The Condorcet Paradox
A majority prefers A to B, and B to C, and C to A. Every voter was honest and nobody made a mistake.
178517 min read
French Enlightenment mathematics and philosophy
Nicolas de Condorcet
1743 – 1794
Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet: mathematician, permanent secretary of the Académie royale des sciences, and the last of the philosophes. His 1785 Essai applied probability theory to voting and juries, producing both the jury theorem and the cycle that bears his name. He was an early opponent of slavery and an advocate of women's suffrage, sat in the Legislative Assembly, and voted against executing the king. Proscribed during the Terror, he wrote his Esquisse d'un tableau historique des progrès de l'esprit humain while in hiding, and was found dead in a cell at Bourg-la-Reine in March 1794.
2 entries
Arrow's Impossibility Theorem
There is no fair way to turn what a group of people each want into what the group wants. This is not a complaint about politics. It is a theorem.
1950 (paper), 1951 (book), 1963 (corrected second edition)25 min read