Condorcet method: Difference between revisions
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{{Wikipedia}}
Any election method conforming to the [[Condorcet criterion]] - that is, one which always elects the pairwise champion if such 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.
At present, the synonymous phrase '''"[[Instant-Round-Robin Voting|Instant Round Robin Voting]]" (IRRV)''' is being coined to leverage the public's greater familiarity with [[IRV |
'''Condorcet''' is sometimes used to indicate the family of Condorcet methods as a whole.
▲== Simple Explanation ==
If one candidate defeats all others head-to-head, that candidate is the [[Condorcet Criterion|Condorcet Winner]]. This can be determined through use of ranked ballots. In rare occasions, each candidate is defeated by at least one other (e.g. rock, paper, scissors), so there is no Condorcet Winner. In that case it is necessary to use some tiebreaking procedure.
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Each voter fills out a [[preferential voting|ranked ballot]]. 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. However, some variations allow a "no opinion" default option where no for- or against- preference is counted for that candidate. 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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If a candidate is preferred over all other candidates, that candidate is the [[Condorcet Criterion|Condorcet candidate]]. However, a Condorcet candidate may not exist, due to a fundamental [[Voting paradox|paradox]]: It is possible for the electorate to prefer A over B, B over C, and C over A simultaneously. This is called a majority rule cycle, and it must be resolved by some other mechanism.
=== Counting with matrices ===
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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.
== Key terms in ambiguity resolution ==
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*# no proper (smaller) subset of the set fulfills the first property
* '''Cloneproof''': a method that is immune to the presence of '''clones''' (candidates which are essentially identical to each other). In some voting methods, a party can increase its odds of selection if it provides a large number of "identical" options. A cloneproof voting method prevents this attack. See [[strategic nomination]].
== Different ambiguity resolution methods ==
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== 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.
In essence, RP and its variants (such as MAM and MMV) treat each majority preference as evidence that the majority's more preferred alternative should finish over the majority's less preferred alternative, the weight of the evidence depending on the size of the majority.
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 ==
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In other words, this procedure repeatedly throws away the narrowest defeats, until finally the largest number of votes left over produce an unambiguous decision.
== Related terms ==
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* '''weak Condorcet winner''': a candidate who beats or ties with every other candidate in a pair wise matchup. There can be more than one weak Condorcet winner.
* '''weak Condorcet loser''': a candidate who is defeated by or ties with every other candidate in a pair wise matchup. Similarly, there can be more than one weak Condorcet loser.
== An example ==
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In this election, Nashville is the Condorcet winner and thus the winner under all possible Condorcet methods.
== Use of Condorcet voting ==
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# The [http://www.gentoo.org/ Gentoo Linux] project uses the [[Schulze method]].
# The [http://www.userlinux.com/ UserLinux] project uses the [[Schulze method]].
# The [[W:Free State Project|Free State Project]] used a Condorcet method for choosing its target state
# The voting procedure for the uk.* hierarchy of Usenet
#[http://www.rsabey.pwp.blueyonder.co.uk/rpc/fscc/ Five-Second Crossword Competition]
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* [http://radicalcentrism.org/majority_voting.html Maximum Majority Voting] by Ernest Prabhakar
* [http://www.mcs.vuw.ac.nz/~ncj/comp303/schulze.pdf A New Monotonic and Clone-Independent Single-Winner Election Method] ([[Portable Document Format|PDF]]) by Markus Schulze ([http://www.citizensassembly.bc.ca/resources/submissions/csharman-10_0409201706-143.pdf mirror1], [http://lists.gnu.org/archive/html/demexp-dev/2003-09/pdflQW7IlpAfC.pdf mirror2])
* [http://www.OpenSTV.org/ OpenSTV]
* [http://www5.cs.cornell.edu/~andru/civs/ CIVS, a free web poll service using the Condorcet method] by Andrew Myers
* [http://www1.fee.uva.nl/creed/pdffiles/MoulinCh4Elferink.pdf Voting and Social Choice] Demonstration and commentary on Condorcet method. ([[Portable Document Format|PDF]]) By Herve Moulin
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