The most controversial book of the year is still on its way! I found two other publishers willing to give it a look, and they’re reviewing it now.
If they don’t love it, then I’ll still bring it out on my own. Meanwhile, the big title reveal!
Everything You Know Is Wrong
A book for our progressives friends and families! Words to wake the woke! A book for those who know what is going on out their windows is wrong, but don’t know how to express it. People who want to counter the “academic expert” on his own terms, the expert who is on CNN assuring viewers that drag queens in libraries are a good thing.
Large number of topics covered in the book, including voting. There is no wisdom in crowds. Averaging non-wisdom produces average non-wisdom, not wisdom. Where might you have seen the idea that “the people have spoken” because of a vote? If crowds don’t have wisdom, what do votes mean? Not all voting—but some. Which kinds? Read and learn!
Here is a small section in the chapter on Voting. This is a completely rewritten and greatly expanded blog post from many years ago (look for a long-time reader’s name call out). This is the only real math in the book, and this in text form. It’s to ease readers, with something non-controversial, into the discussion on how voting can cause grief, sorry, angst, anger, dissension, and splits, which will be controversial.
Out By A Nose
Have you heard of Mesd-su-Re? One of the participants of the Great Harem Conspiracy under Ramses III? No? I’m surprised you haven’t. Made all the news. The scandal was carved into all the better hieroglyphic columns. Are you sure he’s not ringing any bells? Mesd-su-Re? 1155 BC?
If you haven’t heard of him, then I’m not sure how you can help me. Because it turns out I need to know the length of Mesd-su-Re’s nose right before he died. It’s for a research project I’m working on. I don’t know the answer, but need it, so I thought I’d invoke the “wisdom of crowds” and run a little poll. Do me a favor and send my request to everybody you know, the more people the better. Have everybody write down what they think the length of this fellow’s nose was—in inches or centimeters, I can convert—and send it to me. I’ll take the average of all the answers. The result has got to be a pretty good guess of the actual nose length, right?
On second thought, let’s tweak the process and improve it. This Chapter, however deserving of the honor, is not likely to be read by multitudes, and so my little poll will not be well subscribed to. Suppose instead we run a well-funded national campaign to “raise awareness” of the importance of estimating Mesd-su-Re’s nose length. TV ads, radio spots, pundits, community organizers, teachers, bureaucrats all getting the word out about this most important subject. Hey, we might even get a celebrity endorsement. That’d really bring the numbers in!
It should work, shouldn’t it?
No. Of course not. If our respondents had no information other than the usual olfactory arcana we all possess—e.g., none of us has seen a human nose longer than, say, one meter, and we all know it impossible for a nose to have negative length—then there is no reason to suppose guessing-and-averaging is helpful. How could it be? If one person (perhaps yourself) does not know the answer, this is ignorance. Your guess will be of no real value. Agreed? If two people do not know, ignorance plus ignorance divided by two is still ignorance, or “mean ignorance” if you like. Averaging ignorance hoping to come to the truth, or something like it, is a fallacy which is well known, and sometimes goes by the name the Chinese Emperor’s Nose Fallacy. Because it has many forms, and is so popular we can also call it the Voting Fallacy.
Let’s look into the simple mathematical details of this fallacy. If we collect people’s guesses about Mesd-su-Re’s nose length, the numbers will have a minimum, maximum, and some arithmetic mean which lies between (or possibly at one of) these two extremes. This assumes not everybody guessed the same length, but it doesn’t matter if everybody did. To make the explanation easier, we’ll assume a range of guesses.
If people have no idea about the length except the rough bounds mentioned above, then the mean of the guesses is probably nearer the midpoint than the extremes, i.e. it will be near or at the center of the guesses. If the maximum guess was, say, six inches, and the minimum one inch, then the center of the guesses, and also likely the mean, will be three-and-a-half inches. Then, regardless of where the real answer lies, the error—the distance from guess to real answer—averaged across all the guesses will be the same as the error using the mean.
In other words, we take the mean of the guesses, and then, imagining it were possible, we calculate the error of this guess. It will be something like $mean – truth$. And then we take each individual error, $guess_1 – truth$, $guess_2 – truth$, and so on, and take the mean of these individual errors. Once we have even a modest number of guesses, the error of the mean and of the averaged individual guesses will be about the same.
