Majority criterion: Difference between revisions
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{{wikipedia|Majority criterion}} |
{{wikipedia|Majority favorite criterion}} |
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The '''majority criterion''' is a criterion for evaluating [[voting system]]s. |
The '''majority favorite criterion''' is a criterion for evaluating [[voting system]]s. It can be most simply thought of as "if a candidate would get >50% of the [[FPP]] vote, that candidate should win". In other words, if a majority selects a candidate as their unique 1st choice, this candidate must win. |
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It can be stated as follows: |
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{{definition|If a majority of the voters endorse a given candidate X more than any other candidate, then X must win.}} |
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Or in plain English as |
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{{Definition| If one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win}} |
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<br /> |
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== Example == |
== Example == |
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The [[mutual majority criterion]], which is sometimes simply called the majority criterion, generalizes the constraint to sets of candidates. |
The [[mutual majority criterion]], which is sometimes simply called the majority criterion, generalizes the constraint to sets of candidates. |
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The [[Condorcet criterion]] implies the majority criterion. |
The [[Condorcet criterion]] implies the majority criterion. |
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=== Weaker forms of the criterion === |
=== Weaker forms of the criterion === |
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The difference between the two versions can be seen with this example:<blockquote>51 A:1 |
The difference between the two versions can be seen with this example:<blockquote>51 A:1 |
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49 B:5</blockquote>If the highest score is a 5, then the majority criterion for rated ballots allows either A or B to win. This is in contrast to the regular majority criterion, which requires A to win. Arguably, the majority criterion for rated ballots is more appropriate in the context of rated ballots, since a voter who doesn't give their 1st choice a perfect score is essentially choosing not to use all of their voting power, and thus their preference need not be (or even perhaps, shouldn't) be maximally respected or enforced. |
49 B:5</blockquote>If the highest score is a 5, then the majority criterion for rated ballots allows either A or B to win. This is in contrast to the regular majority criterion, which requires A to win. Arguably, the majority criterion for rated ballots is more appropriate in the context of rated ballots, since a voter who doesn't give their 1st choice a perfect score is essentially choosing not to use all of their voting power, and thus their preference need not be (or even perhaps, shouldn't) be maximally respected or enforced. |
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== Notes == |
== Notes == |
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=== Independence of irrelevant alternatives === |
=== Independence of irrelevant alternatives === |
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The majority criterion implies failure of the [[Independence of irrelevant alternatives]] criterion; see the [[Condorcet paradox]] for an example. |
The majority criterion implies failure of the [[Independence of irrelevant alternatives]] criterion; see the [[Condorcet paradox]] for an example. |
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== Majority rule as an approximation of utilitarianism == |
== Majority rule as an approximation of utilitarianism == |
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