Majority loser criterion explained

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.

See also

• Majority criterion
• Mutual majority criterion
• Voting system

Notes and References

1. Lepelley. Dominique. Merlin. Vincent. 1998. Choix social positionnel et principe majoritaire. 20076136. Annales d'Économie et de Statistique. 51. 29–48. 10.2307/20076136.
2. Sertel. Murat R.. Yılmaz. Bilge. 1999-09-01. The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable. Social Choice and Welfare. en. 16. 4. 615–627. 10.1007/s003550050164. 0176-1714. 10.1.1.597.1421. 128357237 .
3. Book: Felsenthal . Dan S . Nurmi . Hannu . Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes . 2018 . Springer . Cham, Switzerland . 978-3-319-74033-1.
4. Measuring Majority Power and Veto Power of Voting Rules. 2020. 10.1007/s11127-019-00697-1. 1811.06739. Kondratev. Aleksei Y.. Nesterov. Alexander S.. Public Choice. 183. 1–2. 187–210. 53670198.
5. Sanver. M. Remzi. 2002-03-01. Scoring rules cannot respect majority in choice and elimination simultaneously. Mathematical Social Sciences. 43. 2. 151–155. 10.1016/S0165-4896(01)00087-7.
6. Woeginger. Gerhard J.. December 2003. A note on scoring rules that respect majority in choice and elimination. Mathematical Social Sciences. 46. 3. 347–354. 10.1016/S0165-4896(03)00050-7.