This statistical result shows that crowds have no expected wisdom in subjects on which they are ignorant. You may as well use your own guess as the crowd’s. The so-called Wisdom Of The Crowd isn’t wise. Except in special circumstances.
That the wisdom of crowds can sometimes provide reasonable predictions is true, because it has been observed from time to time. But this strictly depends on the composition of the “crowd”. For instance, a group, a crowd, of economists might toss a predictive equation at a list of stocks and discover it sticks. That’s a form of wisdom. Two parents, which is not a large crowd but of satisfactory size for our consideration, might guess within minutes when little Susie will come home. A group of physicians might nail the day a patient finishes circling the drain. And so on. Crowd wisdom can be successful when people have information relevant to the answer.
If we ask a group of Egyptologists we’d almost certainly get a better guess of Mesd-su-Re’s nose length than if we ran, say, an Internet poll. If individuals in a group had considered or informed opinions on the question at hand like, “I don’t know exactly what the answer is, but from everything I’ve read, I think it’s about X plus-or-minus” then averaging these experts’ guesses might very well provide a superior guess to that of the average individual, in the sense that the error of the expert-crowd-wisdom guess is expected to be smaller than any individual’s error.
This finding is necessarily only an “in general” proposition, of course, because there might be in our crowd a person who knows the precise answer (to whatever question is being asked), and his answer cannot be beat. Plus, there will always be one answer in any group of guesses that is closest to the truth. That applies to any crowd, expert or not. Melding the correct answer with a sea of incorrect ones only dilutes the truth.
So crowds are not universal tools at filling in information holes. It should be equally obvious that when a crowd is fed and relies upon biased information the game is off.
Example. You might look at that jar of jelly beans or pennies (a long-time reader of my blog “DAV” reminded me of this example) and know that it can’t contain a million pennies, nor even a hundred thousand. We all know lots of things about pennies and jars, and many of us have or have had jars of change, so we are all experts of a sort on this matter. We could form a not-wild crowd-wisdom idea of the number. The average of our guesses in this case is likely to be a good guess.
Now imagine a mustachioed slickster stands by the jar and whispers to passersby, “Psst, buddy. There’s a solid cone of cork in the middle. It only looks like there’s a lot of pennies. Word to the wise.” You recall that this cork ploy is, indeed, an old-time carnival trick. The mystery man slips his finger across his nose and scuttles off. “Hey,” you think, “He might be in on it. This could be a hot tip!” Only our man is lying. There is no cork. The information is biased. If our slickster touts enough folks, the accuracy of the average will be far too low.
This kind of touting works in a more complicated way at horse tracks. If touters can find enough suckers to bet a certain way, the odds can be manipulated. This works, when it works, because race odds are formed by the money bet on the race. When it works, it proves crowds are susceptible to false and misleading information. Of course, our beneficent leaders would never use these gimmicks to tout stocks or other investments, right?
Voters, too, base decisions based in large part of information provided by the media, information which all can see is biased when produced by the “other side”. Voting is an appeal to the so-called wisdom of crowds.
These small examples are enough to prove crowd wisdom is of no worth when individuals in the crowd are ignorant of the subject matter, or when the crowd is based on experts fed misleading information. Averaging wisdom of the wise, or semi-wise, can and does work when the wise use unbiased information. But even pros can be misled. Generals must rely on their lieutenants. The bad news, already well known, is that propaganda works. That is why, after all, it is so often used, and why it will continue to be used. People, including experts, will come to wrong conclusions when conditioning on flawed premises.
Meanwhile, here’s the answer to the question posed at the beginning of the Chapter. Zero. In inches or centimeters, the length of Mesd-su-Re’s nose was a big skinny nothing at the end of his life. Ramses had it sliced off for daring to corrupt his harem. Ouch. He’s lucky that’s all he lost. The lesson is: don’t guess unless you have to, and when you do, be less confident.
The next section shows how wisdom of crowds can work, and how badly it can go wrong. All building to the conclusion that voting, like we do it in democracies, is a bad thing.
To support this site and its wholly independent host using credit card or PayPal (in any amount) click here