James Surowiecki starts his book The Wisdom of Crowds telling how Francis Galton in 1907 used a crowd to guess an ox’s weight:
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. … The crowd has 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 weighted 1,198.
David Levy and Sandra Peart say Surowiecki got it all wrong. Galton did not [AT FIRST] even bother to calculate a mean, as he saw his data was clearly not normally distributed. He used the median (of 1207), which was much further off than the mean, but by modern standards clearly the better estimator.
It was Karl Pearson in 1924 who calculated the mean. (Line crossed out, and [clarifier] added later.)
This description of what Galton did with the guesses misrepresents what Galton actually did. Galton was clear that the distribution of guesses was not normal, writing that "The abnormality of the distribution of the estimates now becomes manifest, …” (Galton 1907b, p. 451). Surowieki has replaced Galton’s statement with the claim that Galton "graphed them [the guesses] to see if they would form a bell curve" – allowing the remaining possibility that the guesses might be normal. Galton’s principled opposition to the mean as the voice of the people, which Pearson supplemented by the use of the mean, is now described as Galton’s use of the mean. Finally, the reported estimate of the vox populi has been changed from 1207 to 1197.
Several authors, "Sunstein (2006, p. 24), Solomon (2006), Caplan (2007, p. 8)", copied Surowiecki’s
error [VERSION], and several recent papers have argued about how close prediction market prices are to mean beliefs. The original Galton paper can be found reprinted in Levy and Peart’s book Vanity of the Philosopher and online.
Added: In the comments, Surowiecki says Levy and Peart are very wrong: Galton did too mention the mean, when responding a few weeks later to a letter that mentioned the mean. He cited this letter in his book footnotes. Hopefully we can get Levy and Peart to respond.
Added: Here are Surowiecki’s comments and Levy and Peart’s responses in full: