Statistics

The Non-Wisdom Of Crowds And Voting

This post first appeared in modified form on 29 Januarty 2014. It also appears (also modified) in Chapter 4 of Everything You Believe Is Wrong.

Have you heard of Mesd-su-Re? One of the participants of the Great Harem Conspiracy under Ramses III? Probably not. But I need to know the length of his nose right before he died (don’t ask why). I thought I’d invoke the “wisdom of crowds”, i.e. the Internet, and run a reader poll. Send this request to everybody you know, the more the better. Write down what you think the length was (inches or centimeters) and I’ll take the average. Got to be a pretty good guess, right?

Let’s tweak it, make it better. Suppose we run a national campaign to raise awareness about estimating Mesd-su-Re’s nose. TV ads, radio spots, pundits, community organizers, teachers, even bureaucrats all getting the word out about this important subject. That’ll really bring ’em in!

Before we begin, I should tell you that only vile racists guess lengths under four inches. Only those sympathetic with the war on women go short. The right side of history is with the long nose! Elites stand as one. Stars and starlets agree: length matters.

Okay, everybody. Put down your numbers. I’ll wait here.

Argumentum ad populum.

He said what?

Ignore the blatant political prompting and suppose only that I had asked for the length of Mesd-su-Re’s nose. If people had no information, other than the usual olfactory arcana we all possess—e.g., none of us has seen a human nose longer than one meter and noses can’t have negative length—there is no reason to suppose just guessing-and-averaging is helpful. How could it be?

Ignorance plus ignorance divided by two is still ignorance. Ignorance-averaging is a fallacy which is well known; goes by the name The Chinese Emperor’s Nose. I changed it to an Egyptian Prince here for variety and for a second reason to be revealed below.

The proof the Wisdom of Crowds is the Chinese Emperor’s Nose fallacy is somewhat involved, but here’s a rough sketch. People’s guesses about Mesd-su-Re’s nose will have a minimum, maximum, and some arithmetic mean which lies between (or at one of) these two. If people have no idea about the length (except possibly rough bounds; this is the key) then the mean of guesses is probably near the midpoint, the center of maximum minus minimum. Then regardless of where the real answer lies, the error (distance from guess to real answer) averaged across people will be the same as the error using the mean. In other words, crowds have no wisdom of subjects in which they are ignorant.

Wait! That the Wisdom of Crowds can sometimes provide reasonable predictions is obviously true. It could work in the sense as when an economist throws an equation at a list of stocks which sticks. But that’s luck. Crowd wisdom is also successful when people have some unbiased idea of the answer. If individuals in a group had opinions like, “I don’t know exactly what the answer is, but I know or can see it’s X plus-or-minus” then averaging can provide superior guesses to the average individual.

Yet when a crowd is fed biased information the game is off.

Example. You might look at that jar of pennies (long-time reader and contributor DAV reminded me of this example) and know that it can’t contain a million pennies; no, nor a hundred thousand. But we all know pennies and many of us have jars of change, so we could all form a crude but not insane idea of the number. The average of many in this case is likely to be a good guess.

Then imagine a moustachioed slickster standing by the jar whispering, “Psst, buddy. There’s a solid cone of cork in the middle. Only looks like there’s a lot of pennies. Word to the wise.” Finger on the nose and everything. Hey, he might be in on it: could be a hot tip—and if many think so there goes the accuracy of the average (supposing he’s fibbing).

Recapitulation. Wisdom of the crowds isn’t worth squat when individuals are ignorant of the subject matter they’re guessing. Averaging is okay, but only when folks are using unbiased information. The bad news is already well known: spreading misinformation works. People, even groups of them, will come to wrong conclusions conditioning on flawed premises.

So what does this have to do with voting? Everything. And for all the obvious reasons.

Here’s the answer. Zero, you racist. Inches or centimeters. The length of Mesd-su-Re’s nose at the end of his life. Ramses had it sliced off for daring to corrupt his (Ramses’s) harem. Ouch.

See also Voting (And Wisdom of the Crowds). And our friend Jaap Hanekamp’s blog for an entry on how this applies to science.

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Categories: Statistics

16 replies »

  1. Voting is even worse than you describe, when the ‘right answer’ is not known.

    One can construct *some kind* of argument for the ‘wisdom’ of voting, when the results of voting can be compared with the known right answer; but when the right answer is defined as… “whatever is the result of a vote” – as is the case with innumerable committees, and with elections; then we have an ineradicable, uncorrectable problem.

    The *assumption* that voting leads to the best/ morally-right outcomes (by definition), then dictates in advance that all and any possible outcomes as automatically the best, and morally superior to any other mechanism for answer questions.

    And yet it has long been *known* (at least the arguments seem solid to me) that voting leads to irrational outcomes – https://infogalactic.com/info/Arrow%27s_impossibility_theorem .

    All that aside; voting also prevents any individual taking moral responsibility for resulting decisions – which means that *nobody* is responsible – which means that voting is a moral ‘black box’; which means that being bound to decide by the results of voting is intrinsically immoral.

    In a genuinely Christian society, there would be no voting.

  2. Changed my mind, downvoting instead — Briggs used the word, “folks” — Obama popularized that word, instead of “people”, trying to be folksy, the phony.

  3. Okay, changing my mind again, pretty funny this Medusa dude, or whatever, had his schnozz chopped off. I wonder if maybe it was some other part what got departed… two thumbs up.

  4. Whoops, just read NYTimes headline condemning this post — changing back to downvote.

    Checking Twitter now…

  5. “In a genuinely Christian society, there would be no voting.”

    That’s overstating it. The Holy Roman Emperors were originally elected. The Popes to this day are still elected. There is a place for voting, the problem is that it’s seen as an absolute good instead of a means to an end. That’s how universal suffrage ended up looking like a good idea instead of the immoral insanity that it actually is.

  6. Murphy’s 2nd law: the majority is always wrong. (The prob that the majority is wrong on any issue varies directly with the complexity of the issue relative to the knowledge level of the time and place).

    Corolaries: climate is complex; most of what people believe about progressives ideas is wrong….

    (PS. Negative snooz length is possible, briefly.)

  7. Look on the bright side.

    Once upon a time, when people had no choice in the matter, the ruler or ruling classes themselves were solely at fault and judged by God as is fitting of their rank and responsibility.

    But now that everyone is in on it, or are convinced they are, the blood is on their hands too. They CHOSE THIS! And even those who did not ratified it with their consent by recognition to be governed . So there is plenty of blame to spread around. Responsibility is evenly distributed. Equally! Equity! Goodness gracious harmony!

  8. I’m mostly enjoying the book, but it’s a bit of a slog because of the length. I’m about half way through chapter 18. I have difficulty finding time to read, so getting this far through the book is a complement in and of itself.

  9. Noseless Egyptian guy apparently mispelled his own name. The question is: What’s the measured length of Mea-su-Red’s nose?

  10. Perhaps it’s amusing that Aristotle called democracy the “tyranny of the ignorant”.

    I don’t think that the “elite” would be proposing and imposing “democracy” all over the World if it didn’t suit their megalomaniac ambitions.

  11. Precisely. Do we really think that if voting worked they’d let us do it?

    It’s the illusion that allows oligarchic control, although it seems they are tiring of the illusion now

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