The intelligence of the creature known as a crowd, is the square root of the number of people in it
– Terry Pratchett
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Samizdata quote of the dayOctober 11th, 2009 |
 32 comments to Samizdata quote of the day |
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That seems intuitively wrong, to me. The relationship seems pretty good up to about 2 or 3 people, but then Pratchett’s formula has intelligence continuing to increase, whereas experience suggests that some time after 2 or 3 it begins to decrease, and is soon below 1. (I suppose that depends on the starting point, though.)
Is there a market into a crowd?
Is there a book of Pratchett quotes yet?
My favorite (paraphrased a bit) is “The compassion proper to a headsman is a sharp axe.”
On this basis elections should not be held, since the electorate is a crowd, and the market is always crazily wrong for the same reason.
In reality it depends- does everyone in the crowd have a stake in getting the right answer? Do they act independantly (a secret ballot goes a long way to bring this about- and we buy stuff independantly of others), are they diverse (a crowd all of one peruasion or one trade will never get the right answer to suit the generality)- do they have multiple sources of information (which is one reason not to have a monopoly on news and information, however sincerely they try to be objective).
Nice sentiment; bad math. The number goes up as the size of the crowd increases. It should be some inverse correlation, but that is counterintuitive and moreover wouldn’t have the same catchiness of phrase.
Pat, all these qualifiers make a group of people less of a crowd and more of a group of individuals, so no argument there.
Good point Laird, the fact that I missed that is so depressing 😐
I thought the intelligence of a committee was inversely proportional to the number of its members. But if we are going for a root, I suggest the cube.
That would only be correct if the purpose of elections was to produce the best possible decision-making body and if there was some other process for forming a decision-making body that would reliably produce a superior one. I think both those premises are wrong.
The purpose of an election is to form a decision-making body in which anyone who wants to can have a say. Following from democratic premises, that is the “best” decision-making body, regardless of whether some other kind of body might be able to make decisions that were superior in some technical sense.
The argument that such a body has inferior decision-making skill to an individual, whether true or not, doesn’t argue against forming such a body, but it does argue in favour of limiting such a body’s power to allow more decisions to be made by individuals.
Best Pratchett quote IMO:
‘I’m sure we can all pull together, sir’
Lord Vetinari raised his eyebrows. ‘Oh I do hope not, I really do hope not. Pulling together is the aim of despotism and tyranny. Free men pull in all different directions’
Vimes had once discussed the Ephebian idea of ‘democracy’ with Carrot, and had been rather interested in the idea that everyone* had a vote until he found out that while he, Vimes, would have a vote, there was no way in the rules that anyone could prevent Nobby Nobbs from having one as well. Vimes could see the flaw there straight away.
* Apart from the women, children, slaves, idiots and people who weren’t really our kind of people.
Tedd:
But there is a stronger argument against forming such a body, and that is the impossibility of deciding precisely where to draw the limit to such a body’s power. Given the natural tendency of such bodies to grow and to acquire more power rather than the reverse, the logical conclusion is that their power should be limited to a zero, thus effectively eliminating the need to form them in the first place.
The purpose of an election is to make sure that any sufficiently* bad government can be removed.
Thus engaging market competition: to be slightly less bad than the nearest competitor.
It’s certainly not to give people a say. A data rate of roughly 1 bit every five years shared amongst 40 million** people is not “a say”. Even broadband providers with their “up to…” advertising would be ashamed of that one.
* i.e. one that has managed to annoy everyone.
** Or however many where you are.
Alisa, here’s a better formula: 101 minus the cube root of the crowd size. That puts the IQ at 100 (the population norm) for a single individual, declines to just about 80 (bottom end of “normal” range) for 10,000 people, and flattens out in the range of 65 (moron level) once you get to about 45,000. Is that being too generous?
Not too catchy, though, is it?
“On this basis elections should not be held, since the electorate is a crowd…”
You can’t accuse Discworld of not being internally consistent. Ankh-Morpork is a Platonically ideal benevolent dictatorship, even if Vetinari does style himself ‘tyrant’.
There’s a another good quote from Terry Pratchett on the subject democracy but unfortunately I can’t find it. I believe it’s in one of the earlier books. From memory it goes something like:
“It was suggested that Ankh-Morpork become a democracy. It was explained that the elected representatives would be men of good character with only the welfare of the city at heart. They would not adopt airs and graces and lord it over their fellow citizens. Everybody had a good laugh and then got on with their lives.”
