Copeland's method

Copeland's method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories.

Proponents argue that this method is easily understandable to the general populace, which is generally familiar with the sporting equivalent. In many round-robin tournaments, the winner is the competitor with the most victories.

When there is no Condorcet winner (i.e. when there are multiple members of the Smith set), this method often leads to ties. For example, if there is a three-candidate majority rule cycle, each candidate will have exactly one loss, and there will be an unresolved tie between the three.

Critics argue that it also puts too much emphasis on the quantity of pairwise victories and defeats rather than their magnitudes.

Example of the Copeland Method

In an election with 5 candidates competing for 1 seat the following votes were cast:

31: A>E>C>D>B

30: B>A>E

29: C>D>B

10: D>A>E

The results of the 10 possible pairwise comparisons between the candidates are as follows:

Comparison	Result	Winner	Comparison	Result	Winner
A v B	41 v 59	B	B v D	30 v 70	D
A v C	71 v 29	A	B v E	59 v 41	B
A v D	61 v 39	A	C v D	60 v 10	C
A v E	71 v 0	A	C v E	29 v 71	E
B v C	30 v 60	C	D v E	39 v 61	E

No Condorcet winner (candidate who beats all other candidates in pairwise comparisons) exists.

Candidate	Wins	Losses
A	3	1
B	2	2
C	2	2
D	1	3
E	2	2

The table above shows the number of wins and losses for each candidate. Candidate A has the greatest number of wins (3 out of 4) and is therefore the Copeland winner.

As a Condorcet completion method Copeland requires a Smith set containing at least 5 candidates to give a clear winner unless two or more candidates tie in pairwise comparisons.

See also

• List of democracy and elections-related topics
• Voting systems

External references

1. E Stensholt, "Nonmonotonicity in AV"; Electoral Reform Society Voting matters - Issue 15, June 2002 (online).
2. A.H. Copeland, A 'reasonable' social welfare function, Seminar on Mathematics in Social Sciences, University of Michigan, 1951.
3. V.R. Merlin, and D.G. Saari, "Copeland Method. II. Manipulation, Monotonicity, and Paradoxes"; Journal of Economic Theory; Vol. 72, No. 1; January, 1997; 148-172.
4. D.G. Saari. and V.R. Merlin, 'The Copeland Method. I. Relationships and the Dictionary'; Economic Theory; Vol. 8, No. l; June, 1996; 51-76.