Condorcet Method

The Condorcet method is a family of ranked-voting procedures named after the French mathematician and philosopher Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet, who set out the underlying principle in his 1785 Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix. Voters rank candidates in order of preference, and the system then simulates a separate two-way race between every possible pair of candidates using those rankings. The candidate who defeats every other candidate in these pairwise contests is declared the Condorcet winner.

The appeal of the method is intuitive: if a majority of voters prefer A to B in a direct comparison, then B arguably should not be chosen over A. This is sometimes called the Condorcet criterion, and voting theorists use it as a benchmark for evaluating other systems. Plurality voting and instant-runoff voting (IRV) can fail this criterion; methods such as Schulze, Ranked Pairs (Tideman), Copeland, Minimax, and Kemeny–Young all satisfy it.

A central complication is the Condorcet paradox: pairwise majorities can cycle (A beats B, B beats C, C beats A), so no Condorcet winner exists. Different Condorcet-compliant methods resolve such cycles in different ways, which is why "the Condorcet method" is really a class rather than a single algorithm. Kenneth Arrow's 1951 impossibility theorem later generalized this tension, showing that no ranked voting rule can simultaneously satisfy a small set of seemingly reasonable fairness conditions.

In practice, Condorcet variants are used by private organizations rather than national governments. The Debian project, Software in the Public Interest, the Pirate Party in several countries, and Wikimedia bodies have used Schulze-method elections. Governmental adoption remains rare, partly because pairwise tabulation is harder to explain to voters than plurality or IRV ballots, even though the ranked ballot itself is identical to those used in other preferential systems.