Majority loser criterion

# Majority loser criterion

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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.

Either of the Condorcet loser criterion
Condorcet loser criterion
In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....

or the mutual majority criterion
Mutual majority criterion
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion...

imply the majority loser criterion. However, the Condorcet criterion
Condorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...

does not imply the majority loser criterion. Neither does the majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....

imply the majority loser criterion.

Methods that comply with this criterion include Schulze
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...

, 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....

, Kemeny-Young
Kemeny-Young method
The Kemenyâ€“Young method is a voting system that uses preferential ballots and pairwise comparison counts to identify the most popular choices in an election...

, Nanson
Nanson's method
The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method.- Nanson method :The Nanson method is based on the original work of the mathematician Edward J...

, Baldwin, Coombs
Coombs' method
The Coombs' method is a voting system created by Clyde Coombs used for single-winner elections in which each voter rank the candidates in order of preference. It is very similar to instant-runoff voting , a more common preferential voting system.-Procedures:Each voter rank-orders all of the...

, Borda
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...

, Bucklin
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...

, 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 voting
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...

, and anti-plurality voting
Anti-plurality voting
Anti-plurality voting describes a voting method in which each voter votes against a single candidate, and the candidate with the fewest votes against wins. Anti-plurality voting is an example of a positional voting method.- An Example :...

.

Methods that do not comply with this criterion include plurality
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...

, MiniMax
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...

, Sri Lankan contingent voting, supplementary 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...

, and 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...

.