Majority: Difference between revisions

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*'''relative majority''' usually means "plurality"

*'''simple majority''' means "more than half of cast votes"

*'''absolute majority''' means "more than half of eligible voters"

*'''[[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"

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The remaining three categories allow mutual majorities to reveal themselves (in the absence of a self-defeating strategy by supporters of this majority, or something like a [[chicken dilemma]]). Strong majority rule methods not only reveal mutual majorities, but they reveal [[minimal dominant set]]s and [[Condorcet winner|Condorcet winners]] (in the absence of a severe [[Burying|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===

==== Criterion 1 only - Pseudo-Majority Rule Methods====

Methods which pass criterion 1 only include [[First-past-the-post electoral system|Plurality]], [[approval voting|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:

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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 may play a game of "[[Chicken dilemma|chicken]]", refusing to vote for the other, because they believe their candidate should win.

===Criteria 1 and 2 - Weak Majority Rule Methods===

====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.

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Looking at this election [[Pairwise counting|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===

==== 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.

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[[Minmax|Minimax]] (aka Simpson-Kramer, PC, etc.), [[Nanson]], [[Black]], etc.

=== Criteria 1,2,3, and 4 - Strong Majority Rule Methods===

==== Criteria 1,2,3, and 4 - Strong Majority Rule Methods====

[[Ranked pairs]], [[Schulze method|Schulze]], [[River]],

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''Derived from an e-mail by James Green-Armytage''

=== Criticism of this scheme ===

==== Criticism of this scheme ====

While criteria 2-4 above are popular, only criterion 2 (the [[Majority criterion for solid coalitions]] a.k.a. the [[Mutual majority criterion]]) deals with "majority" in the sense of "more than half of the voters," and even this criterion applies only in the peculiar special case that more than half of the voters rank the same set of candidates uninterrupted, in some order, in the top positions of the ballot.