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Concept
Copeland's method
Summary
Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history:
Ramon Llull described the system in 1299, so it is sometimes referred to as "Llull's method"
The Marquis de Condorcet described a similar system in the 1780s, so the method could be referred to as "Condorcet's method", but instead other systems were subsequently devised that choose the Condorcet winner.
Arthur Herbert Copeland described the system in the 1950s, so it has been frequently been called "Copeland's method".
Each voter is asked to rank candidates in order of preference. A candidate A is said to have majority preference over another candidate B if more voters prefer A to B than prefer B to A; if the numbers are equal then there is a preference tie. The Copeland score for a candidate is the number of other candidates over whom they have a majority preference plus half the number of candidates with whom they have a preference tie. The winner of the election under Copeland's method is the candidate with the highest Copeland score; under Condorcet's method this candidate wins only if they have the maximum possible score of n − 1 where n is the number of candidates. Hence victory under this system amounts to satisfying the Condorcet criterion.
Any voting method satisfying the Condorcet winner criterion may sometimes be referred to as "a Condorcet method". Other methods that satisfy the Condorcet winner criterion include the Kemeny–Young method, the Schulze method, and Minimax.
Copeland's method was devised by Ramon Llull in his 1299 treatise Ars Electionis and discussed by Nicholas of Cusa in the fifteenth century and by the Marquis de Condorcet in the eighteenth (who drew attention to the related criterion). However, it is frequently named after Arthur Herbert Copeland who advocated it independently in a 1951 lecture.
The input is the same as for other ranked voting systems: each voter must furnish an ordered preference list on candidates where ties are allowed (a strict weak order).
Official source
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