Copeland's method
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.
A results matrix r is constructed as follows:[4] rij is This may be called the "1/1⁄2/0" method (one number for wins, ties, and losses, respectively).
Otherwise the Condorcet method produces no decision and the candidate with greatest score is the Copeland winner (but may not be unique).
Llull himself put forward a 1/1/0 method, so that two candidates with equal support would both get the same credit as if they had beaten the other.
[6] It was adopted in the first season of the English Football League (1888–1889), the organisers having initially considered using a 1/0/0 system.
The Borda count is analogous to a tournament in which every completed ballot determines the result of a game between every pair of competitors.)
Partha Dasgupta and Eric Maskin sought to justify Copeland's method in a popular journal, where they compare it with the Borda count and plurality voting.
[8] Their argument turns on the merits of the Condorcet criterion, paying particular attention to opinions lying on a spectrum.
If there were 100 times as many voters, but they voted in roughly the same proportions (subject to sampling fluctuations), then the numbers of ballots would scale up but the Copeland scores would stay the same; for instance the 'A' row might read: The risk of ties is particularly concerning because the main aim of Copeland's method is to produce a winner in cases when no candidate satisfies the Condorcet criterion.
A simulation performed by Richard Darlington implies that for fields of up to 10 candidates, it will succeed in this task less than half the time.
Nicolaus Tideman and Florenz Plassman conducted a large study of reported electoral preferences.
They concluded that it was consistent with their data to suppose that "voting cycles will occur very rarely, if at all, in elections with many voters".
The first two are not frequently advocated for this use but are sometimes discussed in connection with Smith's method where similar considerations apply.
Dasgupta and Maskin proposed the Borda count as a Copeland tie-break: this is known as the Dasgupta-Maskin method.
When results for every possible pairing have been found they are as follows: The wins and losses of each candidate sum as follows: Nashville, with no defeats, is the Condorcet winner.
Since the voters expressed a preference one way or the other between every pair of candidates, the score under the 1/+1/2/0 method is just the number of wins, likewise maximized by Nashville.
