Condorcet's Terrifying Assumption

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Hello, I'm Niccolò Pescetelli and this is Collective Intelligence, why groups get smart,
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strange and stuck. In the autumn of 1793, there is a man hiding in a boarding house on the Rue
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Servandoni in Paris, about 200 metres from the Church of Saint-Sulpice. He does not go out,
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he has been condemned in his absence, and there is a decree with his name on it. And if he is
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recognised in the street, he will be dead inside the week. The woman who owns the house, Madame
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Vernet, has agreed to keep him, which is an act of considerable courage given what happens to people
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who shelter the proscribed. So he sits in a room he cannot leave, and he writes. And what he writes
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in that room, while a state he helped to build is hunting him, is one of the most staggeringly
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optimistic documents any human being has ever produced. It is a sketch of the progress of the
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human mind, and he argues that there is no limit, that errors and superstition and tyranny are
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temporary, that education and the free circulation of knowledge will go on improving us indefinitely,
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that the species is perfectible. He is writing this while listening for footsteps on the stairs.
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His name is Marie-Jean-Antoine Nicolas de Caritat, Marquis de Condorcet. He is a mathematician,
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one of the very best in Europe. He was permanent secretary of the Academy of Sciences. He was,
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before all this, a genuine aristocrat who decided that aristocracy was indefensible. He argued for the
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abolition of slavery. He argued for the rights of Protestants and Jews. He argued in 1790,
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when essentially nobody was arguing this, that women should have the vote, on the straightforward grounds
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that either rights come from being a rational being, or they do not. And if they do, then half of the
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population has been robbed. And eight years before he went into that room, he published a book, which is
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the reason why I'm talking about him now. It is called, roughly, an essay on applying analysis
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to the probability of decisions, reached by a plurality of votes. He came out in 1785 from the Royal Printing House,
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four years before the revolution. In it, he does something nobody has done. He takes the question,
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should we let the majority decide? And he treats it as a mathematics problem. Not a philosophy
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problem. Not a question about rights or legitimacy or the consent of the governed. But a calculation. He
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asks, under what conditions does asking a lot of people and counting the votes actually get you the
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right answer. And it produces a result which, for 200 years, has been the single strongest argument
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anyone has for democracy. It is also, and this is the thing I want to spend most of the episode on,
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one of the most alarming results in the whole of social science. Because the same piece of mathematics
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that says, a large public is almost certain to be right, also says, with exactly the same confidence,
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under conditions that are barely different, that a large public is almost certain to be wrong.
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And the quantity that decides which of those two worlds you are living in is a number that nobody
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has ever been able to measure. Five months after he finishes writing in that room, he is dead in a cell.
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Okay, let's do the mathematics first, and then we will come back to the cell.
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To understand why a mathematician was writing about voting at all, you have to understand what the
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enlightenment was, or, like, thought mathematics was for. Condorcet opens the 1785 book by talking
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about a dead friend. He does not name him in the sentence, but he means Turgo, the economist and
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reforming minister who had been his mentor and who had died in 1781. And what he says about him is that
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Turgot had been persuaded of something: that the truths of the moral and political sciences are capable of the
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the same certainty as the truth of the physical sciences. That a claim about how a society should
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be arranged could, in principle, be as solid as a claim about where Jupiter will be next Thursday.
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Now, sit with how strange and how enormous that is. Astronomy in the 18th century was the miracle
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science. Newton had taken the movements of the heavens, which had been the property of gods and omens for
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the whole of human history, and reduced them to a few lines of algebra that worked. You could predict
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an eclipse. You could predict it to the minute, decades out, and be right. And a certain kind of mind looked
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at that and thought: why should this stop at the sky? Why should the motion of a planet be calculable
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and the arrangement of a state not be? We do not have a science of moral things yet, but there is
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no reason in principle that we cannot have one. We just have not done the work. That project has a name
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in French: mathématique sociale, social mathematics, and Condorcet is its most serious advocate. In 1785,
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the essay is an installment of this mathématique sociale. He's not writing about juries because he's
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interested in juries. He's writing about juries because a jury is the simplest possible case of the thing he
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actually cares about, which is whether a society can reason. It is worth knowing who was making this
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argument because the biography is not just context here. It explains why he cared. He was born in 1743 in
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Picardy into the minor nobility, and he was a prodigy. By his mid-twenties, he was in the Academy of
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Sciences. D'Alembert, one of the editors of the great encyclopedia, took him up. And he could have
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had that life, you know, the life that came with that: silence, pensions, a reputation, an easy path,
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and instead he kept using it on things that could only cost him. In 1781, eight years before the
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Revolution, he published An Attack on Slavery. He published it in Switzerland, and he published it
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under a false name, a fictious Swiss pastor called Joachim Schwartz, which tells you what he thought he
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would do to do to him at home. The argument is not economic, and it is not sentimental. It is that
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black people have the same mind, the same reason, the same virtues as white people, and that owning
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them is therefore a violation of right, full stop. He wanted emancipation to be gradual, which is, you know,
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a real limitation, and I'm not going to paper over it. But he was arguing that the thing was indefensible
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in principle, in 1781, in a France that was getting extremely rich from it. In 1790, he wrote an essay
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arguing that women should have full political rights, not improved conditions, but the votes and citizenship
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on the same terms as men. His reasoning is almost brutally simple: rights follow from being a creature
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with reason and a moral sense. Women are such creatures, therefore, excluding them is not a
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tradition or a convention, but it is a straightforward breach of the rights the Revolution claimed to be
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founded on. Almost nobody was saying this. He said it in print under his own name. And he married Sophie
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de Grouchy, who translated Adam Smith and ran one of the serious intellectual salons in Paris.
