Coombs' method
Encyclopedia
The Coombs' method is a voting system
created by Clyde Coombs
used for single-winner election
s in which each voter rank the candidates in order of preference. It is very similar to instant-runoff voting
(also known as the alternative vote), a more common preferential voting
system.
could be considered a variation of Coombs' method, with sequential voting rounds. Everyone votes for one candidate they support for elimination each round, and the candidate with a plurality of that vote is eliminated. A strategy difference is that sequential rounds of voting means the elimination choice is fixed in a ranked ballot Coombs' method, until that candidate is eliminated.
and teaming
.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
created by Clyde Coombs
Clyde Coombs
Clyde Hamilton Coombs was an American psychologist specializing in the field of mathematical psychology. He devised a voting system, that was hence named Coombs' method....
used for single-winner election
Election
An election is a formal decision-making process by which a population chooses an individual to hold public office. Elections have been the usual mechanism by which modern representative democracy operates since the 17th century. Elections may fill offices in the legislature, sometimes in the...
s in which each voter rank the candidates in order of preference. It is very similar to instant-runoff voting
Instant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
(also known as the alternative vote), a more common preferential voting
Preferential 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...
system.
Procedures
Each voter rank-orders all of the candidates on their ballot. If at any time one candidate is ranked first (among non-eliminated candidates) by an absolute majority of the voters, then this is the winner. As long as this is not the case, the candidate which is ranked last (again among non-eliminated candidates) by the most (or a plurality of) voters is eliminated. Conversely, under instant run-off voting the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.An example
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:| City | Round 1 | Round 2 | ||
|---|---|---|---|---|
| First | Last | First | Last | |
| Memphis | 42 | 58 | |
|
| Nashville | 26 | 0 | |
|
| Chattanooga | 15 | 0 | 15 | |
| Knoxville | 17 | 42 | 17 | |
- In the first round, no candidate has an absolute majority of first place votes (51).
- Memphis, having the most last place votes (26+15+17=58), is therefore eliminated.
- In the second round, Memphis is out of the running, and so must be factored out. Memphis was ranked first on Group A's ballots, so the second choice of Group A, Nashville, gets an additional 42 first place votes, giving it an absolute majority of first place votes (68 versus 15+17=32) thus making it the winner. Note that the last place votes are disregarded in the final round.
Use
The voting rounds used in Survivor (TV series)Survivor (TV series)
Survivor is a reality television game show format produced in many countries throughout the world. In the show, contestants are isolated in the wilderness and compete for cash and other prizes. The show uses a system of progressive elimination, allowing the contestants to vote off other tribe...
could be considered a variation of Coombs' method, with sequential voting rounds. Everyone votes for one candidate they support for elimination each round, and the candidate with a plurality of that vote is eliminated. A strategy difference is that sequential rounds of voting means the elimination choice is fixed in a ranked ballot Coombs' method, until that candidate is eliminated.
Potential for strategic voting
The Coombs' method is vulnerable to three strategies: compromising, push-overTactical voting
In voting systems, tactical voting occurs, in elections with more than two viable candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.It has been shown by the Gibbard-Satterthwaite theorem that any voting method which is...
and teaming
Strategic nomination
Strategic nomination is the manipulation of an election through its candidate set...
.