How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

The political virtue Condorcet did possess was a passionate, never-wavering belief in reason, and especially mathematics, as an organizing principle of human affairs. His allegiance to reason was standard stuff for the Enlightenment thinkers, but his further belief that the social and moral world could be analyzed by equations and formulas was novel. He was the first social scientist in the modern sense. (Condorcet’s term was “social mathematics.”) Condorcet, born into the aristocracy, quickly came to the view that universal laws of thought should take precedence over the whims of kings. He agreed with Rousseau’s claim that the “general will” of the people should hold sway on governments but was not, like Rousseau, content to accept this claim as a self-evident principle. For Condorcet, the rule of the majority needed a mathematical justification, and he found one in the theory of probability. Condorcet lays out his theory in his 1785 treatise Essay on the Application of Analysis to the Probability of Majority Decisions. A simple version: suppose a seven-person jury has to decide a defendant’s guilt. Four say the defendant is guilty, and only three believe he’s innocent. Let’s say each of these citizens has a 51% chance of holding the correct view. In that case, you might expect a 4−3 majority in the correct direction to be more likely than a 4−3 majority favoring the incorrect choice.