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And who is the reason? We have the manuscript I mentioned at the start. So, a man who believed that
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human reason was general, that it did not come in grades according to race or sex, and that a society
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organised around it would keep improving. Now, you can see why the question of whether a group of
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ordinary people can reason their way to the truth is not an abstract exercise for him. It is the main claim
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of his entire life. And there was an argument going on that he wanted to win. The other side of it was
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Rousseau. Now, Rousseau had an idea called the general will, which is not the same as what, you know,
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the majority happens to want. The general will is what the people would want if they were thinking
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about the common good, rather than their own interests. It is a real thing out there, discoverable,
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and it is the only legitimate basis for law. Which sounds wonderful, until you ask the obvious
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question: who gets to say what the general will is? And Rousseau's answer is a figure he calls the
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legislator, a kind of super wise outsider who perceives the common good and explains it to a
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people who cannot quite see it themselves. And I want you to notice what a dangerous piece of machinery
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that is, because Lex Paulson, in his history of collective intelligence, puts it blindly:
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this is a mega technocrat, and the idea has underwritten authoritarian projects ever since.
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If the general will is a fact, and you are the one who knows it, then people who disagree with you are
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not opponents. They are just wrong. They are obstacles to the truth, and you can do things to
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obstacles that you cannot do to opponents. Now, Condorcet wants the same destination, but refuses that
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approach. He agrees with Rousseau that collective reason is real, and it is the legitimate basis of
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authority. But he will not accept an oracle. What he wants is a procedure, something mechanical, public,
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checkable, that produces the right answer without anybody having to be trusted to know it in advance.
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And because he is a mathematician, when he says procedure, what it really means is
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something you can calculate. So here is the question he sets himself, and it is worth stating precisely,
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because, you know, the mathematics, the precision is the whole point. Now, suppose you have a group of
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people, suppose there is a question with a genuine right answer, and they each give an opinion,
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and you go with the majority. Now, the question is: how likely is the majority to be right?
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Not, you know, is it legitimate, not do they have the right to decide, but how likely are they to be
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correct? Now, nobody had asked it that way before. Okay, so let's build it from the bottom up, because
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the whole thing rests on one small fact that you can check on your fingers. Picture three people deciding
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something. So it's a jury of three. The question has a right answer, and they do not know it.
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But they are not, you know, guessing blindly either. Say each of them, on their own, gets it right 60%
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of the time. Better than a coin, but you know, not much better. Four times in ten, each one of them is wrong.
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If you picked one of them at random and let them decide, you know, by themselves, you would be right 60%
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of the time. So that is your baseline. Now, let all three vote and take the majority. Now, what happens?
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For the majority to be right, you need at least two of the three to be right. Either all three or exactly two.
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And for the majority to be wrong, you need at least two of them to be wrong at the same time.
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And here is the fact that everything else in the episode
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grows out of two people being wrong at the same time is rarer than one person being wrong.
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Each of them is wrong four times in ten. Both of them being wrong together, if they are not influencing each other, happens 60 times in a hundred.
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Being wrong is an event, and events stack up against each other.
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Now, do the arithmetic, and the three-person jury is right 64.8% of the time. So almost 65%.
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That is not much. If I had opened with that number, you know, you would have probably shrugged.
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But look at what just happened, because the direction of change matters more than the size of that step.
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Three people, each individually, let's say mediocre, arranged into a majority, are better than any one of them.
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Not because they talked, not because they pulled their wisdom, but purely because for them to fail collectively,
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more than one of them has to fail at the same moment, and that is harder.
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Now, at people, five jurors, still 60% accurate individually, collectively, they are 68% accurate.
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Nine jurors, 73.
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Eleven jurors, 75.
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In 101 jurors, each of them individually, no better than, you know, slightly informed amateur, each of them wronged two times in five.
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The majority is right 98% of the time.
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If you had a thousand and one jurors, it rounds to certainty, 100%.
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That is Condorcet's result.
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Take people who are individually barely adequate.
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Do not train them.
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Do not improve them.
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Do not have them talk to each other.
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Just add more of them and count and the accuracy of the group climbs towards one.
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And it does not stop, right?
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Climbs to certainty.
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And you can feel why, if you think about what it would take for a thousand person majority to be wrong, right?
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You would need 501 separate people to make a mistake in the same direction, on the same question, and at the same time.
