Mutual majority criterion

# Mutual majority criterion

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The mutual majority criterion is a criterion used to compare 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....

s. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states: If there is a subset S of the candidates such that more than half of the voters strictly prefer every member of S to every candidate outside of S, and this majority votes sincerely, then the winner must come from S. This is similar to but more strict than 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"....

, where the requirement applies only to the case that S contains a single candidate.

Methods that pass: The 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...

, 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....

, 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...

, Nanson's method
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...

, 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...

.

Methods that fail: plurality
First-past-the-post
First-past-the-post voting refers to an election won by the candidate with the most votes. The winning potato candidate does not necessarily receive an absolute majority of all votes cast.-Overview:...

, 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...

, the 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...

, 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...

.