Condorcet method

The Condorcet or majority-rule methods (English: ; French: [kɔ̃dɔʁsɛ]) are a family of election systems that elect the majority-preferred (Condorcet) winner if one exists. A majority-preferred candidate is a candidate who would win a majority of votes in any head-to-head election against any opponent. In other words, they are a candidate who would win in any one-on-one race (one without spoilers). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking. Some elections may not have a Condorcet winner because the majority's preferences can be cyclic: in other words, it is possible every candidate has an opponent that would defeat them in a two-candidate contest. This is similar to a game of rock, paper, scissors: a candidate "scissors" may beat "paper," but still lose to "rock". The possibility of such a cycle is known as Condorcet's paradox. (Empirically, however, such cycles are rare, with most large public elections having a Condorcet winner. As a result, all Condorcet methods reduce to simple majority rule in most cases.) Under many models of voting, the Condorcet winner is typically the same as the socially optimal winner. However, this is not guaranteed to be the case; situations where the two disagree are commonly called tyranny of the majority scenarios (particularly if the disagreement is large). Condorcet voting methods are named for the 18th-century French mathematician, the Marquis de Condorcet, who popularized the concept. Condorcet methods were first extensively analyzed by Ramon Llull, but the manuscripts of these works were lost from the Late Middle Ages until being rediscovered in the 20th century. Condorcet methods are commonly used to vote on motions and amendments in assemblies and legislatures, as they allow replacing paper ballots with a series of simple majority votes, with prominent parliamentary...