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Any individual mistake is common, but 500 simultaneous mistakes, all pointing the same way, all independent of each other, is a coincidence so absurd that it effectively never occurs.
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So, the majority is not smart.
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The majority is safe.
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Those are different things, and the difference is going to matter here.
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I want to slow down on the mechanism, because if you take one idea out of this episode,
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I would like it to be this one, and it is easy to nod, you know, without really seeing this.
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But picture three doctors looking at the same scan.
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Each of them is right 60% of the time, right?
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This is not slander.
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It's roughly, you know, what diagnostic accuracy on a hard case could actually look like.
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Put them in three separate rooms, so they cannot see each other's notes.
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Each makes a call.
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Each makes a call, and you go with two out of three.
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So, for that procedure to fail, it is not enough for one of them to be wrong.
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Doctors are wrong all the time, but you need two of them to be wrong on the same scan, in the same direction, and at the same moment, after having never spoken.
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And that is much rarer than one of them being wrong, not because they are better than they were, but because you have changed what counts as failure.
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You have moved the target from a mistake to a coincidence of mistakes.
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That is the entire engine.
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You know, everything else is kind of a footnote.
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Now, hold that image and make the room bigger.
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Five doctors, nine, 101.
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With 101 doctors, failure means 51 of them going wrong together independently on the same scan.
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The individual competence has not moved at all.
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Every one of them is still the same sort of fallible 60% accuracy that they were at the start.
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What has changed is what the failure condition has become now absurd.
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This is why Condorcet's result feels like a trick the first time you meet it.
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It looks as though information is being created out of nothing, but it is not, right?
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Like, the information was always there, distributed across the group.
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60% of it in each head.
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What the majority rule does is throw away the part of each judgement that is noise.
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And the more heads you have, the more thoroughly it can throw it away.
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The first refinement is about how much competence you need.
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And it is more interesting than, you know, it sounds.
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Everything above assumed 60% accuracy.
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What if your citizens are worse than that?
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What if they are barely better than a coin?
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Well, the mathematics still works.
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It just gets expensive.
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If people are right 51% of the time, 1% better than random, then a majority still converges on the truth.
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But to get to that 99% confidence, you need about thirteen and a half thousand of them.
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At 52%, you need about 3 and a half thousand.
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At 55%, 539.
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At 60%, 131.
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At 70%, 31 people.
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Now look at the shape of that.
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Competence and numbers trade against each other.
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And the exchange rate is brutal at the bottom end, right?
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A barely informed public needs to be a city.
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A moderate or moderately informed public needs a village hall.
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Which is, you know, if you squint, an argument for mass education dressed up as an argument about probability.
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And we will actually come back to that because Condorcet absolutely noticed that.
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The second refinement is the three conditions.
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And I want to name them explicitly because the popular version of these results usually mentions one of them, but tends to forget the other two.
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Condition 1: Each person has to be better than random, better than a coin flip, however slyly.
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Condition 2: They have to vote independently.
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Condition 3: Their errors cannot be connected to each other.
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Condition 3: And this one often gets dropped sometimes.
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They have to vote sincerely.
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They have to say what they actually think is true, rather than what they think will produce a good outcome.
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Or what their side needs or, I don't know, what will make them look sensible afterwards.
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So, three conditions.
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Now, the trapdoor.
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Go back to Condition 1 and try to turn it around.
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What happens if people are slightly worse than random?
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Not catastrophically bad, just under the line.
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Let's say right 49% of the time instead of 51.
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Run exactly the same arithmetic.
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And now three jurors, 48.5%, slightly worse than one person.
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A 101 jurors, 42%.
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A 1,001, 26%.
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10,001 jurors, 2%.
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A 100,000 people, 0%.
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Not, you know, approximately zero, but zero to four decimal places.
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A public of 100,000 individually almost coin-flipping citizens voting independently and sincerely is certain to reach the wrong answer.
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Now, read those two columns next to each other, because this is the thing I want to get to.
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At 51% competence, 100,000 voters are certain to be right.
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At 49% competence, 100,000 voters are certain to be wrong.
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The gap between those two worlds is two percentage points in the ability of the average person.
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And the machine does not care which side of the line you are on.
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It just amplifies with exactly the same ferocity in both directions.
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So Condorcet theorem is not a theorem about the wisdom of crowds.
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It is a theorem about amplification.
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Scale does not make a public wise.
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Scale makes a public certain.
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Whether it is certainly right or certainly wrong depends on a quantity sitting just under one half or just over it.
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And nobody in the 240 years since he published has ever managed to measure that quantity for any real electorate or any real question.
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That is the terrifying assumption.
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Not independence, which, you know, we are coming to, but competence.
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The theorem hands you a machine of enormous power and declines to tell you which way it is pointed.
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Now, the second condition, right?
00:23:14.460 --> 00:23:15.180
Independence.
00:23:15.740 --> 00:23:20.620
Everything I have just shown you depends on people's mistakes being unrelated.
00:23:20.620 --> 00:23:27.260
The whole engine is the improbability of 500 simultaneous errors all pointing the same way.
