Majority rule seems fair — until it eats itself. Three voters can each have perfectly sensible rankings, yet the group majority prefers A to B, B to C, AND C to A: a loop with no winner. Whoever controls the ORDER of votes controls the result. Condorcet found this in 1785, and it haunts every committee since. Slide around the cycle and watch the majority chase its tail.
Condorcet’s paradox: pairwise majority preference can be INTRANSITIVE. With three voters ranking A>B>C, B>C>A, C>A>B, a majority (2 of 3) prefers A over B, another majority prefers B over C, and yet another prefers C over A — a cycle with no Condorcet winner. Rational individuals produce an irrational collective, so the outcome depends on the AGENDA (which pair is voted first). It is the seed of Arrow’s impossibility theorem and the reason committee procedure is never neutral. A fail-loud self-check throws unless all three pairwise majorities point the same way around the cycle. ◆ real social-choice theory, node-verified.
The canonical three-voter cycle (the exact intransitivity); real electorates don’t always cycle (single-peaked preferences avoid it, per Black’s theorem), but the possibility is enough to break neutrality — the no-Condorcet-winner result is exact.