In March of 1907, the journal Nature published a report from the eugenicist and early statistician Francis Galton. Titled simply “Vox Populi,” it described one highlight of a rural fair that took place near Plymouth, England. For sixpence, locals could guess the weight of an oxen to be slaughtered, with the most correct submission receiving a grand prize of the animal’s dressed and butchered carcass. 800 fairgoers participated.
Galton’s observation of the proceedings, which he’d stumbled upon by accident, was the birth of a concept we now call “crowd wisdom.” No one guessed the weight correctly—which is interesting in itself—but Galton calculated the median and mean of their guesses. What he discovered is that, while no one participant got the correct answer spot-on, every participant together made an almost perfect guess. The mean (average) submission was 1,197 pounds—of guesses ranging from about 1,000 to 1,500 pounds—while the correct weight of the oxen was 1,198 pounds. One pound off.
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It might not be terribly surprising to us, but to Galton it was somewhat of a shock. As a eugenicist in favor of “careful breeding,” he tended to have a fairly poor impression of the average person, who, in Galton’s words, were marked by “stupidity and wrongheadedness … so great … as to be scarcely credible.” In the Nature article, he further noted, “This result is, I think, more creditable to the trust-worthiness of a democratic judgment than might have been expected.”
Galton was reasonably confident that his 800 person sample was a general or inexpert slice of the population, despite the sure presence of at least some oxen experts among the rural working-class participant pool. This was an important feature of his fundamental observation of crowd intelligence being a property of reasonably random yet sufficiently large population samples. “The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox,” he wrote, “as an average voter is of judging the merits of most political issues on which he votes.”
In 1869, several decades earlier, Galton had published a volume titled Hereditary Genius which first suggested that intelligence had a basis in genetics. His ideas were rooted in the notion of standard deviation, or how much variance might be expected from a mean average. If the mean guess was 1,198 pounds, how many people would be likely to have guessed 1,300 pounds or 1,290 pounds or even 0 pounds?
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It turns out that using a normal distribution, a bell-shaped curve with the spread’s mean value at its peak (above), is useful for predicting all kinds of statistical behavior in the social and natural sciences. Using just the 1,198 pound mean and the total number of participants, we should be able to say with some accuracy how many people guessed within this or that range of weights. This gives new life to the idea of random error.
Galton was interested in all of this because he was interested in how intelligence varied across a population. Which, for a budding eugenicist, would have been a chief concern. And indeed, the very mathematical notion of standard deviation is usually credited to Galton, who really just wanted a good way to measure and quantify the individual differences and variations that exist among populations of humans. That is, what is normal anyway?
Galton died just a couple of years after his famous “Vox Populi,” so it’s perhaps somewhat comforting to think that as he took his genes with him to the grave—many of which would have been shared with his cousin, Charles Darwin—this notion of normal intelligence had broken through and the absurdity and cruelty of chasing “smart” genes had become at least somewhat clear. The normal distribution spreads both ways.
