Majority criterion

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The majority criterion is a single-winner voting system criterion, used to compare these systems. The criterion says that "if one candidate is liked more by a majority (more than 50%) of voters than all other candidates, then that candidate must win".[1][2][3]

Some voting methods that pass this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, and plurality voting.

Supporters of other voting systems say that the majority criterion is actually bad, since it can lead to a tyranny of the majority where a candidate is elected who is loved by a little over half of the population and hated by everyone else.[4][5][6][7][8] Other systems may be better at electing consensus candidates who have broader support, which is argued to make them better representatives of the population as a whole.[9][10] These are described as "utilitarian" or "consensus-seeking" rather than "majoritarian".[11][12][13] Peter Emerson supports Borda count variants, and believes that majority rule is fundamentally flawed and leads to problems such as bitterness, division, and violence, citing Northern Ireland and Bosnia as examples.[14][15] Note however that in a utilitarian system, when no broadly supported candidate exists, that a minority can beat a majority because their candidate had slightly more support; because of this, utilitarian methods may not always increase consensus.

The mutual majority criterion is a more broad form of the majority criterion which allows a majority to prefer multiple candidates over all of the other candidates, rather than only one; voting methods which pass the majority criterion but fail mutual majority can encourage all but one of the majority's preferred candidates to exit the election so that one of the majority-preferred candidates wins, creating a spoiler effect. The common choose-one First-past-the-post voting method is notable for this, because major political parties often attempt to prevent more than one of their candidates from running and splitting the vote, by using primary elections.

Comparison with the Condorcet criterion[change | change source]

The majority criterion says that a candidate X should win if a majority of voters say "Yes" to the question 'Do you like X more than every other candidate?'.

The Condorcet criterion is stronger. It says that a candidate X should win if for every other candidate Y, more voters agree that they prefer X over Y than the number of voters who prefer Y to X.

Satisfaction of the Condorcet criterion implies that of the majority criterion, but not vice versa. With the Condorcet criterion there may be different majorities depending on who X and Y are, but the majority criterion only applies when there is a single majority which has X as their first choice, preferred over every other candidate.

(When saying that the Condorcet criterion is stronger than the majority criterion, the word criterion should be understood as a criterion that a voting system may or may not satisfy, not as a criterion that a candidate must pass in order to win the election.)

Related pages[change | change source]

  1. Mutual majority criterion
  2. Voting system
  3. Voting system criterion
  4. Condorcet criterion

References[change | change source]

  1. Rothe, Jörg (2015-08-18). Economics and Computation: An Introduction to Algorithmic Game Theory, Computational Social Choice, and Fair Division. Springer. p. 231. ISBN 9783662479049. A voting system satisfies the majority criterion if a candidate who is placed on top in more than half of the votes always is a winner of the election.
  2. Pennock, Ronald; Chapman, John W. (1977). Due Process: Nomos XVIII. NYU Press. p. 266. ISBN 9780814765692. if there is some single alternative which is ranked first by a majority of voters, we shall say there exists a majority will in favor of that alternative, according to the absolute majority (AM) criterion.
  3. "Single-winner Voting Method Comparison Chart". Archived from the original on 2011-02-28. Majority Favorite Criterion: If a majority (more than 50%) of voters prefer candidate A to all other candidates, then A should win.
  4. Smith, Warren D. "The "Majority criterion" and Range Voting". Retrieved 2016-12-03. However, in such a situation we would argue that it is good that Y won and it is good that range voting found a way to evade the "tyranny of the majority." Indeed this is an advantage of range voting that all other common voting method proposals cannot match.
  5. Sheldon-Hess, Dale (2012-03-15). "The Least of All Evils: The Tyranny of the Majority Weak Preferences". The Least of All Evils. Retrieved 2016-12-03. But you still want—no, you still need—a consensus result. The majority criterion is detrimental to that goal.
  6. Beatty, Harry (1973). "Voting Rules and Coordination Problems". The Methodological Unity of Science. Theory and Decision Library. Springer, Dordrecht. pp. 155–189. doi:10.1007/978-94-010-2667-3_9. ISBN 9789027704047. This is true even if the members of the majority are relatively indifferent among a, b and c while the members of the minority have an intense preference for b over a. So the objection can be made that plurality or majority voting allows a diffident majority to have its way against an intense minority.
  7. "Score Voting, Approval Voting, and Majority Rule". The Center for Election Science. 2015-05-21. Retrieved 2016-12-03. Score voting [and] approval voting, are sometimes attacked for not abiding by the majority criterion in all cases. ... This page shows that such an event with these methods is not catastrophic and may even be desirable.
  8. " - Lomax's criticism of Rob Richie's "proof" of the flawed nature of range voting and superiority of IRV". Retrieved 2016-12-03. Please give a cogent argument why the first preference of the majority should win. ... The "preference of a majority" can cause a civil war, if it neglects the needs of a minority.
  9. "Majority Criterion". The Center for Election Science. 2015-05-21. Retrieved 2016-12-03. Sometimes a candidate who is the Condorcet winner, or even the majority winner, isn’t the favored or “most representative” candidate of the electorate.
  10. Lippman, David. "Voting Theory" (PDF). Math in Society. Borda count is sometimes described as a consensus-based voting system, since it can sometimes choose a more broadly acceptable option over the one with majority support.
  11. "Utilitarian vs. Majoritarian Election Methods - The Center for Election Science". Retrieved 2017-01-07.
  12. "Vote Aggregation Methods". Retrieved 2017-01-12.
  13. Hillinger, Claude (2006-05-15). "The Case for Utilitarian Voting". Rochester, NY: Social Science Research Network. SSRN 878008. Cite journal requires |journal= (help)
  14. Emerson, Peter (2016). From Majority Rule to Inclusive Politics (1st ed.). Cham: Springer. ISBN 9783319235004. OCLC 948558369. Unfortunately, one of the worst democratic structures is the most ubiquitous: majority rule based on majority voting. It must be emphasised, furthermore, that these two practices are often the catalysts of division and bitterness, if not indeed violence and war.
  15. Emerson, Peter (2016-03-23). "Majority Rule - A Cause of War?". In Gardner, Hall; Kobtzeff, Oleg (eds.). The Ashgate Research Companion to War: Origins and Prevention. Routledge. ISBN 9781317041108.