The majority criterion is a voting system criterion, used to objectively compare voting systems. The criterion states that if a majority of voters strictly prefers a given candidate to every other candidate (i.e. the given candidate is the first preference of more than half the voters) and they vote sincerely, then that candidate should win. A voting system criterion is a formally defined pass/fail criterion by which a voting system may be assessed. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ...

Condorcet methods (such as the Schulze method and Ranked Pairs), plurality voting, instant-runoff voting, and Bucklin voting comply with the majority criterion, while the Borda count does not. Additionally, methods that do not use a ranked ballot, such as Approval voting and range voting, cannot satisfy it. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... The first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ... Example ballot Instant-runoff voting (IRV) (also known as the Alternative Vote (AV) and by several other names) is an voting system used for single winner elections in which voters rank candidates in order of preference. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, average voting, cardinal ratings, 0–99 voting, or the score system or point system) is a theoretical voting system for single-seat elections in which voters score each candidate, the scores are added up, and the candidate with the highest score wins. ...

Difference to the Condorcet criterion

By the majority criterion, a candidate X should win if a majority of voters answers affirmatively to the question 'Do you prefer X to every other candidate?'.

Condorcet criterion is stronger. According to it, a candidate X should win if for every other candidate Y there is a majority of voters that answers affirmatively to the question 'Do you prefer X to Y?'. The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

Condorcet criterion implies majority criterion, but not vice versa. In the Condorcet criterion the individuals comprising the majorities of voters answering affirmatively may vary according to Y, but the majority criterion requires a single majority which has X as their first choice, preferred to every other candidate.

Examples of failure of the majority criterion

Approval voting

For example 55 voters prefer 3 candidates in the order A>B>C, 35 voters prefer the candidates in the order B>C>A and 10 voters prefer the candidates in the order C>B>A. The 35 B>C>A voters approve only candidate B, the 10 C>B>A voters approve candidates C and B, 35 of the A>B>C voters approve only candidate A and 20 of the A>B>C voters approve both candidates A and B.

A majority of the voters prefer candidate A to all other candidates but candidate B wins.

Borda count

For example 100 voters cast the following votes:

A has 110 Borda points (55 x 2 + 35 x 0 + 10 x 0). B has 135 Borda points (55 x 1 + 35 x 2 + 10 x 1). C has 55 Borda points (55 x 0 + 35 x1 + 10 x 2).

Candidate A is the first choice of a majority of voters but candidate B wins the election.

See also

• Mutual majority criterion
• Voting system
• Voting system criterion
• Condorcet criterion

The mutual majority criterion is a criterion used to compare voting systems. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... A voting system criterion is a formally defined pass/fail criterion by which a voting system may be assessed. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

External links

• Election method criteria at condorcet.org
• Voting definitions and criteria