Condorcet method (English Wikipedia)

Nanson, E. J. (1882). "Methods of election". Transactions and Proceedings of the Royal Society of Victoria. 19: 207–208. although Ware's method cannot return the worst, it may return the next worst.
Nanson, E. J. (1882). "Methods of election". Transactions and Proceedings of the Royal Society of Victoria. 19: 217.

archives-ouvertes.fr (Global: 1,143^rd place; English: 973^rd place)

halshs.archives-ouvertes.fr

Igersheim, Herrade; Durand, François; Hamlin, Aaron; Laslier, Jean-François (January 2022). "Comparing voting methods: 2016 US presidential election". European Journal of Political Economy. 71 102057. doi:10.1016/j.ejpoleco.2021.102057.

arxiv.org (Global: 49^th place; English: 31^st place)

Darlington, Richard B. (2018). "Are Condorcet and minimax voting systems the best?". arXiv:1807.01366 [physics.soc-ph]. CC [Condorcet] systems typically allow tied ranks. If a voter fails to rank a candidate, they are typically presumed to rank them below anyone whom they did rank explicitly.
Schulze, Markus (2018). "The Schulze Method of Voting". p. 351. arXiv:1804.02973 [cs.GT]. The Condorcet criterion for single-winner elections (section 4.7) is important because, when there is a Condorcet winner b ∈ A, then it is still a Condorcet winner when alternatives a1,...,an ∈ A \ {b} are removed. So an alternative b ∈ A doesn't owe his property of being a Condorcet winner to the presence of some other alternatives. Therefore, when we declare a Condorcet winner b ∈ A elected whenever a Condorcet winner exists, we know that no other alternatives a1,...,an ∈ A \ {b} have changed the result of the election without being elected.

books.google.com (Global: 3^rd place; English: 3^rd place)

Hazewinkel, Michiel (2007-11-23). Encyclopaedia of Mathematics, Supplement III. Springer Science & Business Media. ISBN 978-0-306-48373-8. Briefly, one can say candidate A defeats candidate B if a majority of the voters prefer A to B. With only two candidates [...] barring ties [...] one of the two candidates will defeat the other.
Mackie, Gerry. (2003). Democracy defended. Cambridge, UK: Cambridge University Press. p. 6. ISBN 0511062648. OCLC 252507400.

cmu.edu (Global: 2,125^th place; English: 1,347^th place)

cs.cmu.edu

Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.

core.ac.uk (Global: 1,383^rd place; English: 954^th place)

Truchon, Michel (October 1998). "AN EXTENSION OF THE CONDORCET CRITERION AND KEMENY ORDERS" (PDF). A first objective of this paper is to propose a formalization of this idea, called the Extended Condorcet Criterion (XCC). In essence, it says that if the set of alternatives can be partitioned in such a way that all members of a subset of this partition defeat all alternatives belonging to subsets with a higher index, then the former should obtain a better rank than the latter.

doi.org (Global: 2^nd place; English: 2^nd place)

