Condorcet loser criterion
Encyclopedia
In single-winner voting system
theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion
.
A voting system
complying with the Condorcet loser criterion will never allow a Condorcet loser to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition
against each other candidate. (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.)
A slightly weaker (easier to pass) version is the majority Condorcet loser criterion, which requires that a candidate who can be defeated by a majority in a head-to-head competition against each other candidate, lose. It is possible for a system, such as Majority Judgment, which allows voters not to state a preference between two candidates, to pass the MCLC but not the CLC.
Compliant methods include: two-round system
, instant-runoff voting
, contingent vote
, borda count
, Schulze method
, and ranked pairs
.
Noncompliant methods include: plurality voting, supplementary voting, Sri Lankan contingent voting, approval voting
, range voting
, Bucklin voting
and minimax Condorcet
.
Assume that the Condorcet loser is X. For X to win, Ranked Pairs must lock a preference of X over some other candidate Y (for at least one Y) before it locks Y over X. But since X is the Condorcet loser, the victory of Y over X will be greater than that of X over Y, and therefore Y over X will be locked first, no matter what other candidate Y is. Therefore X cannot win.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion
Majority loser criterion
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win....
.
A voting system
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
complying with the Condorcet loser criterion will never allow a Condorcet loser to win. A Condorcet loser is a candidate who can be defeated in a head-to-head competition
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
against each other candidate. (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.)
A slightly weaker (easier to pass) version is the majority Condorcet loser criterion, which requires that a candidate who can be defeated by a majority in a head-to-head competition against each other candidate, lose. It is possible for a system, such as Majority Judgment, which allows voters not to state a preference between two candidates, to pass the MCLC but not the CLC.
Compliant methods include: two-round system
Two-round system
The two-round system is a voting system used to elect a single winner where the voter casts a single vote for their chosen candidate...
, instant-runoff voting
Instant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
, contingent vote
Contingent vote
The contingent vote is an electoral system used to elect a single winner, in which the voter ranks the candidates in order of preference. In an election, if no candidate receives an absolute majority of first preference votes, then all but the two leading candidates are eliminated and there is a...
, borda count
Borda count
The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
, Schulze method
Schulze method
The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners...
, and ranked pairs
Ranked Pairs
Ranked pairs or the Tideman method is a voting system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners....
.
Noncompliant methods include: plurality voting, supplementary voting, Sri Lankan contingent voting, approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
, range voting
Range voting
Range voting is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.A form of range voting was apparently used in...
, Bucklin voting
Bucklin voting
Bucklin voting is a class of voting systems that can be used for single-member and multi-member districts. It is named after its original promoter, James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system...
and minimax Condorcet
Minimax Condorcet
In voting systems, the Minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using preferential voting in a single-winner election...
.
Plurality voting system example
Here, Memphis has a plurality (42%) of the first preferences, so would be the winner under simple plurality voting. However, the majority (58%) of voters have Memphis as their fourth preference, and if two of the remaining three cities were not in the running to become the capital, Memphis would lose all of the contests 58–42. Hence, Memphis is the Condorcet loser.Ranked Pairs
Ranked Pairs work by "locking in" strong victories, starting with the strongest, unless that would contradict an earlier lock.Assume that the Condorcet loser is X. For X to win, Ranked Pairs must lock a preference of X over some other candidate Y (for at least one Y) before it locks Y over X. But since X is the Condorcet loser, the victory of Y over X will be greater than that of X over Y, and therefore Y over X will be locked first, no matter what other candidate Y is. Therefore X cannot win.