Difference between revisions of "Majority loser criterion"

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{{Wikipedia}}The '''majority loser criterion''' is a criterion to evaluate [[single-winner voting system]]s. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
 
{{Wikipedia}}The '''majority loser criterion''' is a criterion to evaluate [[single-winner voting system]]s. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
  
Either of the [[Condorcet loser criterion]] or the [[mutual majority criterion]] implies the majority loser criterion. However, the [[Condorcet criterion]] does not imply the majority loser criterion. Neither does the [[majority criterion]] imply the majority loser criterion.
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Either of the [[Condorcet loser criterion]] or the [[mutual majority criterion]] implies the majority loser criterion. However, the [[Condorcet criterion]] does not imply the majority loser criterion (though the [[Generalized Condorcet criterion]] does). Neither does the [[majority criterion]] imply the majority loser criterion (because the majority is only united in preferring any candidate over the majority loser; they may not necessarily have a single 1st choice candidate that must win).
  
 
Methods that comply with this criterion include [[Schulze method|Schulze]], [[ranked pairs]], [[Kemeny–Young method|Kemeny–Young]], [[Nanson's method|Nanson]], [[Baldwin's method|Baldwin]], [[Coombs' method|Coombs]], [[Borda count|Borda]], [[Bucklin voting|Bucklin]], [[instant-runoff voting]], [[contingent vote|contingent voting]], and [[anti-plurality voting]].
 
Methods that comply with this criterion include [[Schulze method|Schulze]], [[ranked pairs]], [[Kemeny–Young method|Kemeny–Young]], [[Nanson's method|Nanson]], [[Baldwin's method|Baldwin]], [[Coombs' method|Coombs]], [[Borda count|Borda]], [[Bucklin voting|Bucklin]], [[instant-runoff voting]], [[contingent vote|contingent voting]], and [[anti-plurality voting]].
  
 
Methods that do not comply with this criterion include [[Plurality voting system|plurality]], [[Minimax Condorcet|MiniMax]], [[Contingent vote#Sri Lankan contingent vote|Sri Lankan contingent voting]], [[Contingent vote#Supplementary vote|supplementary voting]], [[approval voting]], and [[range voting]].
 
Methods that do not comply with this criterion include [[Plurality voting system|plurality]], [[Minimax Condorcet|MiniMax]], [[Contingent vote#Sri Lankan contingent vote|Sri Lankan contingent voting]], [[Contingent vote#Supplementary vote|supplementary voting]], [[approval voting]], and [[range voting]].
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== Notes ==
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The majority loser criterion could be generalized into the mutual majority loser criterion: if a majority prefers any candidates other than those in a given set, then the candidates in the set must not win.
  
 
== See also ==
 
== See also ==

Latest revision as of 00:42, 17 April 2020

Wikipedia has an article on:

The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.

Either of the Condorcet loser criterion or the mutual majority criterion implies the majority loser criterion. However, the Condorcet criterion does not imply the majority loser criterion (though the Generalized Condorcet criterion does). Neither does the majority criterion imply the majority loser criterion (because the majority is only united in preferring any candidate over the majority loser; they may not necessarily have a single 1st choice candidate that must win).

Methods that comply with this criterion include Schulze, ranked pairs, Kemeny–Young, Nanson, Baldwin, Coombs, Borda, Bucklin, instant-runoff voting, contingent voting, and anti-plurality voting.

Methods that do not comply with this criterion include plurality, MiniMax, Sri Lankan contingent voting, supplementary voting, approval voting, and range voting.

Notes[edit | edit source]

The majority loser criterion could be generalized into the mutual majority loser criterion: if a majority prefers any candidates other than those in a given set, then the candidates in the set must not win.

See also[edit | edit source]

References[edit | edit source]