August 4, 2011

Francis Galton’s Ox

(an excerpt from The Wisdom of Crowds by James Surowiecki)

One day in the fall of 1906, the British scientist Francis Galton left his home in the town of Plymouth and headed for a country fair. Galton was eighty-five years old and beginning to feel his age, but he was still brimming with the curiosity that had won him renown—and notoriety—for his work on statistics and the science of heredity. And on that particular day, what Galton was curious about was livestock.

Galton’s destination was the annual West of England Fat Stock and Poultry Exhibition, a regional fair where the local farmers and townspeople gathered to appraise the quality of each other’s cattle, sheep, chickens, horses, and pigs. Wandering through rows of stalls examining workhorses and prize hogs may seem to have been a strange way for a scientist (especially an elderly one) to spend an afternoon, but there was a certain logic to it. Galton was a man obsessed with two things: the measurement of physical and mental qualities, and breeding. And what, after all, is a livestock show but a big showcase for the effects of good and bad breeding?

Breeding mattered to Galton because he believed that only a very few people had the characteristics necessary to keep societies healthy. He had devoted much of his career to measuring those characteristics, in fact, in order to prove that the vast majority of people did not have them. At the International Exhibition of 1884 in London, for instance, he set up an “Anthropometric Laboratory,” where he used devices of his own making to test exhibition-goers on, among other things, their “Keenness of Sight and of Hearing, Colour Sense, Judgment of Eye, [and] Reaction Time.” His experiments left him with little faith in the intelligence of the average person, “the stupidity and wrong-headedness of many men and women being so great as to be scarcely credible.” Only if power and control stayed in the hands of the select, well-bred few, Galton believed, could a society remain healthy and strong.

As he walked through the exhibition that day, Galton came across a weight-judging competition. A fat ox had been selected and placed on display, and members of a gathering crowd were lining up to place wagers on the weight of the ox. (Or rather, they were placing wagers on what the weight of the ox would be after it had been “slaughtered and dressed.”) For sixpence, you could buy a stamped and numbered ticket, where you filled in your name, your address, and your estimate. The best guesses would receive prizes.

Eight hundred people tried their luck. They were a diverse lot. Many of them were butchers and farmers, who were presumably expert at judging the weight of livestock, but there were also quite a few people who had, as it were, no insider knowledge of cattle. “Many non-experts competed,” Galton wrote later in the scientific journal Nature, “like those clerks and others who have no expert knowledge of horses, but who bet on races, guided by newspapers, friends, and their own fancies.” The analogy to a democracy, in which people of radically different abilities and interests each get one vote, had suggested itself to Galton immediately. “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,” he wrote.

Galton was interested in figuring out what the “average voter” was capable of because he wanted to prove that the average voter was capable of very little. So he turned the competition into an im-promptu experiment. When the contest was over and the prizes had been awarded, Galton borrowed the tickets from the organizers and ran a series of statistical tests on them. Galton arranged the guesses (which totaled 787 in all, after he had to discard thirteen because they were illegible) in order from highest to lowest and graphed them to see if they would form a bell curve. Then, among other things, he added all the contestants’ estimates, and calculated the mean of the group’s guesses. That number represented, you could say, the collective wisdom of the Plymouth crowd. If the crowd were a single person, that was how much it would have guessed the ox weighed.

Galton undoubtedly thought that the average guess of the group would be way off the mark. After all, mix a few very smart people with some mediocre people and a lot of dumb people, and it seems likely you’d end up with a dumb answer. But Galton was wrong. The crowd had guessed that the ox, after it had been slaughtered and dressed, would weigh 1,197 pounds. After it had been slaughtered and dressed, the ox weighed 1,198 pounds. In other words, the crowd’s judgment was essentially perfect. Perhaps breeding did not mean so much after all. Galton wrote later: “The result seems more creditable to the trustworthiness of a democratic judgment than might have been expected.” That was, to say the least, an understatement.

This indicates the reliability of probabilistic statistics.

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