doi.org

Gehrlein, William V.; Valognes, Fabrice (2001). "Condorcet efficiency: A preference for indifference". Social Choice and Welfare. 18: 193–205. doi:10.1007/s003550000071. S2CID 10493112. The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections.
Tideman, T. Nicolaus; Plassmann, Florenz (2011). "Modeling the Outcomes of Vote-Casting in Actual Elections". SSRN Electronic Journal. doi:10.2139/ssrn.1627787. ISSN 1556-5068. A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.
Wallis, W. D. (2014). "Simple Elections II: Condorcet's Method". The Mathematics of Elections and Voting. Springer. pp. 19–32. doi:10.1007/978-3-319-09810-4_3. ISBN 978-3-319-09809-8.
Gehrlein, William V.; Fishburn, Peter C. (1976). "Condorcet's Paradox and Anonymous Preference Profiles". Public Choice. 26: 1–18. doi:10.1007/BF01725789. JSTOR 30022874?seq=1. S2CID 153482816. Condorcet's paradox[6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
Pivato, Marcus (2015). "Condorcet meets Bentham". Journal of Mathematical Economics. 59: 58–65. doi:10.1016/j.jmateco.2015.04.006.
Lehtinen, Aki (2007). "The Welfare Consequences of Strategic Voting in Two Commonly Used Parliamentary Agendas". Theory and Decision. 63 (1): 1–40. doi:10.1007/s11238-007-9028-4. S2CID 153595828.
Colomer, Josep (2013). "Ramon Llull: From Ars Electionis to Social Choice Theory". Social Choice and Welfare. 40 (2): 317–328. doi:10.1007/s00355-011-0598-2. hdl:10261/125715. S2CID 43015882.
McLean, Iain; Urken, Arnold B. (1992). "Did Jefferson or Madison understand Condorcet's theory of social choice?". Public Choice. 73 (4): 445–457. doi:10.1007/BF01789561. S2CID 145167169. Binary procedures of the Jefferson/Robert variety will select the Condorcet winner if one exists
Wallis, W. D. (2014). "Simple Elections II: Condorcet's Method". The Mathematics of Elections and Voting. Springer. pp. 19–32. doi:10.1007/978-3-319-09810-4_3. ISBN 978-3-319-09809-8.
Igersheim, Herrade; Durand, François; Hamlin, Aaron; Laslier, Jean-François (January 2022). "Comparing voting methods: 2016 US presidential election". European Journal of Political Economy. 71 102057. doi:10.1016/j.ejpoleco.2021.102057.
Nurmi, Hannu (2012), "On the Relevance of Theoretical Results to Voting System Choice", in Felsenthal, Dan S.; Machover, Moshé (eds.), Electoral Systems, Studies in Choice and Welfare, Springer Berlin Heidelberg, pp. 255–274, doi:10.1007/978-3-642-20441-8_10, ISBN 9783642204401, S2CID 12562825
Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.
Barberà, Salvador; Bossert, Walter (2025-04-01). "Intermediate Condorcet Winners and Losers". Journal of Public Economic Theory. 27 (2). doi:10.1111/jpet.70024. ISSN 1097-3923. A candidate $x\in S$ is a strong Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)>p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a strong Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed. … A candidate $x\in S$ is a weak Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)\geq p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a weak Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed.
Felsenthal, Dan S.; Tideman, Nicolaus (2014). "Weak Condorcet winner(s) revisited". Public Choice. 160 (3–4): 313–326. doi:10.1007/s11127-014-0180-4. S2CID 154447142. A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW [Condorcet winner].

dx.doi.org

Tideman, T. Nicolaus; Plassmann, Florenz (2011). "Modeling the Outcomes of Vote-Casting in Actual Elections". SSRN Electronic Journal. doi:10.2139/ssrn.1627787. ISSN 1556-5068. A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.

electowiki.org (Global: low place; English: low place)

"Smith Score - electowiki". electowiki.org. Retrieved 2024-12-14.

elekto.dev (Global: low place; English: low place)

"Goldydocs". Elekto. Retrieved 2024-12-14.

equal.vote (Global: low place; English: low place)

"Condorcet". Equal Vote Coalition. Retrieved 2021-04-25.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Colomer, Josep (2013). "Ramon Llull: From Ars Electionis to Social Choice Theory". Social Choice and Welfare. 40 (2): 317–328. doi:10.1007/s00355-011-0598-2. hdl:10261/125715. S2CID 43015882.

jstor.org (Global: 23^rd place; English: 15^th place)

Gehrlein, William V.; Fishburn, Peter C. (1976). "Condorcet's Paradox and Anonymous Preference Profiles". Public Choice. 26: 1–18. doi:10.1007/BF01725789. JSTOR 30022874?seq=1. S2CID 153482816. Condorcet's paradox[6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.

liquidfeedback.org (Global: low place; English: low place)

principles.liquidfeedback.org

Behrens, Jan; Kistner, Axel; Nitsche, Andreas; Swierczek, Bjorn (2014). "The Principles of Liquid Feedback" (PDF) (1 ed.).

lpwa.org (Global: low place; English: low place)

"Constitution of the Libertarian Party of Washington State" (PDF). Libertarian Party of Washington. March 26, 2022. p. 10. Archived (PDF) from the original on 2022-09-14. then the vote shall be performed using either a Condorcet voting system or a score voting system, as the participants shall decide

mcdougall.org.uk (Global: low place; English: low place)

Woodall, D R. "Properties of Preferential Election Rules". Voting Matters (3): 8–15. Retrieved 2024-12-14.

