Like instant runoff, Coombs' method candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes. However, unlike instant-runoff, each round eliminates the candidate rated last by the most voters (instead of first by the fewest voters).
Each voter rank-orders all of the candidates on their ballot. Otherwise, the candidate ranked last by the largest number (plurality) of voters is eliminated, making each individual round resemble anti-plurality voting. Conversely, under instant-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
In some sources, the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters, and the last candidate to be eliminated is the winner.[2] This variant of the method can result in a different winner than the former one (unlike in instant-runoff voting, where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome).
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities and that everyone wants to live as near to the capital as possible.
The candidates for the capital are:
Memphis, the largest city, but located far from the other cities (42% of voters)
Nashville, near the center of the state (26% of voters)
The preferences of the voters would be divided like this:
42% of voters (close to Memphis)
26% of voters (close to Nashville)
15% of voters (close to Chattanooga)
17% of voters (close to Knoxville)
Memphis
Nashville
Chattanooga
Knoxville
Nashville
Chattanooga
Knoxville
Memphis
Chattanooga
Knoxville
Nashville
Memphis
Knoxville
Chattanooga
Nashville
Memphis
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
Coombs' method election results
City
Round 1
Round 2
First
Last
First
Last
Memphis
42
58
42 0
Nashville
26
0
26 68
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), and making it the winner.
Note that the last-place votes are only used to eliminate a candidate in a voting round where no candidate achieves an absolute majority; they are disregarded in a round where any candidate has 51% or more. Thus last-place votes play no role in the final round.
In practiceedit
The voting rounds used in the reality television program Survivor 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 votingedit
Like anti-plurality voting, Coombs' rule is extremely vulnerable to strategic voting. As a result, it is most often considered as an example of a pathological voting rule rather than in any serious use.[3] Coombs' method is extremely sensitive to incomplete ballots, compromising, push-over, and teaming, and the vast majority of voters' effects on the election come from how they fill out the bottom of their ballots.[3] As a result, voters have a strong incentive to rate the strongest candidates last to defeat them in earlier rounds.
This results in a Keynesian beauty pageant that is extremely sensitive to minor variations in the perceived strengths of candidates.
^Grofman, Bernard, and Scott L. Feld (2004) "If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule," Electoral Studies23:641-59.
^Pacuit, Eric, "Voting Methods", The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.)
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Coombs method or the Coombs rule 1 is a ranked voting system which uses a ballot counting method for ranked voting created by Clyde Coombs Coombs method can be thought of as a cross between instant runoff voting and anti plurality voting Like instant runoff Coombs method candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes However unlike instant runoff each round eliminates the candidate rated last by the most voters instead of first by the fewest voters Contents 1 Procedures 2 An example 3 In practice 3 1 Potential for strategic voting 4 See also 5 NotesProcedures editEach voter rank orders all of the candidates on their ballot Otherwise the candidate ranked last by the largest number plurality of voters is eliminated making each individual round resemble anti plurality voting Conversely under instant runoff voting the candidate ranked first among non eliminated candidates by the fewest voters is eliminated In some sources the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters and the last candidate to be eliminated is the winner 2 This variant of the method can result in a different winner than the former one unlike in instant runoff voting where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome An example editvte nbsp Imagine that Tennessee is having an election on the location of its capital The population of Tennessee is concentrated around its four major cities which are spread throughout the state For this example suppose that the entire electorate lives in these four cities and that everyone wants to live as near to the capital as possible The candidates for the capital are Memphis the largest city but located far from the other cities 42 of voters Nashville near the center of the state 26 of voters Chattanooga somewhat east 15 of voters Knoxville in the far northeast 17 of voters The preferences of the voters would be divided like this 42 of voters close to Memphis 26 of voters close to Nashville 15 of voters close to Chattanooga 17 of voters close to Knoxville Memphis Nashville Chattanooga Knoxville Nashville Chattanooga Knoxville Memphis Chattanooga Knoxville Nashville Memphis Knoxville Chattanooga Nashville MemphisAssuming all of the voters vote sincerely strategic voting is discussed below the results would be as follows by percentage Coombs method election results City Round 1 Round 2First Last First LastMemphis 42 58 42 0Nashville 26 0 26 68Chattanooga 15 0 15Knoxville 17 42 17In 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 and making it the winner Note that the last place votes are only used to eliminate a candidate in a voting round where no candidate achieves an absolute majority they are disregarded in a round where any candidate has 51 or more Thus last place votes play no role in the final round In practice editThe voting rounds used in the reality television program Survivor 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 edit Like anti plurality voting Coombs rule is extremely vulnerable to strategic voting As a result it is most often considered as an example of a pathological voting rule rather than in any serious use 3 Coombs method is extremely sensitive to incomplete ballots compromising push over and teaming and the vast majority of voters effects on the election come from how they fill out the bottom of their ballots 3 As a result voters have a strong incentive to rate the strongest candidates last to defeat them in earlier rounds This results in a Keynesian beauty pageant that is extremely sensitive to minor variations in the perceived strengths of candidates See also editList of democracy and elections related topicsNotes edit Grofman Bernard and Scott L Feld 2004 If you like the alternative vote a k a the instant runoff then you ought to know about the Coombs rule Electoral Studies 23 641 59 Pacuit Eric Voting Methods The Stanford Encyclopedia of Philosophy Fall 2017 Edition Edward N Zalta ed a b Data on Manipulability Retrieved from https en wikipedia org w index php title Coombs 27 method amp oldid 1205222487, wikipedia, wiki, book, books, library,
