Condorcet method: Difference between revisions

'''Condorcet''' is sometimes used to indicate the family of Condorcet methods as a whole.

 

 

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, so there is no Condorcet Winner. In that case it is necessary to use some tiebreaking procedure.

 

 

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.

 

 

Ballots are counted by considering all possible sets of two-candidate elections from all available candidates. That is, each candidate is considered against each and every other candidate. A candidate is considered to "win" against another on a single ballot if they are ranked higher than their opponent. All the votes for candidate Alice over candidate Bob are counted, as are all of the votes for Bob over Alice. Whoever has the most votes in each one-on-one election wins.

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.

 

 

A frequent implementation of this method will illustrate the basic counting method. Consider an election between A, B, and C, and a ballot (B, C, A, D). That is, a ballot ranking B first, C second, A third, and D forth. This can be represented as a matrix, where the row is the runner under consideration, and the column is the opponent. The cell at (runner,opponent) has a one if runner is preferred, and a zero if not.

The sum of all ballot matrices, the '''Condorcet pairwise matrix''', is the primary piece of data used to resolve majority rule cycles.

 

 

Handling cases where there is not a single Condorcet winner is called ambiguity resolution in this article, though other phrases such as "cyclic ambiguity resolution" and "Condorcet completion" are used as well.

* '''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]].

 

 

There are a countless number of "Condorcet methods" possible that resolve such ambiguities. The fact that Marquis de Condorcet himself already spearheaded the debate of which particular Condorcet method to promote has made the term "Condorcet's method" ambiguous.

The text below describes (variants of) these methods in more detail.

 

 

In the Ranked Pairs (RP) voting method, as well as the variations Maximize Affirmed Majorities (MAM)

In MMV all such conflicting matchups are ignored (though any non-conflicting matchups of that size are still included).

 

 

The "[[Schulze method|Cloneproof Schwartz Sequential Dropping]]" (CSSD) method resolves votes as follows:

 

The "Beatpath Winner" algorithm produces equivalent results.

 

== Related terms ==

* '''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 ==

 

In this election, Nashville is the Condorcet winner and thus the winner under all possible Condorcet methods.

 

== Use of Condorcet voting ==

#[http://www.rsabey.pwp.blueyonder.co.uk/rpc/fscc/ Five-Second Crossword Competition]

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