meta.wikimedia.org (Global: 2,774^th place; English: 6,614^th place)

"Wikimedia Foundation elections 2013/Results – Meta". meta.wikimedia.org. Retrieved 2017-01-23.

natlib.govt.nz (Global: 785^th place; English: 374^th place)

rsnz.natlib.govt.nz

Hogben, G. (1913). "Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes". Transactions and Proceedings of the Royal Society of New Zealand. 46: 304–308.

ox.ac.uk (Global: 541^st place; English: 356^th place)

nuff.ox.ac.uk

McLean (2002), Australian electoral reform and two concepts of representation (PDF) (paper), UK: Ox, retrieved 2015-06-27

researchgate.net (Global: 96^th place; English: 89^th place)

Colomer, Josep (2013). "Ramon Llull: From Ars Electionis to Social Choice Theory". Social Choice and Welfare. 40 (2): 317–328. doi:10.1007/s00355-011-0598-2. hdl:10261/125715. S2CID 43015882.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Gehrlein, William V.; Valognes, Fabrice (2001). "Condorcet efficiency: A preference for indifference". Social Choice and Welfare. 18: 193–205. doi:10.1007/s003550000071. S2CID 10493112. The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections.
Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.
Gehrlein, William V.; Fishburn, Peter C. (1976). "Condorcet's Paradox and Anonymous Preference Profiles". Public Choice. 26: 1–18. doi:10.1007/BF01725789. JSTOR 30022874?seq=1. S2CID 153482816. Condorcet's paradox[6] of simple majority voting occurs in a voting situation [...] if for every alternative there is a second alternative which more voters prefer to the first alternative than conversely.
Lehtinen, Aki (2007). "The Welfare Consequences of Strategic Voting in Two Commonly Used Parliamentary Agendas". Theory and Decision. 63 (1): 1–40. doi:10.1007/s11238-007-9028-4. S2CID 153595828.
Colomer, Josep (2013). "Ramon Llull: From Ars Electionis to Social Choice Theory". Social Choice and Welfare. 40 (2): 317–328. doi:10.1007/s00355-011-0598-2. hdl:10261/125715. S2CID 43015882.
McLean, Iain; Urken, Arnold B. (1992). "Did Jefferson or Madison understand Condorcet's theory of social choice?". Public Choice. 73 (4): 445–457. doi:10.1007/BF01789561. S2CID 145167169. Binary procedures of the Jefferson/Robert variety will select the Condorcet winner if one exists
Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.
Nurmi, Hannu (2012), "On the Relevance of Theoretical Results to Voting System Choice", in Felsenthal, Dan S.; Machover, Moshé (eds.), Electoral Systems, Studies in Choice and Welfare, Springer Berlin Heidelberg, pp. 255–274, doi:10.1007/978-3-642-20441-8_10, ISBN 9783642204401, S2CID 12562825
Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.
Felsenthal, Dan S.; Tideman, Nicolaus (2014). "Weak Condorcet winner(s) revisited". Public Choice. 160 (3–4): 313–326. doi:10.1007/s11127-014-0180-4. S2CID 154447142. A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW [Condorcet winner].
Green-Armytage, James. "Why majoritarian election methods should be Condorcet-efficient". Economics. S2CID 18348996.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Wallis, W. D. (2014). "Simple Elections II: Condorcet's Method". The Mathematics of Elections and Voting. Springer. pp. 19–32. doi:10.1007/978-3-319-09810-4_3. ISBN 978-3-319-09809-8.
Wallis, W. D. (2014). "Simple Elections II: Condorcet's Method". The Mathematics of Elections and Voting. Springer. pp. 19–32. doi:10.1007/978-3-319-09810-4_3. ISBN 978-3-319-09809-8.

stanford.edu (Global: 194^th place; English: 182^nd place)

plato.stanford.edu

Pacuit, Eric (2019), "Voting Methods", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Fall 2019 ed.), Metaphysics Research Lab, Stanford University, retrieved 2020-10-16

uni-augsburg.de (Global: low place; English: low place)

math.uni-augsburg.de

G. Hägele and F. Pukelsheim (2001). "Llull's writings on electoral systems". Studia Lulliana. 41: 3–38. Archived from the original on 2006-02-07.

usenet.org.uk (Global: low place; English: low place)

