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Voting on the Ox

In response to:

Is the Right Choice a Good Bargain? from the March 5, 2015 issue

To the Editors:

In “Is the Right Choice a Good Bargain?” [NYR, March 5], Michael Walzer asserts that “statistical groups do especially well in answering factual questions,” and refers to an article of Francis Galton (“Vox Populi,” Nature, March 7, 1907) to support the claim. The phrase Walzer puts in quotes—“The ox weighed 1,198 pounds; the average estimate…was 1,197 pounds, more accurate than any individual’s guess”—is nowhere to be found and completely subverts Galton’s main point.

Galton didn’t even bother to compute the average of the 787 contestants who tried to estimate the weight of the ox: he picked out the “middlemost” estimate. One week earlier (“One Vote, One Value,” Nature, February 28, 1907) he had written:

How can the right conclusion be reached…? That conclusion is clearly not the average of all the estimates, which would give a voting power to “cranks” in proportion to their crankiness…. I wish to point out that the estimate to which least objection can be raised is the middlemost estimate, the number of votes that it is too high being exactly balanced by the number of votes that it is too low.

This does not in the least deny Walzer’s assertion, but has enormous importance in determining collective decisions.

Michel Balinski
Directeur de recherche de classe
exceptionnelle (emeritus)
CNRS and École Polytechnique
Paris, France