00:23:27.980 --> 00:23:31.100
Take that improbability away and the engine stops.
00:23:31.980 --> 00:23:34.860
So, what makes errors point the same way?
00:23:35.740 --> 00:23:37.900
Well, someone speaking first.
00:23:38.780 --> 00:23:40.940
A newspaper everybody reads.
00:23:40.940 --> 00:23:42.700
A phrase that catches on.
00:23:42.700 --> 00:23:48.860
A respected person committing to a position in public before the rest of us have decided.
00:23:48.860 --> 00:23:53.900
A shared education that taught everyone the same wrong rule of thumb.
00:23:54.940 --> 00:23:59.580
An expert consensus that is confident and mistaken.
00:23:59.580 --> 00:24:03.100
Anything at all that puts the same thought into more than one head.
00:24:03.980 --> 00:24:04.620
In other words, a society.
00:24:04.620 --> 00:24:06.380
In other words, a society.
00:24:07.820 --> 00:24:10.940
Now, let me put a number on how badly this goes.
00:24:10.940 --> 00:24:13.660
Because I think the number is genuinely shocking.
00:24:14.300 --> 00:24:17.980
And I did not expect it to be that bad before I worked it out.
00:24:19.660 --> 00:24:22.380
Take a simple model of shared influence.
00:24:22.380 --> 00:24:25.500
Most of the time, everybody reasons for themselves.
00:24:25.500 --> 00:24:32.140
But some of the time, with some probability, the whole public is following a single common signal.
00:24:32.540 --> 00:24:36.700
Maybe one story, one frame, one confident voice.
00:24:37.260 --> 00:24:39.340
And their answers move together.
00:24:40.540 --> 00:24:44.460
Call that probability the correlation.
00:24:46.460 --> 00:24:47.740
Set the correlation at 30%.
00:24:48.860 --> 00:24:53.660
Keep everybody at 60% competence, which was our sort of comfortable case.
00:24:54.300 --> 00:24:57.500
The one where 101 jurors go to 98%.
00:25:00.140 --> 00:25:06.300
101 voters now, 86.5%.
00:25:07.100 --> 00:25:09.740
1,000 voters, 88%.
00:25:11.420 --> 00:25:13.420
100,000, 88%.
00:25:14.060 --> 00:25:16.140
10,000, 88%.
00:25:16.140 --> 00:25:17.340
So it basically stops.
00:25:17.340 --> 00:25:18.940
It reaches 88% and it stops.
00:25:20.460 --> 00:25:23.660
It does not creep towards that certainly like before.
00:25:24.620 --> 00:25:28.460
It walks up to 88% accuracy and then it sits.
00:25:30.540 --> 00:25:33.020
The last 12% points are not for sale.
00:25:33.580 --> 00:25:35.180
You cannot buy them with more people.
00:25:35.180 --> 00:25:41.020
Because the thing that was making extra people valuable was the independence of their errors.
00:25:41.740 --> 00:25:43.660
And you have spent 30% of that.
00:25:44.380 --> 00:25:46.460
Even a light coupling costs you.
00:25:47.100 --> 00:25:49.980
A 5% correlation, your ceiling is 98%.
00:25:51.020 --> 00:25:54.140
A 10% correlation, 96%.
00:25:55.180 --> 00:26:02.380
Those, you know, sound tolerable until you notice that no quantity of additional citizens will ever get you past that.
00:26:03.740 --> 00:26:07.820
So here is the shape of Condorcet's results seen as a whole.
00:26:08.380 --> 00:26:15.100
Democracy as an error-correcting machine works beautifully and it works on one condition,
00:26:15.100 --> 00:26:18.140
which is that the citizens are not talking to each other.
00:26:19.180 --> 00:26:22.780
Which brings me to the part of the story I find almost unbearable.
00:26:23.260 --> 00:26:31.740
Because of all the people in the 18th century, the one who did the most to build the machinery that breaks his own assumption was Condorcet.
00:26:32.460 --> 00:26:35.980
In 1792 he is elected to the national convention.
00:26:36.540 --> 00:26:42.300
He is given the job of chairing the committee to write a constitution for the new republic.
00:26:44.300 --> 00:26:51.420
And what he produces is, in Paulson's judgement, the most radical design for collective intelligence since ancient Athens.
00:26:52.140 --> 00:26:54.860
Attempted at the scale of millions of people.
00:26:55.580 --> 00:26:59.580
It is not a representative system, as we would understand it.
00:27:00.060 --> 00:27:04.220
Citizens participate directly in assemblies that nest inside each other.
00:27:04.460 --> 00:27:06.460
Local, then regional, then national.
00:27:07.180 --> 00:27:13.840
The people who sit in the higher assemblies are not representatives and are not meant to be a wiser class of people.
00:27:13.840 --> 00:27:20.080
He calls them mandate holders, delegates operating under constraint.
00:27:21.280 --> 00:27:30.960
And Paulson notes that the constraints resemble those in the Iroquois or Gikuyu systems.
00:27:32.160 --> 00:27:36.400
Which is not a comparison I expected to be making about a French marquise.
