Majority loser criterion

Electoral voting system criterion

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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

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* Majority criterion
* Mutual majority criterion
* Voting system

## References

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1. ^ 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.
2. ^ 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. S2CID 128357237.
3. ^ 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.
4. ^ 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.
5. ^ 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.
6. ^ 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.

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Electoral systems

Part of the politics and Economics series

Single-winner|

* Approval voting
* Combined approval voting
* Unified primary
* Borda count
* Bucklin voting
* Condorcet methods
* Copeland's method
* Dodgson's method
* Kemeny–Young method
* Minimax Condorcet method
* Nanson's method
* Ranked pairs
* Schulze method
* Exhaustive ballot
* First-past-the-post voting
* Instant-runoff voting
* Coombs' method
* Contingent vote
* Supplementary vote
* Simple majoritarianism
* Plurality
* Positional voting system
* Score voting
* STAR voting
* Two-round system
* Graduated majority judgment

Proportional|

| Systems|

* Dual member
* Mixed-member (Additional member)
* Mixed single vote
* Party-list
* Proportional approval voting
* Rural–urban
* Sequential proportional approval voting
* Single transferable vote
* CPO-STV
* Hare-Clark
* Schulze STV
* Spare vote
* Indirect single transferable voting

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Allocation|

* Highest averages method
* Webster/Sainte-Laguë
* D'Hondt
* Largest remainders method

Quotas|

* Droop quota
* Hagenbach-Bischoff quota
* Hare quota
* Imperiali quota

Mixed|

* Parallel voting
* MMP
* Additional member system
* Alternative vote plus
* Mixed single vote
* Mixed ballot transferable vote
* Scorporo

Semi-proportional|

* Single non-transferable vote
* Limited voting
* Cumulative voting
* Satisfaction approval voting

Criteria|

* Condorcet winner criterion
* Condorcet loser criterion
* Consistency criterion
* Independence of clones
* Independence of irrelevant alternatives
* Independence of Smith-dominated alternatives
* Later-no-harm criterion
* Majority criterion
* Majority loser criterion
* Monotonicity criterion
* Mutual majority criterion
* Participation criterion
* Plurality criterion
* Resolvability criterion
* Reversal symmetry
* Smith criterion
* Seats-to-votes ratio

Other|

* Ballot
* Election threshold
* First-preference votes
* Liquid democracy
* Spoilt vote
* Sortition
* Unseating

Comparison|

* Comparison of voting systems
* Voting systems by country

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