Majority loser criterion: Difference between revisions
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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|jstor=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|journal=Social Choice and Welfare|language=en|volume=16|issue=4|pages=615–627|doi=10.1007/s003550050164|issn=0176-1714|citeseerx=10.1.1.597.1421}}</ref> 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|jstor=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|journal=Social Choice and Welfare|language=en|volume=16|issue=4|pages=615–627|doi=10.1007/s003550050164|issn=0176-1714|citeseerx=10.1.1.597.1421}}</ref><ref name="FelsenthalNurmi2018">{{cite book |last1=Felsenthal |first1=Dan S |last2=Nurmi |first2=Hannu |title=Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes |date=2018 |publisher=Springer |location=Cham, Switzerland |isbn=978-3-319-74033-1}}</ref><ref>{{Cite journal|title=Measuring Majority Power and Veto Power of Voting Rules|year=2020|doi=10.1007/s11127-019-00697-1|arxiv=1811.06739|last1=Kondratev|first1=Aleksei Y.|last2=Nesterov|first2=Alexander S.|journal=Public Choice|volume=183|issue=1–2|pages=187–210|s2cid=53670198}}</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|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|journal=Mathematical Social Sciences|volume=46|issue=3|pages=347–354|doi=10.1016/S0165-4896(03)00050-7}}</ref> but several non-positional rules, including many [[Condorcet method|Condorcet rules]], do satisfy both criteria. |
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|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|journal=Mathematical Social Sciences|volume=46|issue=3|pages=347–354|doi=10.1016/S0165-4896(03)00050-7}}</ref> but several non-positional rules, including many [[Condorcet method|Condorcet rules]], do satisfy both criteria. |
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Revision as of 00:57, 21 September 2020
 | This article needs additional citations for verification. (June 2018) |
The majority loser criterion is a criterion to evaluate single-winner voting systems.[1][2][3][4] 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,[5][6] but several non-positional rules, including many Condorcet rules, do satisfy both criteria.
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 score voting [citation needed].
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. JSTOR 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. CiteSeerX 10.1.1.597.1421. doi:10.1007/s003550050164. ISSN 0176-1714.
- ^ Felsenthal, Dan S; Nurmi, Hannu (2018). Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer. ISBN 978-3-319-74033-1.
- ^ Kondratev, Aleksei Y.; Nesterov, Alexander S. (2020). "Measuring Majority Power and Veto Power of Voting Rules". Public Choice. 183 (1–2): 187–210. arXiv:1811.06739. doi:10.1007/s11127-019-00697-1. S2CID 53670198.
- ^ 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.