00:27:37.600 --> 00:27:42.320
And in his speech to the convention, he goes further.
00:27:42.320 --> 00:27:47.680
And he departs from Rousseau in a way that matters enormously for this episode.
00:27:47.680 --> 00:27:50.800
He insists on the value of deliberation.
00:27:51.440 --> 00:27:56.880
Citizens should argue publicly and form their judgements in the course of arguing.
00:27:57.440 --> 00:28:02.800
He insists on the free flow of knowledge through newspapers and through scientific associations.
00:28:03.280 --> 00:28:12.240
And echoing Aristotle, he says none of this work without a system of free public education for everybody.
00:28:12.320 --> 00:28:18.240
Now read that list again with now the mathematics in your hands.
00:28:18.240 --> 00:28:21.680
The liberation is a machine for correlating opinions.
00:28:22.240 --> 00:28:24.480
That is what the liberation is for.
00:28:24.720 --> 00:28:28.840
People come in with different views and live with more similar ones.
00:28:29.600 --> 00:28:34.840
And if it did not do that, we would just not bother.
00:28:35.840 --> 00:28:41.040
Newspapers are a machine for correlating opinions and a spectacularly efficient one.
00:28:41.200 --> 00:28:48.100
The whole point of a newspaper is that a large number of people receive the same account of events on the same morning.
00:28:49.440 --> 00:28:57.440
Scientific associations correlate opinions deliberately by design among exactly the people whose judgements carries most weight.
00:28:58.160 --> 00:29:02.480
And mass public education is the most powerful correlating device ever invented.
00:29:02.480 --> 00:29:08.880
It takes an entire generation and teaches them the same facts, the same methods, the same habits of mind.
00:29:09.680 --> 00:29:12.080
When they are right, they are right together.
00:29:12.200 --> 00:29:17.440
But when the curriculum is wrong, they are wrong together for a generation.
00:29:18.560 --> 00:29:28.820
Condorcet spent the last years of his life fighting for the political programme that most efficiently destroys the assumption his own most famous result depends on.
00:29:29.360 --> 00:29:31.540
I don't think, you know, he was being stupid.
00:29:31.660 --> 00:29:34.460
I think he was doing something more interesting.
00:29:35.120 --> 00:29:39.280
And to see what, you need a result he could not have had at the time.
00:29:40.240 --> 00:29:49.260
In 1992, a political scientist called Krishna Ladha published a paper in the American Journal of Political Science, whose title contains the entire problem.
00:29:49.980 --> 00:29:53.580
The Condorcet Jury Theorem, Free Speech and Correlated Votes.
00:29:54.420 --> 00:29:58.000
Free speech in that title is the thing doing the correlation.
00:29:58.980 --> 00:30:03.420
What Ladha shows is that the theorem does not simply die when votes correlate.
00:30:03.700 --> 00:30:05.560
It survives, but conditionally.
00:30:05.920 --> 00:30:07.780
He derives a bound.
00:30:08.440 --> 00:30:17.920
Given how competent people are on average, there is a maximum average correlation the system can tolerate and still do better than its individual members.
00:30:18.340 --> 00:30:20.560
And still improve as it grows.
00:30:21.300 --> 00:30:23.580
Above that line, majority rule the grades.
00:30:24.200 --> 00:30:25.540
Below it, you're fine.
00:30:26.840 --> 00:30:31.140
Which turns the whole thing from a contradiction into something more useful.
00:30:31.800 --> 00:30:33.620
Shared influence is not poison.
00:30:33.620 --> 00:30:35.060
It is a budget.
00:30:35.920 --> 00:30:39.320
A society can afford some amount of people listening to each other.
00:30:39.920 --> 00:30:44.960
And the amount it can afford depends on how good its citizens are at judging.
00:30:46.100 --> 00:30:49.080
Raise competence and you can afford more conversation.
00:30:49.880 --> 00:30:56.060
That is a coherent position and it is more or less exactly the position Condorcet's political programme takes.
00:30:56.280 --> 00:31:00.100
Which is educate everybody and then let them argue.
00:31:01.200 --> 00:31:07.160
But notice what he could not do and what we will still cannot do.
00:31:07.540 --> 00:31:12.320
To know whether a society is inside its budget, you would have to measure two things.
00:31:12.440 --> 00:31:19.200
The average competence of citizens on the question at hand and the average correlation between their errors.
00:31:19.800 --> 00:31:25.280
Nobody has ever measured either of those for a real electorate on a real issue.
00:31:25.840 --> 00:31:31.220
Condorcet's defence of deliberation is a bet that the budget is large enough.
00:31:31.820 --> 00:31:33.220
It is a reasonable bet.
00:31:33.600 --> 00:31:35.020
It is not a calculation.
00:31:35.800 --> 00:31:40.060
And he, of all people, would have known the difference.
00:31:41.460 --> 00:31:50.080
And there is a deeper objection, which I should give you at full strength, because it's the best reason to doubt the entire edifice.
