Vox Populi vs. Experts

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.


  1. Actually, when it comes to healthcare, at one point or another, or a few or many, and to one degree or another, or a few or many, we all will learn something about healthcare in America. Paul Ryan, or even a practicing physician, can be out-experted in this subject by many a common man on the street. Conflicted interests, from the AMA to the private insurance and pharmaceutical industries, may be “experts,” but expert at what?

    The main reason Obamacare (or something better) was so difficult a sell at the time was because at any given moment, most people are well. But as time goes by, more and more people accumulate who have not been or are not well. So, when Obamacare first passed, many people, being well and not having had much experience dealing with America’s healthcare system, especially the young, fit and brash, couldn’t understand why it was even needed, let alone find it was some national emergency that desperately needed attention.

    Now, the GOP won’t repeal it! Now that some years have passed since it’s inception, enough people have had experience with our healthcare system to have a more developed understanding, and they see that we need Obamacare, and more needs be done. Many of the “experts” (conflicted interests) have been exposed as liars.

    We have to be careful with people who call themselves “experts.” Often they are just liars and thieves looking to get one over on the masses for personal gain. Healthcare, since you brought it up, and the inability of the GOP to get rid of Obamacare in particular, is the perfect example of democracy working and how “experts” are often just con-men.


  2. Briggs —

    What is an informed voter? Who really KNEW Trump would become Romney McCain within three months?

  3. Experts: People who know almost everything about next to nothing.

    Then there is the bubble effect. People surrounding themselves with the like minded ended up missing things, things even quite obvious to other observers.

  4. Who knew that few Americans were sick back when Obamacare was pushed through! Only now, seven years later, have people gotten sick and most Americans are not “well.” I recollect that this was the bill that we had to pass just to find out what was in it. One of the things in it was a phase-in, so that it did not go fully into effect until just this past year, when premiums soared. (Premiums soared for the usual reason: If you can wait until you have an accident before you buy auto insurance, auto insurance will go belly-up very quickly. That’s because it is no longer insurance. When you require someone to underwrite a sure thing, it will cost, a lot.

    Naturally, the proposed rewrite of the time bomb includes the very detonator that made the original unsustainable. No one seems to realize the usefulness of water-tight compartments on keeping the vessel afloat or on the need of would-be central planners to know diddly-squat about the thing they are planning.

    “Why is present government policy… now determined by people who would have serious trouble managing a whelk stall?”
    — Laurie Taylor

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