Editing Condorcet method (section)

==Summary==
In a contest between candidates A, B and C using the preferential-vote form of Condorcet method, a head-to-head race is conducted between each pair of candidates. A and B, B and C, and C and A. If one candidate is preferred over all others, they are the Condorcet Winner and winner of the election.

Because of the possibility of the [[Condorcet paradox]], it is possible, but unlikely,<ref>{{Cite book|title=Voting paradoxes and group coherence : the condorcet efficiency of voting rules|last=Gehrlein, William V.|date=2011|publisher=Springer|others=Lepelley, Dominique.|isbn=9783642031076|location=Berlin|oclc=695387286|quote=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}}</ref> that a Condorcet winner may not exist in a specific election. This is sometimes called a ''Condorcet cycle'' or just ''cycle'' and can be thought of as [[rock paper scissors|Rock beating Scissors, Scissors beating Paper, and Paper beating Rock]]. Various Condorcet methods differ in how they resolve such a cycle. (Most elections do not have cycles. See [[Condorcet paradox#Likelihood of the paradox]] for estimates.) If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent.

*Each voter ranks the candidates in order of preference (top-to-bottom, or best-to-worst, or 1st, 2nd, 3rd, etc.). The voter may be allowed to rank candidates as equals and to express indifference (no preference) between them. Candidates omitted by a voter may be treated as if the voter ranked them at the bottom.<ref>{{cite arXiv |eprint=1807.01366 |quote=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.|last1=Darlington|first1=Richard B.|title=Are Condorcet and minimax voting systems the best?|year=2018|class=physics.soc-ph}}</ref>
*For each pairing of candidates (as in a [[round-robin tournament]]) count how many votes rank each candidate over the other candidate. Thus each pairing will have two totals: the size of its majority and the size of its minority{{citation needed|date=April 2012}}<ref>{{Cite book|last=Hazewinkel|first=Michiel|url=https://books.google.com/books?id=ujnhBwAAQBAJ&pg=PA110|title=Encyclopaedia of Mathematics, Supplement III|date=2007-11-23|publisher=Springer Science & Business Media|isbn=978-0-306-48373-8|language=en |quote=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.}}</ref> (or there will be a tie).

For most Condorcet methods, those counts usually suffice to determine the complete order of finish (i.e. who won, who came in 2nd place, etc.). They always suffice to determine whether there is a Condorcet winner.

Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size. Such ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties. For example, with [[Copeland's method]], it would not be rare for two or more candidates to win the same number of pairings, when there is no Condorcet winner.{{citation needed|date=April 2012}}