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.
Bryan, before you uncritically repeat Levy and Peart's lies, you might want to check your facts -- or just the footnotes to my book. Galton did, in fact, report the mean, long before Karl Pearson did. Galton's calculation appeared in Nature, Vol. 35, No. 1952 (3/28/07), in a response to letters regarding his original article. One of the correspondents had gone ahead and calculated a mean from the data that Galton had provided in his original piece, and had come up with the number 1196. Galton writes, "he makes it [the mean] 1196 lb. . . . whereas it should have been 1197 lb."
I find the fact that Levy and Peart wrote an entire article about Galton (and, to a lesser extent, about my use of him), and never went back and checked the original sources astounding in its own right. (They actually wonder in the paper, "However the new estimate of location came to be part of Surowieki’s account," as if the answer isn't listed right there in the footnotes.) What makes it even more astounding, though, is that they've written an entire paper about the diffusion of errors by experts who "pass along false information (wittingly or unwittingly)" while passing along false information themselves.
It also seems bizarre that Levy and Peart caution, "The expectation of being careful
seems to substitute for actually being careful," and yet they were somehow unable to figure out how to spell "Surowiecki" correctly. The article is a parody of itself.
I'm happy to enter into a discussion of whether the median or the mean should be used in aggregating the wisdom of crowds. But whether Galton himself thought the mean or the median was better was and is irrelevant to the argument of my book. I was interested in the story of the ox-weighing competition because it captures, in a single example, just how powerful group judgments can be. Galton did calculate the mean. It was 1197 lbs., and it was 1 lb. away from the actual weight of the ox. The only "falsehood" being perpetrated here are the ones Levy and Peart are putting out there, and the ones that you uncritically reprinted.
(I've already posted something similar to this at Overcoming Bias, where Robin, like you, went ahead and posted without checking the facts.)
My apologies for repeating Levy and Peart's mistake, James - I posted an update.
I'm puzzled, though, about why you would impugn Levy and Peart's mistakes as "lies." That strikes me as over-the-top. :-)
Thanks, Bryan. And if my rhetoric was a bit strong, I think it was probably in response to the fact that Levy and Peart wrote a paper in which they say "a key question is whether the tale was changed deliberately (falsified)," and never bothered to check the facts at all.
Fair enough, James.
What a fiasco...
Are Levy and Peart the pair who have been smearing the Galtonians for years? Jeez, you'd think they would have something better to do with their time...
Galton was 85 years old when he did the guess-the-weight study and realized that his preconception was completely wrong. So, rather than forget about it and take a nap, he reported his new finding to Nature, which became the starting point for the "Wisdom of Crowds" school of thought that James S. wrote about.
Galton was a great scientist and a great man.
Dear James,
I have had time to reflect and now I would like to offer a more detailed personal apology than what we've jointly posted before.
When I failed to find Galton's mean, in spite of your sufficient directions, I should have asked you directly for help. From these two failures of mine, and because Sandy trusted my work, we were led to the wrong conclusion that your account of Galton's mean was false instead of the right conclusion that your account was simply different than our accounts of Galton's median. If the accounts are merely different then we have many ways of asking which of the two estimators one might prefer. We began that helpful exercise. We did not stop there. When we said that your account was false, and asked a rhetorical question of how this came to be, we called into question my own intentions. We also wrongly called into question the care which scholars took in citing your work.
For all this, again, I offer a personal apology.
Best wishes,
David
Here's a less tendentious assessment of Galton's achievements by Jim Holt in The New Yorker:
http://www.newyorker.com/archive/2005/01/24/050124crbo_books