Majority loser criterion: Difference between revisions
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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. |
The '''majority loser criterion''' is a criterion to evaluate [[single-winner voting system]]s.<ref>{{Cite journal|last=Lepelley|first=Dominique|last2=Merlin|first2=Vincent|date=1998|title=Choix social positionnel et principe majoritaire|url=http://www.jstor.org/stable/20076136|journal=Annales d'Économie et de Statistique|issue=51|pages=29–48|doi=10.2307/20076136}}</ref><ref>{{Cite journal|last=Sertel|first=Murat R.|last2=Yılmaz|first2=Bilge|date=1999-09-01|title=The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable|url=https://link.springer.com/article/10.1007/s003550050164|journal=Social Choice and Welfare|language=en|volume=16|issue=4|pages=615–627|doi=10.1007/s003550050164|issn=0176-1714}}</ref> The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win. |
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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, since the [[Minimax Condorcet|minimax method]] satisfies the Condorcet but not the majority loser criterion. Also, the [[majority criterion]] is logically independent from the majority loser criterion, since the [[Plurality voting|plurality]] rule satisfies the majority but not the majority loser criterion, and the [[Anti-plurality voting|anti-plurality]] rule satisfies the majority loser but not the majority criterion. There is no [[Positional voting|positional scoring rule]] which satisfies both the majority and the majority loser criterion. <ref>{{Cite journal|last=Sanver|first=M. Remzi|date=2002-03-01|title=Scoring rules cannot respect majority in choice and elimination simultaneously|url=http://www.sciencedirect.com/science/article/pii/S0165489601000877|journal=Mathematical Social Sciences|volume=43|issue=2|pages=151–155|doi=10.1016/S0165-4896(01)00087-7}}</ref><ref>{{Cite journal|last=Woeginger|first=Gerhard J.|date=December 2003|title=A note on scoring rules that respect majority in choice and elimination|url=http://www.sciencedirect.com/science/article/pii/S0165489603000507|journal=Mathematical Social Sciences|volume=46|issue=3|pages=347–354|doi=10.1016/S0165-4896(03)00050-7}}</ref> |
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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. Neither does the [[majority criterion]] imply the majority loser criterion. |
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Methods that comply with this criterion include [[Schulze method|Schulze]], [[ranked pairs]], [[Kemeny–Young method|Kemeny–Young]], [[Nanson's method|Nanson]], [[Nanson's method#Baldwin 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]], [[Nanson's method#Baldwin method|Baldwin]], [[Coombs' method|Coombs]], [[Borda count|Borda]], [[Bucklin voting|Bucklin]], [[instant-runoff voting]], [[contingent vote|contingent voting]], and [[anti-plurality voting]]. |
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Methods that do not comply with this criterion include [[Plurality voting system|plurality]], [[Minimax Condorcet| |
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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== See also == |
== See also == |
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Revision as of 09:28, 18 June 2017
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The majority loser criterion is a criterion to evaluate single-winner voting systems.[1][2] 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, since the minimax method satisfies the Condorcet but not the majority loser criterion. Also, the majority criterion is logically independent from the majority loser criterion, since the plurality rule satisfies the majority but not the majority loser criterion, and the anti-plurality rule satisfies the majority loser but not the majority criterion. There is no positional scoring rule which satisfies both the majority and the majority loser criterion. [3][4]
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.
See also
References
- ^ Lepelley, Dominique; Merlin, Vincent (1998). "Choix social positionnel et principe majoritaire". Annales d'Économie et de Statistique (51): 29–48. doi:10.2307/20076136.
- ^ Sertel, Murat R.; Yılmaz, Bilge (1999-09-01). "The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable". Social Choice and Welfare. 16 (4): 615–627. doi:10.1007/s003550050164. ISSN 0176-1714.
- ^ Sanver, M. Remzi (2002-03-01). "Scoring rules cannot respect majority in choice and elimination simultaneously". Mathematical Social Sciences. 43 (2): 151–155. doi:10.1016/S0165-4896(01)00087-7.
- ^ Woeginger, Gerhard J. (December 2003). "A note on scoring rules that respect majority in choice and elimination". Mathematical Social Sciences. 46 (3): 347–354. doi:10.1016/S0165-4896(03)00050-7.