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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Kemeny–Young method

Kemeny-Young methodKemeny-YoungCondorcet–Kemeny
It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.

Condorcet loser criterion

Condorcet loser
A Condorcet loser is a candidate who can be defeated in a head-to-head competition against each other candidate.

Comparison of electoral systems

voting system criterionvoting system criteriavoting method criteria
Scholars of electoral systems often compare them using mathematically defined voting system criteria.
Comparing range voting, Borda count, plurality voting, approval voting with two different absolute approval thresholds, Condorcet voting, and majority judgment, they found that range voting had the highest (worst) strategic vulnerability, while their own method majority judgment had the lowest (best).

Alma Mater Society of the University of British Columbia Vancouver

Alma Mater Society of the University of British ColumbiaAlma Mater SocietyAlma Mater Society of UBC Vancouver
Voter Funded Media and the introduction of Condorcet method style voting for executive positions.

Later-no-harm criterion

later-no-harmHarm
Condorcet voting takes all rankings into account simultaneously, but at the expense of violating the later-no-harm criterion and the later-no-help criterion.

Utility

utility functionutility theoryutilities
The Condorcet winner is also usually but not necessarily the utilitarian winner (the one which maximizes social welfare).

Social welfare function

social welfaresocial efficiencyBergson-Samuelson social welfare function
The Condorcet winner is also usually but not necessarily the utilitarian winner (the one which maximizes social welfare).

Mathematician

mathematiciansapplied mathematicianMathematics
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.

Philosopher

philosopherssagephilosophical
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.

Robert's Rules of Order

Robert's Rules of Order Newly RevisedRobert's RulesRoberts Rules of Order
The procedure given in Robert's Rules of Order for voting on motions and amendments is also a Condorcet method, even though the voters do not vote by expressing their orders of preference.

Rock paper scissors

rock-paper-scissorsRock, Paper, Scissorsrock–paper–scissors
(This is similar to the game rock paper scissors, where each hand shape wins against only one opponent and loses to another).

Single transferable vote

proportionallysingle transferable ballotHare-Clark
In this respect it is the same as an election held under non-Condorcet methods such as instant-runoff voting or the single transferable vote.

Write-in candidate

write-inWrite-inswrite-in campaign
Some Condorcet elections permit write-in candidates but, because this can be difficult to implement, software designed for conducting Condorcet elections often does not allow this option.

Matrix (mathematics)

matrixmatricesmatrix theory
In these matrices, each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'.

Matrix addition

direct sumaddedaddition
Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition.

Political spectrum

political compassPolitical positionpolitical orientation
The idealized notion of a political spectrum is often used to describe political candidates and policies.

Single peaked preferences

single-peakedBlack's Single-Peakedness Theorem
Where this kind of spectrum exists, and voters prefer candidates who are closest to their own position on the spectrum, there is a Condorcet winner (Black's Single-Peakedness Theorem).

Integer programming

integer linear programinteger linear programming0–1 integer programming
However, fast calculation methods based on integer programming allow a computation time in seconds for some cases with as many as 40 choices.

Lexicographical order

lexicographic orderlexicographicallylexicographic
If the largest majority reversed in two orders of finish is the same, the two orders of finish are compared by their second largest reversed majorities, etc. See the discussion of MinMax, MinLexMax and Ranked Pairs in the 'Motivation and uses' section of the Lexicographical Order article).

Later-no-help criterion

Help
Condorcet voting takes all rankings into account simultaneously, but at the expense of violating the later-no-harm criterion and the later-no-help criterion.

Majority rule

majority votingmajoritarianmajority
They see the Condorcet criterion as a natural extension of majority rule.

Median

averagesample medianmedian-unbiased estimator
Condorcet methods tend to encourage the selection of centrist candidates who appeal to the median voter.

Duverger's law

tendencytwo party system which first past the post rewards
The significance of this scenario, of two parties with strong support, and the one with weak support being the Condorcet winner, may be misleading, though, as it is a common mode in plurality voting systems (see Duverger's law), but much less likely to occur in Condorcet or IRV elections, which unlike Plurality voting, punish candidates who alienate a significant block of voters.