"Guidelines for Group Creation for uk.*". www.usenet.org.uk. Retrieved 2024-12-13. For a vote between several mutually exclusive options, the votetaking organisation will establish, for each possible pair of options A and B, how many voters prefer A over B and vice versa. … The method of determining the result when there are several mutually exclusive options, as described in paragraph 4 of The Result, is essentially that devised by the French mathematician the Marquis de Condorcet (1743-94).

vermont.gov (Global: 6,611^th place; English: 3,259^th place)

legislature.vermont.gov

"Bill Status H.424". legislature.vermont.gov. Retrieved 2023-12-22.

votingmatters.org.uk (Global: low place; English: low place)

Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.
Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.

web.archive.org (Global: 1^st place; English: 1^st place)

Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.
G. Hägele and F. Pukelsheim (2001). "Llull's writings on electoral systems". Studia Lulliana. 41: 3–38. Archived from the original on 2006-02-07.
Green-Armytage, James (2011). "Four Condorcet-Hare Hybrid Methods for Single-Winner Elections" (PDF). S2CID 15220771. Archived (PDF) from the original on 2013-06-03.
Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.
"Constitution of the Libertarian Party of Washington State" (PDF). Libertarian Party of Washington. March 26, 2022. p. 10. Archived (PDF) from the original on 2022-09-14. then the vote shall be performed using either a Condorcet voting system or a score voting system, as the participants shall decide

wiley.com (Global: 150^th place; English: 174^th place)

onlinelibrary.wiley.com

Barberà, Salvador; Bossert, Walter (2025-04-01). "Intermediate Condorcet Winners and Losers". Journal of Public Economic Theory. 27 (2). doi:10.1111/jpet.70024. ISSN 1097-3923. A candidate $x\in S$ is a strong Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)>p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a strong Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed. … A candidate $x\in S$ is a weak Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)\geq p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a weak Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Tideman, T. Nicolaus; Plassmann, Florenz (2011). "Modeling the Outcomes of Vote-Casting in Actual Elections". SSRN Electronic Journal. doi:10.2139/ssrn.1627787. ISSN 1556-5068. A common definition of a voting cycle is the absence of a strict pairwise majority rule winner (SPMRW) … if no candidate beats all other candidates in pairwise comparisons.
Gehrlein, William V. (2011). Voting paradoxes and group coherence : the condorcet efficiency of voting rules. Lepelley, Dominique. Berlin: Springer. ISBN 9783642031076. OCLC 695387286. empirical studies ... indicate that some of the most common paradoxes are relatively unlikely to be observed in actual elections. ... it is easily concluded that Condorcet's Paradox should very rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters' preferences reflect any reasonable degree of group mutual coherence
Gehrlein, William V. (2011). Voting paradoxes and group coherence : the condorcet efficiency of voting rules. Lepelley, Dominique. Berlin: Springer. ISBN 9783642031076. OCLC 695387286. empirical studies ... indicate that some of the most common paradoxes are relatively unlikely to be observed in actual elections. ... it is easily concluded that Condorcet's Paradox should very rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters' preferences reflect any reasonable degree of group mutual coherence
Mackie, Gerry. (2003). Democracy defended. Cambridge, UK: Cambridge University Press. p. 6. ISBN 0511062648. OCLC 252507400.
Young, H. P. (1988). "Condorcet's Theory of Voting" (PDF). American Political Science Review. 82 (4): 1231–1244. doi:10.2307/1961757. ISSN 0003-0554. JSTOR 1961757. S2CID 14908863. Archived (PDF) from the original on 2018-12-22.
Barberà, Salvador; Bossert, Walter (2025-04-01). "Intermediate Condorcet Winners and Losers". Journal of Public Economic Theory. 27 (2). doi:10.1111/jpet.70024. ISSN 1097-3923. A candidate $x\in S$ is a strong Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)>p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a strong Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed. … A candidate $x\in S$ is a weak Condorcet winner for $\mathbf {R}$ in $S$ if $p(\mathbf {R} ;x,z)\geq p(\mathbf {R} ;z,x){\text{ for all }}z\in S\setminus \{x\}$ and $x\in S$ is a weak Condorcet loser for $\mathbf {R}$ in $S$ if the inequality … is reversed.

Condorcet method (English Wikipedia)

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