The Wisdom of Crowds

The Wisdom of Crowds

“In these democratic days, any investigation into the trustworthiness and peculiarities of popular judgments is of interest.” (Francis Galton)

65,78,84,85,89,89,90,96,100,113,125,130,145,171,173,215,230,250

Above are the guesses for the number of sweets in the jar for our office Children in Need fund raising competition.

The winning entry to 127 – the correct number – was 125, which was just 2 out.

But the rounded average was 129, also just 2 out.

This is a good illustration of “The Wisdom of Crowds”, a phenomena described in the book of that name by James Surowiecki.

The notion that a group’s judgement can be surprisingly good was most compellingly justified in James Surowiecki’s 2005 book The Wisdom of Crowds, and is generally traced back to an observation by Charles Darwin’s cousin Francis Galton in 1907.

“A weight-judging competition was carried on at the annual show of the West of England Fat Stock and Poultry Exhibition recently held at Plymouth, A fat ox having been selected, competitors bought stamped and numbered cards, for 6d. each, on which to inscribe their respective names, addresses, and estimates of what the ox would weigh after it had been slaughtered and " dressed." Those who guessed most successfully received prizes. About 8oo tickets were issued, which were kindly lent me for examination after they had fulfilled their immediate purpose. These afforded excellent material.”

“The judgments were unbiased by passion and uninfluenced by oratory and the like. The sixpenny fee deterred practical joking, and the hope of a prize and the joy of competition prompted each competitor to do his best. The competitors included butchers and farmers, some of whom were highly expert in judging the weight of cattle; others were probably guided by such information as they might pick up, and by their own fancies.”

“The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is of judging the merits of most political issues on which he votes, and the variety among the voters to judge justly was probably much the same in either case. After weeding thirteen cards out of the collection, as being defective or illegible, there remained 787 for discussion. I arrayed them in order of the magnitudes of the estimates, and converted the cwt., quarters, and lbs, in which they were made, into lbs., under which form they will be treated.”

Galton pointed out that the average of all the entries in a ‘guess the weight of the ox’ competition at a country fair was amazingly accurate – beating not only most of the individual guesses but also those of alleged cattle experts. The arithmetic mean of the 787 guesses came to 1,197lb. The true dressed weight of the ox was 1,197lb!

This is the essence of the wisdom of crowds: their average judgement converges on the right solution.

James Surowiecki takes this up, and argues, with examples, that a diverse collection of independently deciding individuals is likely to make certain types of decisions and predictions better than individuals or even experts.

It is important that the individuals are diverse and independent. In our office, there is quite a diversity in people’s likes and dislikes, hobbies, families or being single, etc. And the slips were placed in an box so no one could be influenced by them. Both are important.

If everyone let themselves be influenced by each other’s guesses, there’s more chance that the guesses will drift towards a misplaced bias. What you can end up with instead is herding towards a relatively arbitrary position.

Diversity is also important. A study in 2011 by a team led by Joseph Simmons of the Yale School of Management in New Haven, Connecticut found that group predictions about American football results were skewed away from the real outcomes by the over-confidence of the fans’ decisions, which biased them towards alleged 'favourites' in the outcomes of games.