Condorcet method

Condorcet votingCondorcet methodsCondorcetCondorcet winnerhead-to-head competitionLlull winnerweak Condorcet winnera more efficient matrix tabulationCondorcet CriterionCondorcet cycle
A Condorcet method is one of several election methods that elects the candidate that wins a majority of the vote in every pairing of head-to-head elections against each of the other candidates, whenever there is such a candidate.wikipedia
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Copeland's method

CopelandCope­landsecond-order Copeland rule
It was equivalent to Copeland's method in cases with no pairwise ties.
Copeland's method or Copeland's pairwise aggregation method is a Condorcet method in which candidates are ordered by the number of pairwise victories, minus the number of pairwise defeats.

Electoral system

multi-membervoting systemvoting systems
A Condorcet method is one of several election methods that elects the candidate that wins a majority of the vote in every pairing of head-to-head elections against each of the other candidates, whenever there is such a candidate.
Ranked systems include Bucklin voting, the various Condorcet methods (Copeland's, Dodgson's, Kemeny-Young, Maximal lotteries, Minimax, Nanson's, Ranked pairs, Schulze), the Coombs' method and positional voting.

Borda count

BordaBorda methodDowdall system
For example, instant-runoff voting and the Borda count are not Condorcet methods. For example, the Black method chooses the Condorcet winner if it exists, but uses the Borda count instead if there is an ambiguity (the method is named for Duncan Black).
In this respect, it is the same as elections under systems such as instant-runoff voting, the single transferable vote or Condorcet methods.

Ranked voting

preferential votingpreferential ballotpreferences
It is important to note that not all single winner, ranked voting systems are Condorcet methods.
Condorcet methods have found more use among private organizations and minor parties.

Marquis de Condorcet

CondorcetNicolas de CondorcetCaritat
Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet, who championed such voting systems.
The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election.

Instant-runoff voting

alternative votepreferential votinginstant run-off voting
For example, instant-runoff voting and the Borda count are not Condorcet methods. While any Condorcet method will elect Nashville as the winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting, these systems would select Memphis and Knoxville respectively.
As Nashville is a Condorcet winner, Condorcet methods would elect Nashville.

Duncan Black

D. Black
For example, the Black method chooses the Condorcet winner if it exists, but uses the Borda count instead if there is an ambiguity (the method is named for Duncan Black).
In particular he was responsible for unearthing the work of many early political scientists, including Charles Lutwidge Dodgson, and was responsible for the Black electoral system, a Condorcet method whereby, in the absence of a Condorcet winner (e.g. due to a cycle), the Borda winner is chosen.

First-past-the-post voting

first past the postfirst-past-the-postFPTP
While any Condorcet method will elect Nashville as the winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting, these systems would select Memphis and Knoxville respectively.
Examples include preferential voting systems, such as instant runoff voting, as well as the two-round system of runoffs and less tested methods such as approval voting and Condorcet methods.

Minimax Condorcet method

MinimaxMinimax Condorcetminimax method
In voting systems, the minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election.

Schulze method

SchulzeCloneproof Schwartz Sequential Droppingmodified minimax
The Schulze method resolves votes as follows:
The Schulze method is a Condorcet method, which means that if there is a candidate who is preferred by a majority over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied.

Condorcet paradox

voting paradoxCondorcet's paradoxBy
The possibility of such cyclic preferences in a group of voters is known as the Condorcet paradox.
When a Condorcet method is used to determine an election, the voting paradox of cyclical societal preferences implies that the election has no Condorcet winner: no candidate who can win a one-on-one election against each other candidate.

Smith set

Smith criterionTop cycle
If the Condorcet winner (A) is part of an A beats B beats C beats A Smith set, supporters of Candidate C will know that Candidate C would win a recall election if candidate B is somehow kept off the ballot.

Ramon Llull

Raymond LullRamon LullArs Magna
Ramon Llull devised the earliest known Condorcet method in 1299.
The terms Llull winner and Llull loser are ideas in contemporary voting systems studies that are named in honor of Llull, who devised the earliest known Condorcet method in 1299.

Nanson's method

NansonBaldwin's method
Condorcet methods are not known to be currently in use in government elections anywhere in the world, but a Condorcet method known as Nanson's method was used in city elections in the U.S. town of Marquette, Michigan in the 1920s, and today Condorcet methods are used by a number of private organizations.
It was systematized by Joseph M. Baldwin in 1926, who incorporated a more efficient matrix tabulation, extending it to support incomplete ballots and equal rankings.

Ranked pairs

Maximum majority voting
Because of this property, RP is, by definition, a Condorcet method.

Dodgson's method

Dodgson
The method is to extend the Condorcet method by swapping candidates until a Condorcet winner is found.

Tactical voting

strategic votingvote tacticallystrategically
All three systems are susceptible to tactical voting, but the types of tactics used and the frequency of strategic incentive differ in each method.
For example, in the Borda count or in a Condorcet method, a voter may insincerely rank a perceived strong alternative last in order to help their preferred alternative beat it.

Majority criterion

agreement of the majoritywho would win an absolute majority in a plurality election
However, the Condorcet criterion implies the majority criterion; the Condorcet criterion is incompatible with independence of irrelevant alternatives, later-no-harm, the participation criterion, and the consistency criterion.
Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, and plurality voting.

Tideman alternative method

These methods are Smith- and Schwartz-efficient, respectively, and thus are Condorcet methods.

Plurality voting

majority votefirst past the postsingle-member
Plurality voting is simple, and theoretically provides incentives for voters to compromise for centrist candidates rather than throw away their votes on candidates who can't win.
Examples include the commonly used two-round system of runoffs and instant runoff voting, along with less tested systems such as approval voting, score voting and Condorcet methods.

Participation criterion

participationPartic­ipation
However, the Condorcet criterion implies the majority criterion; the Condorcet criterion is incompatible with independence of irrelevant alternatives, later-no-harm, the participation criterion, and the consistency criterion.
All Condorcet methods, Bucklin voting, and IRV fail.

Plurality criterion

Woodall's plurality criterion
Only methods employing winning votes satisfy Woodall's plurality criterion.
Among Condorcet methods which permit truncation, whether the Plurality criterion is satisfied depends often on the measure of defeat strength.

Nicolaus Tideman

In 1987, he devised the voting system called ranked pairs, which is a Condorcet method, and in 2000 the CPO-STV proportional voting method.

Free State Project

New Hampshire Free PressPorcupine Freedom FestivalFree Press
In September 2003, the state vote was held and participants voted using the Condorcet method to choose the state.