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Majority: Difference between revisions
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== Majority rule/Majority winner ==
Many methods claim to elect the "majority winner" or work by "majority rule".
*Criterion 1: If a majority of the electorate coordinates their efforts, they can assure
*Criterion 2: [[Mutual majority criterion]]
*Criterion 3: [[Condorcet criterion]]
*Criterion 4: Minimal dominant set ([[Smith set|Smith]], GeTChA) efficiency
* Intermediate majority rule methods: [[Minimax]] (aka SD, PC, etc.), [[Nanson]], [[Black]], etc.▼
* Strong majority rule methods: [[ranked pairs]], [[beatpath]], [[river]], ▼
In pseudomajority 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 majorities to '''reveal''' themselves, without any need for prior coordination. I think that voting methods that facilitate this process of revelation are superior to those that do not.
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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). 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 especially valuable because it means revealing possible compromises on divisive issues, thus avoiding a lot of political polarization and strife.
=== Criterion 1 only ===
''Derived from an e-mail by James Green-Armytage''▼
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, the coordination problem can 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 ==
[[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===
Methods that pass the Condorcet criterion would always elect B, the Condorcet winner, in that election.
=== Criteria 1,2,3, and 4 ===
▲''Derived from an e-mail by James Green-Armytage''
[[Category:Voting theory]]
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