So, the “crowd” that voted for Bush is intelligent? Or the millions that follow organized religion?
This “formula” is beyond stupid.
I propose a further improvement of Laird’s formula: 100 – 2*ln(size):
1 —> 100 (individual)
10 —> 95.4 (committee)
100 —> 90.8 (small cult)
1,000 —> 86.2 (town)
10,000 —> 81.6 (small city)
100,000 —> 77.0 (small party)
1,000,000 —> 72.4 (small nation/party)
10,000,000 —> 67.8 (nation)
100,000,000 —> 63.2 (large nation)
1,000,000,000 —> 58.6 (major religion/continent/global movement (AGW, etc.))
10,000,000,000 —> 53.9 (world+)
As fun as the math exercise is, I lost interest the moment I remembered that a crowd doesn’t have an IQ:-) As to individuals, it is a matter of relying on someone else’s thinking rather than on one’s own (of which more often than not they are perfectly capable). When enough people do that, very few bother to actually think, and the results are as can be expected.
I suspect that what Pratchett was reaching for was sqrt(n)/n which has something to do with random walks.
Nevermind, I’m a bit foggy this morning 🙂
sqrt(n)/n is, of course, 1/sqrt(n). That may still work though.
Sorry, Richard, that doesn’t work. Even assuming that you meant to multiply the result by 100 (or express it as a percentage), it gets down to 33.3 with n equal to just 9, and approaches zero at just 45,000.
I like Plamus’ formula. He’s obviously a better mathematician than I am! (Although that isn’t saying much.)
LeBon’ “The Crowd” was translated from the French
Poor memory, at times; but, LeBon’s first name may’ve
been “Gustav”. Have no idea if Pratchett’s quote is
in reference to that book or some other. I don’t recall
statistical figures being used in “The Crowd”
The best estimate of the IQ of a committee is the IQ of the member with the lowest IQ divided by the number of members of the committee. This I can confirm personally after 40 years in business.
I see no good reason why this formulation is inapplicable to larger groups.
I think Richard Thomas is on the right track. If, like good individualists, we expect the aims of individual intelligences to be orthogonal, then we should expect crowd intelligence to aggregate with an RMS rule like this one.
Makes perfect sense to me.
good quote and so true, its always the loudest rather than the smartest controlling the crowd.Two Voices | Two Guys
Laird: “It should be some inverse correlation, but that is counterintuitive and moreover wouldn’t have the same catchiness of phrase.”
I beg to differ. I once knew a junior Air Force officer who kept a sign on the wall of his office: “Rank x Intelligence = A Constant”
I think something similar can be said of a crowd. “Intelligence x Number of People = A Constant”
My comment has been swallowed by the smitebot who apparently liked it so much that he doesn’t seem intent on spitting it back out. Or he may have chocked on it, so if this blog is suddenly filled with smite, you will know why.
A crowd’s intelligence cannot be measured, because there is no any such thing, no more than there is such thing as ‘common good’ or ‘the interests of society’. What does happen is that individuals stop using their own intelligence (i.e. stop thinking), because they rely on other people’s thinking (“so many people can’t be wrong” kind of reasoning), and as a result no thinking ends up being done.
Alisa, you’re no fun at all. If you don’t like our game don’t play it.
You are right Laird – sorry. I guess I’m just annoyed that I am not as good at math as I used to be:-)
Decent writer, rubbish mathematician.
Pratchett’s silly axiom shows the inherent difficulty of trying to make a sound-bite from a simple mathematical formula.
Although I have to admit that the “military rank + intelligence = K” is a funny one (albeit also, spectacularly, wrong).
Talk about “people who do not get it”. Anyone who challenges Pratchett’s remark as a “mathematical formula” rather than a humorous slogan should be responded to with mostly silence punctuated by the occasional embarrassed giggle. I suspect Pratchett also knows that crowds are also not actually ‘creatures’.
Remember, though – if the crowd has intelligence equal to sqrt(n), that means that each member of a crowd has intelligence sqrt(n)/n = 1/sqrt(n). In other words, the bigger a crowd you’re in, the dumber you are.
What does that say about the crowd of Obama supporters?