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Majority: Difference between revisions
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*'''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 [[Center for Voting and Democracy|CVD]]'s talking points re: IRV: [http://www.fairvote.org/irv/talking.htm]). 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
*Criterion 1: If a majority of the electorate coordinates their efforts,
or that another given candidate is not elected.
*Criterion 2: [[Mutual majority criterion]]
*Criterion 3: [[Condorcet criterion]]
*Criterion 4: Minimal dominant set ([[Smith set|Smith]], GeTChA) efficiency
In
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 set]]s 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 [[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 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.
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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.
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[[Minimax]] (aka SD, PC, etc.), [[Nanson]], [[Black]], etc.
=== Criteria 1,2,3, and 4 - Strong Majority Rule Methods===
[[ranked pairs]], [[beatpath]], [[river]],
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