00:31:50.600 --> 00:32:00.060
In 2008, the philosopher Franz Dietrich published a paper arguing that the premises of the jury theorem cannot be simultaneously justified.
00:32:00.540 --> 00:32:07.680
Not that they are empirically unlikely, but that they cannot both be defended at once.
00:32:08.660 --> 00:32:12.680
His argument turns on what you take probability to mean.
00:32:13.180 --> 00:32:23.960
The interpretation of probability under which the competence assumption looks reasonable is not the interpretation under which the independence assumption looks reasonable.
00:32:24.960 --> 00:32:28.920
And under most readings, independence has to be weakened.
00:32:30.080 --> 00:32:37.340
If he is right, then the theorem has never supported democracy in the way people have been claiming it does for two centuries.
00:32:37.900 --> 00:32:41.320
And the problem is not that the world fails to match the model.
00:32:41.400 --> 00:32:43.260
The problem is inside the model.
00:32:44.400 --> 00:32:49.560
I do not think that, you know, that just by itself ends the argument.
00:32:49.920 --> 00:32:57.080
But anyone who quotes the jury theorem at you, and I include myself, you know, an hour ago, owes you that objection.
00:32:58.660 --> 00:33:02.540
And I have not even mentioned the third condition, which is sincerity.
00:33:02.980 --> 00:33:09.800
Everybody voting for what they believe rather than for what helps their side.
00:33:09.980 --> 00:33:14.520
I invite you to hold that thought against any election you have watched in your lifetime.
00:33:15.800 --> 00:33:18.280
So, what do you do with this?
00:33:18.600 --> 00:33:30.420
Here is the practical residue, and it is uncomfortable, because it takes the thing we most want to believe about large-scale democracy and puts two conditions on it that nobody can check.
00:33:31.360 --> 00:33:41.460
Whenever you are shown a large majority and invited to be impressed by its size, there are two questions that decide whether the size means anything at all.
00:33:42.100 --> 00:33:50.400
How good are these people, on average, at judging this particular question, and how much of their errors are moving together?
00:33:52.200 --> 00:33:55.060
Notice that neither question is about the number.
00:33:55.400 --> 00:34:00.040
The number is the thing everybody quotes and the thing that carries the least information.
00:34:01.040 --> 00:34:02.140
Take a referendum.
00:34:02.140 --> 00:34:12.040
Now, one question, one national electorate, tens of millions of votes, and the result is treated as an oracle precisely because so many people spoke.
00:34:12.500 --> 00:34:15.780
But a referendum is the worst case the jury theorem has.
00:34:16.420 --> 00:34:23.060
The electorate has spent months inside a campaign explicitly designed to make people's errors move together.
00:34:23.900 --> 00:34:25.700
That is what campaigns are, right?
00:34:26.180 --> 00:34:32.980
Two well-funded operations spend a year pushing the correlation as high as they can get it.
00:34:33.600 --> 00:34:40.820
And then we treat the output as though it were the independent judgement of 40 million separate minds.
00:34:41.280 --> 00:34:43.760
On the mathematics, the guarantee is simply gone.
00:34:44.580 --> 00:34:50.160
Not just weakened, just gone, in the sense that the theorem no longer applies and it has nothing to say.
00:34:51.180 --> 00:34:55.520
The theorem's best case, on the other hand, looks nothing like an election.
00:34:56.000 --> 00:35:06.100
It looks like a lot of people who do not know each other, quietly forming a view on a question where being wrong in one direction is no more tempting than being wrong in the other.
00:35:07.160 --> 00:35:08.620
And then being counted.
00:35:09.420 --> 00:35:13.260
It looks, in fact, like the queue in Plymouth from the last episode.
00:35:14.300 --> 00:35:15.300
And that is not a coincidence.
00:35:15.740 --> 00:35:23.200
Condorcet was one of the early contributors to the law of large numbers that Galton's Ox was a demonstration of.
00:35:23.700 --> 00:35:30.440
Two men, a century apart, who found the same machine and wrote down the same condition for running it.
00:35:32.140 --> 00:35:35.100
And now think about what we have built since.
00:35:35.560 --> 00:35:42.480
Every correlating device Condorcet wanted has been constructed at a scale he could not have pictured.
00:35:43.200 --> 00:35:44.940
Universal education, achieved.
00:35:45.120 --> 00:35:48.580
Newspapers, superseded by something far more powerful.
00:35:49.380 --> 00:35:51.320
Scientific associations, global.
00:35:51.960 --> 00:36:05.020
And on top of all of that, in the last 15 years, an information architecture whose explicit optimization target is to show a large number of people the same thing at the same time.
00:36:05.020 --> 00:36:09.100
And to reward them for agreeing about it in public.
00:36:10.040 --> 00:36:23.140
And now, in the last few years, something with no precedent at all, a handful of very large models that a substantial fraction of the species is beginning to consult before forming a view.
00:36:23.880 --> 00:36:33.200
If you want a device for driving the correlation between human errors towards one, it is difficult to improve on everybody asking the same oracle.
00:36:34.840 --> 00:36:37.180
Now, I'm not saying that that is bad.
