On 7 March 1907, Francis Galton wrote a brief, but interesting article for Nature entitled Vox Populi, which opens, “In these democratic days, any investigation into the trustworthiness and peculiarities of popular judgments is of interest.” True then, and true now, only more important these days.
Galton’s article revolved around a set of observations, to be described in a moment. His conclusion about them is of more interest. He said his results were “more creditable to the trustworthiness of a democratic judgement that might be expected.” Let’s see if that’s true.
Now Galton’s real purpose in this article, and in an earlier letter to the editor “One Vote, One Value”, was to advocate the median and not the mean as a summary measure. In this, I heartily and enthusiastically agree. Means, Galton wisely said, are subject to the wild speculations of “cranks”, which is to say, of lunatics, ideologues, and activists (but I repeat myself), which is to also say to extreme numbers. Medians are robust. His analysis of the observations nicely shows this. But that discussion we can have another day.
The observations were taken from a fair and consisted of a bunch of guesses of an ox’s dressed weight, in a manner similar to a jelly bean contest. Whoever was closest to the real weight won. Galton showed that the median of the guesses was close to the actual weight.
Many people, reading Galton, have said his analysis points to the so-called wisdom of the crowds (there is even a book with this title). One man might not know a lot, but many man cobbled together do. Or something. But, strictly speaking, the wisdom of the crowds is a fallacy. The Chinese Emperor’s Nose fallacy is one name for it.
If you ask a guy who hasn’t a clue about the value of some thing, his guess is useless. This follows from the “no clue” premise (having some clue is not having no clue). And a group of clueless is just as ignorant as the one man. Forming the mean or median or whatever from a collection of baseless guesses is no better than using the guess from any one man. This, Galton, good eugenicist that he was, would agree also has deep implications for democracy.
When quoting from his paper, people often forget these words. Speaking of the “judgments” of dressed weight, he said:
The judgments were unbiased by passion and uninfluenced by oratory and the like. The [then not unsubstantial] sixpenny fee deterred practical joking, and the hope of a prize and the joy of competition prompted each competitor to do his best. The competitors included butchers and farmers, some of whom were highly expert in judging the weight of cattle; others were probably guided by such information as they might pick up, by their own fancies.
His next sentence is key: “The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is of judging the merits of most political issues on which he votes, and the variety among the voters to judge justly was probably much the same in either case.”
This conclusion does not follow, nor even come close to following, from the premises. The premises are a group of uninfluenced interested experts made guesses about a matter in their expertise. And they did well, even very well. Their errors were small.
Contrast that to a largely ill- or uneducated harangued and harassed and increasingly largely disinterested citizenry asked to vote in national elections, or to express an opinion on something as complex as the Ryan health bill. Their guesses as to the “best weight” will be closer to the Chinese Emperor’s nose than the dressed ox. We have all seen those videos in which voters are asked who the Vice President is, or how many justices serve on the Supreme Court, and fail and flail. Or why we celebrate the Fourth of July or Memorial Day.
Yet Galton said, “The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is of judging the merits of most political issues on which he votes, and the variety among the voters to judge justly was probably much the same in either case.”
Times change. The voting franchise in 1907 is not what it is today, and not what some desire it to be (some call for kids to vote, etc.), and it’s fair to say that Galton did not anticipate this. In his time, when voting was (let us say) a more specialized activity, his judgement was closer to being true.
On the other hand, as has often been observed, experts are increasingly poor. Probably ox-weight guessers are as good as ever, but experts in any field which is in any way politicized are not. The love of theory, the fear of ridicule and ostracism, the derangement of activism and the other usual suspects corrode expertise. That, too, is an essay for another day.
Little wisdom of crowds, little skill in experts. An unhappy combination.