Definition Copeland's method is a ranked-choice voting system that belongs to the class of Condorcet methods. It determines a winner by conducting a series of pairwise comparisons between all candidates. For each candidate, a score is accumulated based on how many other candidates they defeat in a head-to-head matchup. The candidate with the highest total score is declared the winner.
Overview In Copeland's method, voters rank candidates in order of preference. These rankings are then used to simulate every possible head-to-head contest between two candidates. If candidate A is preferred over candidate B by a majority of voters in their direct comparison, candidate A "wins" that matchup. A candidate receives one point for each such win. In the event of a tie in a pairwise comparison (i.e., an equal number of voters prefer each candidate), both candidates receive half a point. The candidate who accumulates the greatest number of points across all pairwise comparisons is selected as the winner. A key feature of Copeland's method is that it will always elect a Condorcet winner if one exists—a candidate who can defeat every other candidate in a pairwise comparison.
Etymology/Origin Copeland's method is named after Arthur Herbert Copeland Sr. (1898–1970), an American mathematician. He developed and proposed this voting system in 1951. Copeland was a professor at the University of Michigan and contributed to the fields of probability theory and mathematical logic, among others.
Characteristics
- Condorcet Criterion: Copeland's method satisfies the Condorcet criterion, meaning if a Condorcet winner exists, they will be elected.
- Pairwise Comparisons: The core mechanism involves evaluating every possible two-candidate matchup. This can be computationally intensive as the number of candidates increases, requiring N*(N-1)/2 comparisons for N candidates.
- Score-based System: Unlike some other Condorcet methods that focus on creating a directed graph or manipulating preference schedules, Copeland's method assigns a quantifiable score to each candidate based on their wins and ties in pairwise contests.
- Tie-breaking: While it effectively identifies a clear winner in many cases, it is possible for two or more candidates to have the same highest Copeland score, resulting in a tie. External tie-breaking rules (e.g., random selection, specific secondary criteria) would then be necessary.
- Independence of Irrelevant Alternatives: Like most Condorcet methods, Copeland's method does not satisfy the independence of irrelevant alternatives criterion, meaning the ranking of two candidates can be affected by the presence or absence of a third, "irrelevant" candidate.
- Monotonicity: The method satisfies monotonicity, meaning that ranking a winning candidate higher, or a losing candidate lower, will not prevent the winning candidate from winning (or cause the losing candidate to win).
Related Topics
- Condorcet Method: A class of voting systems that elect the Condorcet winner if one exists. Other Condorcet methods include the Schulze method and Ranked Pairs (or Tideman method).
- Ranked-choice Voting: A broad category of voting systems where voters rank candidates in order of preference rather than choosing only one.
- Pairwise Comparison: A fundamental technique used in many decision-making processes, including various voting systems, where options are compared against each other in pairs.
- Arrow's Impossibility Theorem: A theorem in social choice theory that demonstrates inherent difficulties in designing voting systems that satisfy a range of seemingly desirable criteria simultaneously.
- Voting System: Any method by which a group of voters collectively makes a decision or expresses an opinion.