Copeland's method
Encyclopedia
Copeland's method or Copeland's pairwise aggregation method is a Condorcet method
in which candidates are ordered by the number of pairwise victories, minus the number of pairwise defeats.
Proponents argue that this method is easily understood by the general populace, which is generally familiar with the sporting equivalent. In many round-robin tournament
s, the winner is the competitor with the most victories. It is also easy to calculate.
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.
method (100 votes with four distinct sets):
The results of the 10 possible pairwise comparisons between the candidates are as follows:
No Condorcet winner (candidate who beats all other candidates in pairwise comparisons) exists.
The table above shows the number of wins and losses for each candidate in the pairwise comparisons. Candidate A has the greatest number of wins minus losses, and is therefore the Copeland winner.
As a Condorcet completion method, Copeland requires a Smith set
containing at least five candidates to give a clear winner unless two or more candidates tie in pairwise comparisons.
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
in which candidates are ordered by the number of pairwise victories, minus the number of pairwise defeats.
Proponents argue that this method is easily understood by the general populace, which is generally familiar with the sporting equivalent. In many round-robin tournament
Round-robin tournament
A round-robin tournament is a competition "in which each contestant meets all other contestants in turn".-Terminology:...
s, the winner is the competitor with the most victories. It is also easy to calculate.
When there is no Condorcet winner (i.e. when there are multiple members of the Smith set
Smith set
In voting systems, the Smith set, named after John H. Smith, is the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome...
), 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 five candidates competing for one seat, the following votes were cast using a preferential votingPreferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
method (100 votes with four distinct sets):
| 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 | Wins - Losses |
|---|---|---|---|
| A | 3 | 1 | 2 |
| B | 2 | 2 | 0 |
| C | 2 | 2 | 0 |
| D | 1 | 3 | -2 |
| E | 2 | 2 | 0 |
The table above shows the number of wins and losses for each candidate in the pairwise comparisons. Candidate A has the greatest number of wins minus losses, and is therefore the Copeland winner.
As a Condorcet completion method, Copeland requires a Smith set
Smith set
In voting systems, the Smith set, named after John H. Smith, is the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome...
containing at least five candidates to give a clear winner unless two or more candidates tie in pairwise comparisons.