential for wisdom. In group meetings, for example, research shows that people have an unfortunate tendency to talk about the information that they share, thereby undermining the diversity of knowledge in the group. Similarly, social dynamics can lead to diseases of the crowd such as "group think", in which the pursuit of consensus undermines the very independence of each individual's input that is so vital for the wisdom of the crowd to emerge.
Other new exciting research in this field suggests that individuals may be able to exploit the principles of the wisdom of the crowd on their own, by making repeated, independent judgements and averaging them.
Returning to Derren Brown's lottery explanation, we can see that the wisdom of crowds has no use for predicting the lottery. His group of 24 individuals did not have diverse insight into what numbers will come next. The history of lottery results has no bearing on each successive draw, so there was no purpose in the group studying the archives of past results. Even if past results did affect future results, the 24 individuals sat staring at the same data. They didn't each bring their own unique knowledge to the table. Moreover, if Brown had really wanted to exploit the wisdom of crowds, he ought to have kept the members of his group separate so as to maintain their independence and prevent them biasing each others' input. And finally, why on earth would he have had a group of just 24 people? With so much at stake, if there had been any sense in attempting to pool the collective wisdom on this challenge (which there wasn't), Brown should have exploited the combined wisdom of as many people as he possibly could.
These are the views of the Digest editor, not the British Psychological Society.
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