Surowiecki's Levy and Peart's Mistake
By Bryan Caplan
In my book, I reference Surowiecki’s “guess-the-weight-of-an-ox” anecdote. My colleague David Levy and his co-author Sandra Peart show that isn’t quite right. Contrary to Surowiecki, Galton reported the median guess, not the mean – which was reported by Pearson years later. (Since my account doesn’t mention Galton or Pearson, I said nothing false; but I was thinking something false…)
For historians of thought, Surowiecki’s error is serious. But note that Levy and Peart don’t claim that Surowiecki’s numbers are incorrect. Surowiecki correctly reports the mean of the distribution; he just failed to correctly report who calculated that mean.
On reflection, moreover, it’s clear why Surowiecki wanted to report the mean. As he explains at length, it’s possible for the mean guess to be more accurate than any individual’s guess. It’s not possible, however, for the median guess to be more accurate than any individual’s guess – because the median guess IS the guess of the median individual!*
The other funny thing: Despite Levy’s love of medians, this is an example where the mean is closer to the truth!
* Unless there is an even number of respondents, and the two middle respondents disagree.
Update: By their own admission, Levy and Peart didn’t check Surowiecki’s footnote. Galton provided the mean guess in a letter to Nature. My apologies to James Surowiecki for repeating their mistake.