Condorcet method: Difference between revisions
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FF (French Fries) is the CW here.
|caption=Example of finding the Condorcet winner|border=|max-width=}}Any election method conforming to the [[Condorcet criterion]] - that is, one which always elects the [[beats-all winner]], a candidate who can beat any other candidate in a runoff, if one exists - is known as a '''Condorcet method'''. The name comes from the 18th century mathematician and philosopher [[Marquis de Condorcet]], although the method was previously described by [[Ramon Llull]] in the 13th century. Many Condorcet advocates agree that a further criterion that Condorcet methods should pass is the [[Smith criterion]], which means the Condorcet method will always elect someone from the [[Smith set]] when there is no beats-all winner (usually due to the [[Condorcet paradox]]).
'''Condorcet''' is sometimes used to refer to the family of Condorcet methods as a whole.
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:''See also: [[Ballot]]''
Each voter fills out a [[preferential voting|ranked ballot]] or [[Cardinal voting|rated ballot]] (i.e. they rank the candidates 1st, 2nd, 3rd, or they rate the candidates, for example, a 0 out of 5, a 3 out of 5, etc.) The voter can include less than all candidates under consideration. Usually when a candidate ''is not listed'' on the voter's ballot they are considered less preferred than listed candidates, and ranked accordingly, with the voter considered to have no preference between any of them. However, some variations allow a "no opinion" default option where no for- or against- preference is counted for that candidate.
=== Write-in option ===
Write-ins are possible, but are somewhat more difficult to implement for automatic counting than in other election methods. This is a counting issue, but results in the frequent omission of the write-in option in ballot software.
==Counting ballots==
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The sum of all ballot matrices, the '''Condorcet pairwise matrix''', is the primary piece of data used to resolve majority rule cycles in [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]], and can be used to find the Condorcet winner and [[Smith set]] in any Condorcet method.
=== Finding the Condorcet winner ===
There are various ways to find the Condorcet winner from the pairwise matrix. The simplest is to look for a single candidate who has a positive margin of votes against all other candidates in each matchup (i.e. if they got 5 votes and another candidate 4 votes in the pair's matchup, then the margin is 1 vote in favor of the first candidate, indicating they won the matchup), if one exists. [[Copeland]] more generally can help find the Smith set by looking for a smallest group of candidates that have victories against all others, by starting from the candidates with the most victories in their head-to-head matchups.
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**'''[[Baldwin]]''' computes the [[Borda count]] for all candidates, then iteratively deletes (eliminates) the candidate with the lowest count.
=== Defeat-dropping Condorcet methods ===
<sup>1</sup> There are different ways to measure the strength of each defeat in some methods; see the [[defeat strength]] article. Some use the margin of defeat (the difference between votes for and votes against), while others use winning votes (the votes favoring the defeat in question).
Electionmethods.org argues that there are several disadvantages of systems that use margins instead of winning votes.
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The text below describes (variants of) the defeat-dropping methods in more detail.
====Ranked Pairs, Maximize Affirmed Majorities (MAM), and Maximum Majority Voting (MMV)====
In the Ranked Pairs (RP) voting method, as well as the variations Maximize Affirmed Majorities (MAM) and Maximum Majority Voting (MMV), pairs of defeats are ranked (sorted) from largest majority to smallest majority. Then each pair is considered, starting with the defeat supported by the largest majority. Pairs are "affirmed" only if they do not create a cycle with the pairs already affirmed. Once completed, the affirmed pairs are followed to determine the winner.
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The difference between RP and its variants is in the details of the ranking approach. Some definitions of RP use margins, while other definitions use winning votes (not margins). Both MAM and MMV are explicitly defined in terms of winning votes, not winning margins. In MAM and MMV, if two defeat pairs have the same number of votes for a victory, the defeat with the smaller defeat is ranked higher. If this still doesn't disambiguate between the two, MAM and MMV perform slightly differently. In MAM, information from a "tiebreaker" vote is used (which could be a distinguished vote such as the vote of a "speaker", but unless there is a distinguished vote, a randomly-chosen vote is used). In MMV all such conflicting matchups are ignored (though any non-conflicting matchups of that size are still included).
====Schulze method ====
The [[Schulze method]] resolves votes as follows:
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==Notes ==
All Condorcet methods pass the [[mutual majority criterion]] when there is a Condorcet winner. This is because the CW is guaranteed to be a member of any set of candidates that can pairwise beat all candidates not in the set, and the mutual majority set is such a set, because all candidates in it are ranked by a majority over all candidates not in the set. [[Smith-efficient]] Condorcet methods always pass the [[mutual majority criterion]]. ▼
The fundamental argument for Condorcet over other extensions of [[majority rule]] is that it explicitly monitors for the [[Condorcet paradox]]. This is what makes it vulnerable to [[Favorite Betrayal]], however, since voters can make their lesser evil become the CW by preventing their favorite from pairwise beating them. See the [[Tied at the top rule]] for a way out of this. ▼
=== Comparison to other extensions of majority rule ===
▲The fundamental argument for Condorcet over other extensions of [[majority rule]] is that it explicitly monitors for the [[Condorcet paradox]]. This is what makes it vulnerable to [[Favorite Betrayal]], however, since voters can make their lesser evil become the CW by preventing their favorite from pairwise beating them. See the [[Tied at the top rule]] for a way out of this. Another possible argument is that it may be the best way to avoid the [[center squeeze effect]].
