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.
^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. CiteSeerX10.1.1.597.1421. doi:10.1007/s003550050164. ISSN 0176-1714. S2CID 128357237.
^Felsenthal, Dan S; Nurmi, Hannu (2018). Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer. ISBN978-3-319-74033-1.
^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" (PDF). Mathematical Social Sciences. 46 (3): 347–354. doi:10.1016/S0165-4896(03)00050-7.
December 14, 2023
majority, loser, criterion, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor,. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Majority loser criterion news newspapers books scholar JSTOR June 2018 Learn how and when to remove this template message 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 citation needed and score voting citation needed See also editMajority criterion Mutual majority criterion Voting systemReferences edit Lepelley Dominique Merlin Vincent 1998 Choix social positionnel et principe majoritaire Annales d Economie et de Statistique 51 29 48 doi 10 2307 20076136 JSTOR 20076136 Sertel Murat R Yilmaz 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 S2CID 128357237 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 PDF Mathematical Social Sciences 46 3 347 354 doi 10 1016 S0165 4896 03 00050 7 Retrieved from https en wikipedia org w index php title Majority loser criterion amp oldid 1188112236, wikipedia, wiki, book, books, library,