00:36:37.340 --> 00:36:38.860
Ladha's point stands.
00:36:39.240 --> 00:36:40.900
Correlation is a budget, not poison.
00:36:41.320 --> 00:36:44.280
And a better informed public can afford more of it.
00:36:45.720 --> 00:36:48.820
It might be that we are inside our budget.
00:36:49.020 --> 00:36:53.220
It might be that raising competence has outrun the rise in correlation.
00:36:53.840 --> 00:36:56.240
And Condorcet's bet is, you know, coming in.
00:36:56.760 --> 00:36:59.300
What I'm saying is that nobody knows.
00:36:59.300 --> 00:37:11.520
And that the most famous argument for trusting large numbers has a condition attached, which we have spent two centuries systematically undermining while quoting that result.
00:37:12.180 --> 00:37:15.860
Which brings me back to the man in the boarding house.
00:37:16.500 --> 00:37:20.600
In June 1793, the convention debates his constitution.
00:37:22.260 --> 00:37:30.840
It is, by any measure, the most ambitious attempt anyone had made to build his mathematics into an actual state.
00:37:30.840 --> 00:37:33.180
And the timing could hardly be worse.
00:37:33.520 --> 00:37:36.560
The spring of 1793 is when the revolution turns.
00:37:37.180 --> 00:37:38.760
There is a war on several fronts.
00:37:39.000 --> 00:37:40.520
There is a revolt in the Vendée.
00:37:40.980 --> 00:37:42.400
There is bread rationing.
00:37:42.720 --> 00:37:52.220
And the convention is splitting into factions that are beginning to understand that losing an argument there will soon mean losing your head.
00:37:53.220 --> 00:37:57.640
Condorcet belongs loosely to the Girondins, who are about to lose.
00:37:57.640 --> 00:38:04.360
On the 2nd of June, an armed crowd surrounds the convention and the leading Girondin deputies are arrested.
00:38:05.140 --> 00:38:10.620
The faction Condorcet is associated with has just been removed from politics by siege.
00:38:11.640 --> 00:38:14.300
His constitution is blocked at the verge of adoption.
00:38:15.020 --> 00:38:22.880
Robespierre and the Montagnards produce their own document, faster and more centralized, and push it through in a matter of weeks.
00:38:24.220 --> 00:38:32.040
And Condorcet, who has just watched his colleagues taken away, does the thing that a man who genuinely believes in public reason would do.
00:38:32.400 --> 00:38:38.820
He writes a pamphlet explaining why the new constitution is bad, and he arranges for it to be distributed.
00:38:39.180 --> 00:38:43.460
He is denounced within days, and a warrant goes out for his arrest.
00:38:44.340 --> 00:38:51.300
That is when he goes into Madame Vernet's house and starts writing about the perfectibility of the species.
00:38:52.320 --> 00:39:00.240
There is a version of this story where the irony is so much, I want to resist it slightly, because I do not think he was a fool.
00:39:00.760 --> 00:39:04.760
He had spent his life arguing that reason would win because it was reason.
00:39:05.760 --> 00:39:16.300
What he was watching was a revolutionary assembly, following a procedure, reaching decisions by majority, and using them to kill people, including, shortly, him.
00:39:17.140 --> 00:39:27.860
If you wanted a demonstration that a large group can converge with total confidence on a catastrophic answer, the terror is sitting right there in his own biography,
00:39:28.200 --> 00:39:32.960
being run by his own colleagues, under voting rules he had helped design.
00:39:33.900 --> 00:39:39.980
In March 1794, he leaves the house, apparently because he fears he is endangering the woman sheltering him.
00:39:40.420 --> 00:39:45.820
He walks out into a country where being unrecognised is the only thing keeping him alive.
00:39:46.200 --> 00:39:54.860
He is arrested at Clamart, and he is taken to a cell in Bourg-Larenne, which the revolutionaries had renamed Bourg-Egalité.
00:39:55.640 --> 00:40:01.120
Two days later, on the 29th of March, he is found dead on the floor.
00:40:01.960 --> 00:40:02.520
He is 50.
00:40:04.200 --> 00:40:05.780
And nobody knows what killed him.
00:40:05.980 --> 00:40:12.640
The most common account is poison, supplied earlier by his friend, the physician Cabanis, taken to avoid the guillotine.
00:40:13.280 --> 00:40:26.540
There is a competing account in which his guards killed him on instruction because the Committee of Public Safety did not want the public spectacle of executing a famous mathematician with admirers across Europe.
00:40:27.020 --> 00:40:34.400
And there is the plain possibility that a 50-year-old man, who had spent months in hiding and then walked a long way and slept rough,
00:40:34.860 --> 00:40:37.900
simply died of exhaustion and illness in a cold room.
00:40:38.580 --> 00:40:40.980
He was found with nothing obvious on him.
00:40:42.920 --> 00:40:46.320
I have seen all three asserted confidently.
00:40:46.940 --> 00:40:50.600
The honest position is that the cause of his death is unknown.