=== Making any voting method Condorcet-efficient ===
Any voting method can be made a Condorcet method by simply adding a condition that a Condorcet winner will win if one exists before running the voting method. It is possible to further make a voting method [[Smith-efficient]] by taking various approaches, such as eliminating candidates one by one until there is a Condorcet winner (like in [[Benham's method]]) or eliminating all candidates not in the [[Smith set]] before running the voting method's procedure (i.e. [[Smith//IRV]]), or taking a more complex approach of repeatedly eliminating all candidates not in a particular set and eliminating the loser of another voting method [[Tideman's Alternative methods]]).
It is possible to do a first round where the [[Smith set]] of candidates is identified, and then a second round where another voting method is used to select among the Smith set (or any set). For example, [[Smith//Approval]] is the automatic form of doing this with [[Approval voting]].
=== Connection to Asset voting negotiations ===
Condorcet methods can be seen as highly related to [[Asset voting]]: the voters indicate their preferences on how they'd negotiate and form majority coalitions for their favorite candidates, and when those candidates aren't viable or aren't in consideration, would intervene to help elect some candidates they prefer more than others. In this sense, extending Condorcet to PR ([[Condorcet PR]]) is not too difficult: [[Droop proportionality criterion|Droop proportionality]] must be met, because Droop quotas can force their preference in any negotiation where each person can only maximally support up to a candidate, and certain other constraints must be met, such as allowing B to win in the following example:
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because while A does pairwise beat B, C would always have 49 votes and thus actually win overall if the A-top voters try to only support A and not shift towards B, because A would have 26 votes, B 25, but C 49. In general, this type of "semi-solid coalition" where a group of voters are almost a [[solid coalition]] except that some in the group prefer another candidate over the solid coalition's candidates, with no voters outside of the coalition having preferences between the semi-solid coalition's candidates, has to always elect the candidate that everyone in the coalition supports to be related to Asset. In addition, the Condorcet PR method must be based on [[D'Hondt]], because Asset voting allows voters to split their votes to obtain more seats (similar to [[free riding]]).
=== Utilitarianism ===
▲All Condorcet methods pass the [[mutual majority criterion]] when there is a Condorcet winner. This is because the CW is guaranteed to be a member of any set of candidates that can pairwise beat all candidates not in the set, and the mutual majority set is such a set, because all candidates in it are ranked by a majority over all candidates not in the set. [[Smith-efficient]] Condorcet methods always pass the [[mutual majority criterion]].
Most Condorcet methods allow for equal-ranking. Because of this, it is possible to vote [[Approval voting]]-style. In fact, if all voters vote Approval-style, the Smith set will only have candidates who pairwise tie, rather than who have [[Condorcet cycle|Condorcet cycles]]. And in fact, if every voter ranks a candidate either 1st or last with a probability proportional to their cardinal [[utility]] for that candidate, then you get a [[Smith set ranking]] mirroring the [[Score voting]] ranking with probability approaching 1 when there are many voters. This is because if 100 voters consider a candidate a 3 out of 10, then if they use a 30% probability of ranking that candidate 1st, otherwise ranking them last, then it is very likely the candidate will end up ranked 1st on 30 of their ballots and last on 70, similar to being approved by only 30 of them. This mitigates one common utilitarian concern with Condorcet, that it might let a majority force its weak preference onto the minority; this is because voters with weak preferences may be willing to equally rank candidates in order to allow voters with stronger preferences to have the deciding vote. See also the [[KP transform]], which can be used to model transforming cardinal utilities into ranked ballots by making Score ballots into Approval ballots, and then Approval ballots into ranked ballots.
=== Difficulty of vote-counting ===
One concern with Condorcet methods is that it is very difficult to do [[pairwise counting]] for elections with 10 of more candidates, since that is at least (0.5*10*((10-1)=9))=45 pairwise matchups to record the details of. Allowing write-in candidates makes things even more complex. One possible solution would be to have a primary beforehand using a voting method better than [[FPTP]] to pick 5 top candidates, and then only allow voters to rank those top 5. For all other candidates, they'd be able to approve or score each of them. The rated information could then be used to elect someone other than one of the top 5 when the non-top 5 candidates have significantly higher ratings, but otherwise only elect one of the top 5. The primary itself could be made slightly semi-proportional as well. An alternative solution if using a [[:Category:Condorcet-cardinal hybrid methods|Condorcet-cardinal hybrid method]] is to count the ballots twice, first only recording the cardinal information, and then use this to select the 5 to 10 best candidates who qualify to win, between whom the pairwise matchups will also be recorded. Also see [[Condorcet criterion#Criticisms]].
At one point, the synonymous phrase (to Condorcet voting) '''"[[Instant-Round-Robin Voting|Instant Round Robin Voting]]" (IRRV)''' was being coined to leverage the public's greater familiarity with [[IRV |Instant Runoff Voting]] (IRV). This phrase was being used in a [http://groups.yahoo.com/group/Condorcet legislative effort] to implement a Condorcet variant ([[CSSD]]) in the state of Washington. ▼
== Use of Condorcet voting==
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Nanson's method, which is a Condorcet method, was used in city elections in the U.S. town of Marquette, Michigan in the 1920s.<ref name="Mclean">{{cite conference | last=Mclean | first=Iain | title=Australian electoral reform and two concepts of representation | url=http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.362.5357 |date=October 2002|access-date=2020-04-02|conference=APSA Jubilee Conference}}</ref>
▲At one point, the synonymous phrase (to Condorcet voting) '''"[[Instant-Round-Robin Voting|Instant Round Robin Voting]]" (IRRV)''' was being coined to leverage the public's greater familiarity with [[IRV
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== See also ==
[[Pairwise preference]]
==External links==
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