Majority
A majority means, literally, "more than half". Compare this with plurality, which means "the most of the group". When applied to specific situations, majority can take on different meanings, depending on how you apply it:
- relative majority usually means "plurality"
- simple majority means "more than half of cast votes"
- absolute majority means "more than half of eligible voters"
- a supermajority is a fraction of the voters between half and all (e.g. 2/3)
- consensus usually means complete agreement or "all voters"
Majority rule/Majority winner - Four Critera
Many methods claim to elect the "majority winner" or work by "majority rule" (See, for example, the CVD's talking points re: IRV: [1]). However, Condorcet's paradox raises an issue: with some groups of voters, no matter which candidate wins, some majority of the voters will prefer a different candidate. Below is a list of criterion, in ascending order of strictness, which could be used to rank the relative strengths of a "majority."
- Criterion 1: If a majority of the electorate coordinates their efforts, they can assure that a given candidate is elected, or that another given candidate is not elected.
- Criterion 2: Mutual majority criterion
- Criterion 3: Condorcet criterion
- Criterion 4: Minimal dominant set (Smith, GeTChA) efficiency
In pseudo-majority methods (like plurality and range voting), a given majority of the electorate can coordinate their intentions and decide the winner, but this merely postpones the question of how they do this. The stronger majority methods not only enable firmly coordinated majorities to assert themselves, but they allow un-coordinated majorities to reveal themselves, without any need for prior coordination. Voting methods that facilitate this process of revelation are considered superior to those that do not.
The remaining three categories allow mutual majorities to reveal themselves (in the absence of a self-defeating strategy by supporters of this majority). Strong majority rule methods not only reveal mutual majorities, but they reveal minimal dominant sets and Condorcet winners (in the absence of a severe burying strategy). This is considered especially valuable because it means revealing possible compromises on divisive issues, thus avoiding a lot of political polarization and strife.
Criterion 1 only - Pseudo-Majority Rule Methods
Methods which pass criterion 1 only include Plurality, Approval, Cardinal Ratings, and the Borda count. Although it is always possible in these systems for a coordinated majority to elect their preferred candidate, coordination may be difficult. For example, take an electorate with preferences as follows:
31 A > B > C * 29 B > A > C 20 C > B > A 20 C > A > B
In a plurality election, a clear majority (60-40) prefer both A and B to C. But unless A and B voters know whether to vote for A or whether to vote for B, C may win a plurality of votes. In addition, voters for A and B voters may play a game of "chicken", refusing to vote for the other, because they believe their candidate should win.
Criteria 1 and 2 - Weak Majority Rule Methods
Instant-runoff voting (aka IRV, Single-winner STV) passes the mutual majority criterion. In the example above, IRV enables A and B to coordinate. If all voters voted their sincere preferences, B would be eliminated first, but their votes would transfer to A, resulting in a majority for A.
However, IRV doesn't pass the Condorcet criterion. In an election with preferences as follows:
31 A > B > C 29 B > C > A 40 C > B > A
Looking at this election pairwise, there are three majorities: a majority (69 to 31) prefer B to A, a majority (69-31) prefer C to A, and a majority (60-40) prefer B to C. If you were to award the title "majority winner" to any candidate, B has the fairest claim to that title, as (different) majorities of voters prefer B to each other candidate. However, in IRV, B is eliminated first and does not win.
Criteria 1,2, and 3 - Intermediate Majority Rule Methods
Methods that pass the Condorcet criterion would always elect B, the Condorcet winner, in that election.
Minimax (aka SD, PC, etc.), Nanson, Black, etc.
Criteria 1,2,3, and 4 - Strong Majority Rule Methods
ranked pairs, beatpath, river,
Derived from an e-mail by James Green-Armytage