How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

It’s a little like the World Series. If the Phillies and the Tigers are facing off, and we agree that the Phillies are a bit better than the Tigers—say, they have a 51% chance of winning each game—then the Phillies are more likely to win the Series 4−3 than to lose by the same margin. If the World Series were best of fifteen instead of best of seven, Philadelphia’s advantage would be even greater. Condorcet’s so-called “jury theorem” shows that a sufficiently large jury is very likely to arrive at the right outcome, as long as the jurors have some individual bias toward correctness, no matter how small.* If the majority of people believe something, Condorcet said, that must be taken as strong evidence that it is correct. We are mathematically justified in trusting a sufficiently large majority—even when it contradicts our own preexisting beliefs. “I must act not by what I think reasonable,” Condorcet wrote, “but by what all who, like me, have abstracted from their own opinion must regard as conforming to reason and truth.” The role of the jury is much like the role of the audience on Who Wants to Be a Millionaire? When we have the chance to query a collective, Condorcet thought, even a collective of unknown and unqualified peers, we ought to value their majority opinion above our own.