Secondary method

The Copeland method

The simplest Condorcet method: count the duels won and lost. Easy to tally by hand, but often tied on a cycle. It has no real advantage over Schulze.

When to choose it: if your bylaws require it, or if everyone must be able to redo the calculation in their head. In that case, plan a rule for ties.

Origin: Arthur H. Copeland, 1951; the idea goes back to Ramon Llull in the 13th century
Variants offered: Copeland
Computation: Polynomial, in n² for n options

The principle

Counting the duels won.

Each option gets one point per duel won and loses one per duel lost; the ranking follows that score. The Condorcet winner, which wins all its duels, is always elected.

But Copeland ignores the size of the victories: on a cycle, each option wins as many duels as it loses, and they all end up tied, whatever the number of voters.

Step by step

The same cycle, counted duel by duel.

The 100 ballots of the example

Camille , then Adèle , then Sophie 40 voters
Adèle , then Sophie , then Camille 35 voters
Sophie , then Camille , then Adèle 25 voters

1 Camille. Wins against Adèle, loses against Sophie: score 0.
2 Adèle. Wins against Sophie, loses against Camille: score 0.
3 Sophie. Wins against Camille, loses against Adèle: score 0.

Copeland score

Camille 1 won, 1 lost 0
Adèle 1 won, 1 lost 0
Sophie 1 won, 1 lost 0

Result: a perfect tie, where Schulze picks Camille.

Properties

What the method guarantees, compared with first-past-the-post.

The whole family of majority and Condorcet criteria, but neither independence of clones nor ties that fade as the number of voters grows.

Criterion	Copeland	First-past-the-post
Majority An option ranked first by more than half of the voters wins.	Yes	Yes
Majority loser An option ranked last by more than half of the voters never wins.	Yes	No
Mutual majority If a majority ranks a group of options ahead of all the others, the winner belongs to that group.	Yes	No
Condorcet winner The option that beats each of the others in a duel is always elected.	Yes	No
Condorcet loser The option beaten by each of the others in a duel is never elected.	Yes	No
Smith criterion The winner belongs to the smallest group of options that beat every option outside it.	Yes	No
Independence of clones Adding an option very similar to another does not change the outcome among the others.	No	No
Monotonicity Ranking the winner higher can never make them lose.	Yes	Yes
Local independence Removing the option that finished last (or first) in the result does not change the order of the others.	No	No
Reversal symmetry If every ballot is reversed, the former winner no longer wins.	Yes Note 1	No
Participation Voting sincerely can never leave a voter worse off than abstaining.	No	Yes
Consistency If an option wins in two separate groups, it wins when they are combined.	No	Yes
Later-no-harm Ranking an additional choice can never hurt those already ranked ahead of it.	No	Yes Note 2
Resolvability A final tie becomes unlikely as the number of voters grows.	No	Yes
Fast computation The result is computed in polynomial time, even with many options.	Yes	Yes

✓ always satisfied
✕ can be violated in some votes
? no published source establishes it

1 Blank cell in Wikipedia’s general table; “yes” in its table of Condorcet methods and in the legacy condorcet.vote table.
2 Trivially: first-past-the-post never looks beyond the first choice.

All the methods, criterion by criterion

In Condorcet.Vote

Our implementation choices.

Wins minus losses. Each duel won adds a point, each duel lost takes one away, and a tied duel counts for nothing.
No added tie-breaker. Neither Borda nor a drawing of lots: options with the same score share the rank.
A complete ranking. Options are ordered by decreasing score.

Sources

Type	Reference
Encyclopedia	Copeland’s method Wikipedia
Documentation	Voting Methods CondorcetPHP · docs.condorcet.io
Paper	The Copeland method: I. Relationships and the dictionary Donald G. Saari, Vincent R. Merlin (1996) · Economic Theory 8(1)

The other methods

Back to Condorcet ranking