Editing Condorcet method (section)

==Definition==
A Condorcet method is a voting system that will always elect the Condorcet winner (if there is one); this is the candidate whom voters prefer to each other candidate, when compared to them one at a time. This candidate can be found (if they exist; see next paragraph) by checking if there is a candidate who beats all other candidates; this can be done by using [[Copeland's method]] and then checking if the Copeland winner has the highest possible Copeland score. They can also be found by conducting a series of pairwise comparisons, using the procedure given in Robert's Rules of Order described above. For ''N'' candidates, this requires ''N'' − 1 pairwise hypothetical elections. For example, with 5 candidates there are 4 pairwise comparisons to be made, since after each comparison, a candidate is eliminated, and after 4 eliminations, only one of the original 5 candidates will remain.

To confirm that a Condorcet winner exists in a given election, first do the Robert's Rules of Order procedure, declare the final remaining candidate the procedure's winner, and then do at most an additional ''N'' − 2 pairwise comparisons between the procedure's winner and any candidates they have not been compared against yet (including all previously eliminated candidates). If the procedure's winner does not win all pairwise matchups, then no Condorcet winner exists in the election (and thus the Smith set has multiple candidates in it).

Computing all pairwise comparisons requires ½''N''(''N''−1) pairwise comparisons for ''N'' candidates. For 10 candidates, this means 0.5*10*9=45 comparisons, which can make elections with many candidates hard to count the votes for.{{citation needed|reason=Do you mean, "time consuming," "difficult to compute," or something else entirely|date=May 2021}}

The family of Condorcet methods is also referred to collectively as Condorcet's method. A voting system that always elects the Condorcet winner when there is one is described by electoral scientists as a system that satisfies the Condorcet criterion.<ref>{{cite web |last1=Wang |first1=Tiance |last2=Cuff |first2=P. |last3=Kulkarni |first3=Sanjeev |title=Condorcet Methods are Less Susceptible to Strategic Voting |date=2013 |s2cid=8230466 |url=https://www.princeton.edu/~cuff/publications/wang_strategic_voting.pdf |archive-url=https://web.archive.org/web/20211102025031/https://www.princeton.edu/~cuff/publications/wang_strategic_voting.pdf |archive-date=2021-11-02 |url-status=live }}</ref> Additionally, a voting system can be considered to have Condorcet consistency, or be Condorcet consistent, if it elects any Condorcet winner.<ref name=":2">{{Citation|last=Pacuit|first=Eric|title=Voting Methods|date=2019|url=https://plato.stanford.edu/archives/fall2019/entries/voting-methods/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Fall 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-10-16}}</ref>

In certain circumstances, an election has no Condorcet winner. This occurs as a result of a kind of tie known as a ''majority rule cycle'', described by [[Voting paradox|Condorcet's paradox]]. The manner in which a winner is then chosen varies from one Condorcet method to another. Some Condorcet methods involve the basic procedure described below, coupled with a Condorcet completion method, which is used to find a winner when there is no Condorcet winner. Other Condorcet methods involve an entirely different system of counting, but are classified as Condorcet methods, or Condorcet consistent, because they will still elect the Condorcet winner if there is one.<ref name=":2" />

Not all single winner, [[ranked voting systems]] are Condorcet methods. For example, [[instant-runoff voting]] and the [[Borda count]] are not Condorcet methods.<ref name=":2" /><ref>[https://economics.stanford.edu/sites/g/files/sbiybj9386/f/publications/cook_hthesis2011.pdf Thesis] {{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }} "IRV satisfies the later-no-harm criterion and the Condorcet loser criterion but fails monotonicity, independence of irrelevant alternatives, and the Condorcet criterion."</ref>