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Course: Wireless Philosophy > Unit 10
Lesson 12: The jury theoremThe jury theorem
In this Wireless Philosophy video, Geoff Pynn (Elgin Community College) examines Nicolas de Condorcet's jury theorem, a mathematical discovery which provides an argument that democratic elections are the best way to make decisions that are good for society. But can the argument’s assumptions be accepted without reasonable doubt? Created by Gaurav Vazirani.
Video transcript
Hi, I’m Geoff Pynn, and I teach
philosophy at Elgin Community College. In this video, I’m going to talk about
a famous argument for democracy based on a mathematical theorem. Plato argued that
democracy led to tyranny. That’s because most people don’t
have the intelligence, education, or interest in the matter to know
what’s best for society as a whole. Plus, people are generally
motivated by their own interests more than the common good. This makes it easy for a
demagogue to hijack an election by manipulating people’s
ignorance and self-interest for his own nefarious ends. Instead, Plato thought, the only
way to ensure that a society flourished was to put an elite
guardian class in charge. Through their natural intelligence, broad
education, and rigorous training in virtue, Plato’s guardians would be motivated
to do what’s best for society as a whole and they would
know what that was. Rousseau disagreed. He thought that democratic
elections were the best way to figure out what’s best
for society as a whole. You ask the citizens whether a certain
policy would promote the common good, and “Each man, in giving his
vote, states his opinion on that point; and the general will is
found by counting votes.” Just as Plato’s scheme
assumes that the guardian class would rule in
society’s best interests, and not for their
own personal gain, Rousseau’s argument
assumes that people vote from the point of view
of the common good. He thought that the right kind of
education and social institutions would ensure that democratic
citizens would vote this way. “We can not doubt,” he wrote, that people brought up in his
envisioned democratic society “will learn to cherish one
another mutually as brothers, and to will nothing contrary
to the will of society.” Well suppose we could somehow
ensure that democratic citizens cast their votes for the general
will, and not their particular ends. And, let’s also assume
that they have some ability to discern what really is
in our common interest. They still might not know as
much about the needs of society as a brilliant, virtuous,
very well-informed ruler would. So why would taking a vote
be a more effective method for promoting
society’s best interests than letting a wise ruler
make the decisions for us? Nicolas de Condorcet was a
French contemporary of Rousseau’s. He defended liberal
ideas about voting, education, social reform,
women’s rights, and more. He was a supporter of
the French Revolution, until his views put him out of favor
with the leaders of the Revolution, leading to his
imprisonment and death. Today he is remembered for his optimistic
defense of science and rationalism as the keys to human progress. But the idea that he’s best known for is a mathematical discovery
called the Jury Theorem. Many thinkers have
viewed the Jury Theorem as a vindication of Rousseau’s idea
that democratic elections are the best way to discern what’s
best for society. Imagine a twelve-person jury tasked with determining whether
a suspect is guilty or not guilty. Each juror is intelligent, reasonable,
and wants to make an accurate decision. But of course, each of them is limited. Like all of us, they bring their own
assumptions and biases to the table, and none of them has
access to all of the facts. Plus, everybody makes mistakes. Given their individual limitations,
why think that letting the jury as a whole decide the question is a reliable
way to arrive at the correct verdict? Condorcet provided a
mathematical answer to this question. He showed that, as long
as each member of the jury is more than 50% likely to be right, the jury’s collective decision is more likely to be correct
than the average juror is. He also showed that the more
individuals you add to the jury, the more likely it is to
make a correct decision. All you need is for
each added juror to be slightly more than 50%
likely to get the answer right — and the bigger the jury,
the more reliable it will be. The same principle
applies to voters. If each voter is more than 50% likely to
be correct about the answer to a question, taking a vote and going
with the majority’s opinion is significantly more likely
to lead to the right answer. Remarkably, Condorcet showed,
if you have 10,000 voters, and each voter is only 51%
likely to get the right answer, the answer that gets the most
votes is almost certain to be correct. That's not just philosophical
speculation. It’s a mathematical fact. So in a large enough electorate, if we assume that voters are
deciding whether a certain policy is in our common interest,
and that each of them is just slightly more likely to get
the answer right than to get it wrong, the outcome of an election
will almost certainly be correct about whether the policy would
advance the common good. Contrary to Plato’s pessimism, Condorcet’s Jury Theorem suggests
democracy really does have the best chance of leading to the best
outcomes for society as a whole. Of course, it rests on some
pretty strong assumptions. No matter how rigorously they’ve
been trained in democratic values, it’s not clear how many
people would vote for a policy they thought was best for society if they perceived that it
wasn’t in their own interest. Rousseau thought
that in his ideal society, people would identify the
general will with their own, but that seems pretty optimistic. The deeper problem
isn’t about people’s values, integrity, or attitude
towards voting. It’s about their knowledge. It is very hard to figure out
what’s truly in our common interest. Partly, this is because society is
an immensely complicated system, and we can’t predict
with any confidence everything that will happen
as a result of a new law. This is what economists call the
“law of unintended consequences”– that any large-scale action
will have significant effects that were neither
foreseen, nor intended. But it’s also hard for
philosophical reasons. We don’t all agree on what it
even means to benefit society. Disagreements about morality,
values, and so on are pervasive, and these disagreements will lead us to
different views about what’s really best. Given the empirical and philosophical
complexities of discerning the common good, how can we be confident
that a typical voter is more than 50% likely to know
what’s in the common interest? It seems like we can’t. And if we can’t, not only does Condorcet’s theorem fail to
provide an argument in favor of democracy – it threatens to
provide one against it. That’s because another
consequence of Condorcet’s theorem is that if all the voters are less than
50% likely to get the answer right, the outcome of their vote
is even less likely to do so. The more ignorant
voters there are, the less likely the election is
to determine the right outcome. If 10,000 voters are
each 49% likely to be right, the outcome of their election
is almost certain to be wrong. So if the voters are even slightly
more likely to be wrong than right, elections may inevitably lead us astray. Since Condorcet, many theorists have
demonstrated versions of his Jury Theorem that model more accurately the
conditions of actual group decision-making. But still, there’s no consensus that
any actual election is sufficiently similar to the ideal conditions required
for a Jury Theorem to apply. So it’s not clear whether we
have mathematical reason to be confident about any
actual democratic process. The jury’s still out. What do you think?