In an election, a candidate is called a Condorcet (English: /kɒndɔːrˈseɪ/), beats-all, or majority-rule winner[1][2][3] when a majority of voters support them against any other candidate. Such a candidate is also called an undefeated or tournament champion (by analogy with round-robin tournaments). Voting systems where a majority-rule winner will always win the election are said to satisfy the majority-rule principle, also known as the Condorcet criterion. Condorcet voting methods extend majority rule to elections with more than one candidate.
Surprisingly, an election may not have a beats-all winner, because there can be a rock, paper, scissors-style cycle, where multiple candidates all defeat each other (Rock < Paper < Scissors < Rock). This is called Condorcet's voting paradox.[4] When there is no single best candidate, tournament solutions (like ranked pairs) choose the candidate closest to being an majority winner.
If voters are arranged on a left-right political spectrum and prefer candidates who are more similar to themselves, a majority-rule winner always exists, and is also the candidate whose ideology is most representative of the electorate. This result is known as the median voter theorem.[5] While political candidates differ in ways other than left-right ideology, which can lead to voting paradoxes,[6][7] such cases tend to be rare in practice.[8]
^Brandl, Florian; Brandt, Felix; Seedig, Hans Georg (2016). "Consistent Probabilistic Social Choice". Econometrica. 84 (5): 1839–1880. arXiv:1503.00694. doi:10.3982/ECTA13337. ISSN 0012-9682.
^Sen, Amartya (2020). "Majority decision and Condorcet winners". Social Choice and Welfare. 54 (2/3): 211–217. doi:10.1007/s00355-020-01244-4. ISSN 0176-1714. JSTOR 45286016.
^Lewyn, Michael (2012), Two Cheers for Instant Runoff Voting (SSRN Scholarly Paper), Rochester, NY, retrieved 2024-04-21{{citation}}: CS1 maint: location missing publisher (link)
^Fishburn, Peter C. (1977). "Condorcet Social Choice Functions". SIAM Journal on Applied Mathematics. 33 (3): 469–489. doi:10.1137/0133030. ISSN 0036-1399.
^Black, Duncan (1948). "On the Rationale of Group Decision-making". The Journal of Political Economy. 56 (1): 23–34. doi:10.1086/256633. JSTOR 1825026. S2CID 153953456.
^Alós-Ferrer, Carlos; Granić, Đura-Georg (2015-09-01). "Political space representations with approval data". Electoral Studies. 39: 56–71. doi:10.1016/j.electstud.2015.04.003. hdl:1765/111247. The analysis reveals that the underlying political landscapes ... are inherently multidimensional and cannot be reduced to a single left-right dimension, or even to a two-dimensional space.
^Black, Duncan; Newing, R.A. (2013-03-09). McLean, Iain S. [in Welsh]; McMillan, Alistair; Monroe, Burt L. (eds.). The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing. Springer Science & Business Media. ISBN 9789401148603. For instance, if preferences are distributed spatially, there need only be two or more dimensions to the alternative space for cyclic preferences to be almost inevitable
^Van Deemen, Adrian (2014-03-01). "On the empirical relevance of Condorcet's paradox". Public Choice. 158 (3): 311–330. doi:10.1007/s11127-013-0133-3. ISSN 1573-7101.
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majority-rule winner will always win the election are said to satisfy the majority-rule principle, also known as the Condorcetcriterion. Condorcet voting methods...
have the Condorcetwinner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcetwinner, and is thus...
satisfies the Smith criterion if it always elects a candidate from the Smith set, which generalizes the idea of a "Condorcetwinner" to cases where there...
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majority loser criterion but does not imply the Condorcetwinnercriterion. A voting system complying with the Condorcet loser criterion will never allow...
systems, the Minimax Condorcet method is a single-winner ranked-choice voting method that always elects the majority (Condorcet) winner. Minimax compares...
with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, plurality voting, and approval voting. The criterion was originally...
Certain conditions weaker than the participation criterion are also incompatible with the Condorcetcriterion. For example, weak positive involvement requires...
one exists, is known as Condorcet consistent or as satisfying the Condorcetcriterion. Such systems are referred to as Condorcet methods. However, in elections...
proportionality criterion. All Smith-efficient Condorcet methods pass the mutual majority criterion. Methods which pass mutual majority but fail the Condorcet criterion...
Either of the Condorcet loser criterion or the mutual majority criterion implies the majority loser criterion. However, the Condorcetcriterion does not imply...
Smith set. ISDA implies the Condorcetcriterion. The following table compares ranked pairs with other preferential single-winner election methods: Rather...
losing in a head-to-head matchup with Democrat Andy Montroll (the Condorcetwinner). However, if Kiss had gained more support from Wright voters, Kiss...
single winner ranked-choice voting rule developed by Markus Schulze. It is also known as the beatpath method. The Schulze method is a Condorcet method...
utility or benefit, and j represents the player. Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known...
the winner must not change due to the addition of a non-winning candidate who is similar to a candidate already present. It is a relative criterion: it...
fails to satisfy the Condorcetcriterion and can elect a Condorcet loser. Strategic Approval can guarantee electing the Condorcetwinner in some special circumstances...
voters and perfect information the Condorcetwinner is a Nash equilibrium. It does not satisfy the later-no-harm criterion, meaning that giving a positive...
perhaps less-understood systems such as approval voting, score voting and Condorcet methods. This is when a voter decides to vote in a way that does not represent...
the Condorcetwinner to cases where no such winner exists, by allowing cycles of candidates to be treated jointly as if they were a single Condorcet winner...
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