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Copeland's method

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2249002

Copeland's method

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Copeland's method

The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.

In the system, voters rank candidates from best to worst on their ballot. Candidates then compete in a round-robin tournament, where the ballots are used to determine which candidate would be preferred by a majority of voters in each matchup. The candidate is the one who wins the most matchups (with ties winning half a point).

Copeland's method falls in the class of Condorcet methods, as any candidate who wins every one-on-one election will clearly have the most victories overall. Copeland's method has the advantage of being likely the simplest Condorcet method to explain and of being easy to administer by hand. On the other hand, as one-on-one ties are common or score ties are common, the procedure frequently results in ties, hence often producing no Condorcet winner. As a result, it is typically only used for low-stakes elections.

A special case of this method is promoted by Better Choices for Democracy under the name Consensus Choice Voting.

Copeland's method was devised by Ramon Llull in his 1299 treatise Ars Electionis, which was discussed by Nicholas of Cusa in the fifteenth century. 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).

This can be done by providing each voter with a list of candidates on which to write a "1" against the most preferred candidate, a "2" against the second preference, and so forth. A voter who leaves some candidates' rankings blank is assumed to be indifferent between them but to prefer all ranked candidates to them.

A results matrix r is constructed as follows: rij is

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