Today, an excerpt of Chapter 5 from Everything You Believe Is Wrong. This is only a brief excerpt from a long chapter which lists a number of voting fallacies and arguments against democracy, the worst of which is the Wisdom of Crowds Fallacy.
You may also download a PDF of the entire first chapter (with Table of Contents).
This comes in the middle of the chapter with many examples given before Galton. I hope you will be able to infer the gist, however.
On 7 March 1907, Francis Galton wrote a brief but interesting article for Nature magazine entitled “Vox Populi”, which opened, “In these democratic days, any investigation into the trustworthiness and peculiarities of popular judgments is of interest.” This was true then, and it is true now, only it is more important these days.
Galton’s article revolved around a set of observations he made at a fair. Galton apparently liked democracies and sought evidence justifying them through the crowd-wisdom of voting. He said his results were “more creditable to the trustworthiness of a democratic judgment than might be expected.” Let’s see if that’s true.
The main purpose of Galton’s article, and in an earlier letter to the editor “One Vote, One Value”, was to advocate the median and not the mean as a routine summary measure of sets of numbers. This is an obscure statistical argument of little interest to the average reader (a pun), but I heartily and enthusiastically agree with him. But if you won’t mind indulging me for two paragraphs, we can come to a larger point. Arithmetic means, Galton wisely said, are subject to the wild speculations of “cranks”, which is to say, of lunatics, idealogues, and activists. These eccentrics are more likely, when asked to make guesses, to offer extreme numbers.
Recall the example of Mesd-su-Re’s nose length [which starts this Chapter]. Suppose we had three guesses by men in the street, say, 2 inches, 3 inches, and 42 inches. The arithmetic mean of these is (2 + 3 + 42)?3 = 15.7. The median, which is the center measure, is 3 inches. The median comes far closer to the truth (which was 0) than the mean. Medians are robust, Galton says, and we must agree. His analysis of the observations he chose nicely shows this. Thus endeth the math.
Galton’s observations were taken from a county fair and consisted of guesses of an ox’s dressed weight, in a manner similar to the 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. And he marveled.
Many people reading Galton through the years have said that his analysis points to the wisdom of crowds. One man might not know a lot, but many man cobbled together do. Or so the story goes. But, strictly speaking, the wisdom of the crowds is a fallacy, as we saw.
Some Clue Is Not No Clue
If you ask a man 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 the same as having no clue. A group of clueless is just as ignorant as one clueless man. Forming the mean or median (or any other measure) from a collection of baseless guesses is no better than using the guess from any one man. Galton, good eugenicist that he was, would agree that this also has deep implications for democracy. But he never managed to draw that lesson.
When quoting from Galton’s paper in support of crowd wisdom, people often forget these words. Speaking of the “judgments” of the dressed ox’s 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 this: 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. As we should expect and hope them to be.
Did you also notice the poll tax? The six-penny fee to insure “skin in the game”. Poll taxes are out of favor.
No Clue Is No Clue
Contrast Galton’s “election” 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 a national health bill. Their guesses as to the “best weight” will be closer to the situation of guessing Mesd-su-Re’s nose length than guessing the weight of a dressed ox. We have all seen videos in which voters are asked who the Vice President is, or how many justices serve on the Supreme Court, and we see how the respondents flail and fail.
Galton was wrong. The average expert competitor is vastly more fitted for making guesses over matters on which he is expert than the average uneducated voter is of “judging the merits of most political issues on which he votes”. This judgment may well be true in small, local elections, where the average voter is or can be an expert. But it has not proved to be so for large elections, where most voters are anything but experts, and where the propaganda is thick and abundant.
Times change. The voting franchise in 1907 is not what it is today, and not what some desire it to be (some now call for children 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 judgment was closer to being true. Mathematics, however, is not going to rescue the justification for one-man-one-vote.
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