00:40:51.180 --> 00:40:55.480
And I would rather leave it unknown than hand you, you know, a tidy ending.
00:40:56.460 --> 00:40:57.820
The manuscript survived.
00:40:58.060 --> 00:41:00.180
His widow, Sophie, published it the following year.
00:41:00.520 --> 00:41:09.140
And the sketch for a historical picture of the progress of the human mind became one of the founding documents of the idea that things get better.
00:41:09.560 --> 00:41:17.980
Written by a man in hiding from a state he built who died in a cell, arguing that humanity has no ceiling.
00:41:18.780 --> 00:41:21.300
So here is where I want to leave you.
00:41:21.300 --> 00:41:28.640
Condorcet's answer to the correlation problem, though he never phrased it that way, was education.
00:41:29.820 --> 00:41:34.480
Make people better at judging and you can afford to let them talk to each other.
00:41:35.260 --> 00:41:37.280
Competence buys you conversation.
00:41:38.000 --> 00:41:38.860
That is the bet.
00:41:39.120 --> 00:41:41.980
And the whole of his politics follows from it.
00:41:42.700 --> 00:41:47.300
But the last two episodes have both ended in the same place, from opposite directions.
00:41:47.960 --> 00:41:50.760
Galton's ox worked because nobody spoke.
00:41:51.340 --> 00:41:54.580
Condorcet's theorem works because nobody listens.
00:41:54.580 --> 00:42:03.040
And every institution we actually value, every parliament and jury and committee, peer review, public argument,
00:42:03.360 --> 00:42:09.000
is built on the opposite conviction, that talking to each other makes us better.
00:42:10.180 --> 00:42:12.560
But both of those cannot be simply true, right?
00:42:13.400 --> 00:42:16.080
Now you might expect the next step to be an experiment.
00:42:16.220 --> 00:42:20.540
Somebody puts people in a room, lets them talk, and measure what happens to their judgement.
00:42:21.240 --> 00:42:24.400
That does eventually happen, and we will get there.
00:42:25.740 --> 00:42:31.780
But for most of the century after Condorcet died, almost nobody thought the question needed an experiment.
00:42:32.200 --> 00:42:37.880
They thought the answer was obvious, and the answer they had in mind was the opposite of his.
00:42:38.720 --> 00:42:46.720
In 1841, a journalist called Charles Mackay published a long and rather gleeful catalogue of collective insanity.
00:42:47.360 --> 00:42:54.240
Dutch tulip bulbs, trading for fortunes, the South Sea bubble, the Mississippi scheme, witch hunts, crusades.
00:42:54.640 --> 00:42:56.580
The title is the part that everybody remembers.
00:42:57.160 --> 00:43:00.660
Extraordinary popular delusions and the madness of crowds.
00:43:02.080 --> 00:43:06.680
And in 1895, a French writer called Gustave Le Bon went even further.
00:43:07.100 --> 00:43:11.780
He argued that when individuals gather in a crowd, a new thing appears.
00:43:11.780 --> 00:43:20.100
A single creature that is scredulous, impulsive, and capable of violence that none of its members would commit alone.
00:43:20.720 --> 00:43:24.100
Here is the detail that made me stop when I found it.
00:43:24.540 --> 00:43:29.220
When Le Bon wants an example of ordinary, decent people turned savage by a crowd,
00:43:29.540 --> 00:43:32.940
the example he reaches for is the French Convention.
00:43:33.440 --> 00:43:39.880
The same assembly that blocked Condorcet's constitution and issued the warrant and sent him into hiding.
00:43:40.280 --> 00:43:49.740
Le Bon describes its most ferocious members as men who, in calmer times, would have been harmless notaries and upright magistrates,
00:43:50.180 --> 00:43:55.360
and who went quietly back to being exactly that once the storm had passed.
00:43:56.320 --> 00:44:03.000
So, the man who proved that a large public converges on the truth was destroyed by the institution
00:44:03.000 --> 00:44:06.920
that became the textbook case for the opposite view.
00:44:07.620 --> 00:44:13.460
Over the next two episodes, I want to take Mackay and Le Bon seriously, one at a time.
00:44:13.800 --> 00:44:19.320
They are easy to dismiss, and Le Bon in particular writes with open contempt for the people he's describing.
00:44:19.700 --> 00:44:28.580
But I think they saw something real, and I think the mathematics of the last two episodes let us say precisely what it was.
00:44:29.020 --> 00:44:33.040
They were describing a crowd whose errors had stopped being independent.
00:44:33.940 --> 00:44:36.080
We start with Mackay and with Tulips.
00:44:36.080 --> 00:44:38.080
That is next time.
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Thanks for listening.
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The essay is Condorcet, 1785, and the readable part is the preliminary discourse.
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Lex Paulson's History of Collective Intelligence is the opening chapter of the Routledge Handbook of Collective Intelligence for Democracy and Governance,
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and it is open access.
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Ladha on correlated votes is in the American Journal of Political Science, 1992.
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Franz Dietrich's Objection is in Episteme in 2008, all in the notes.