Editing Condorcet method (section)

==Condorcet ranking methods==
Some Condorcet methods produce not just a single winner, but a ranking of all candidates from first to last place. A '''Condorcet ranking''' is a list of candidates with the property that the Condorcet winner (if one exists) comes first and the Condorcet loser (if one exists) comes last, and this holds recursively for the candidates ranked between them.

Single winner methods that satisfy this property include:
* [[Copeland's method]]
* [[Kemeny–Young method]]
* [[Ranked pairs]]
* [[Schulze method]]

Proportional forms which satisfy this property include:
* [[CPO-STV]]
* [[Schulze STV]]

Though there will not always be a Condorcet winner or Condorcet loser, there is always a Smith set and "Smith loser set" (smallest group of candidates who lose to all candidates not in the set in head-to-head elections). Some voting methods produce rankings that sort all candidates in the Smith set above all others, and all candidates in the Smith loser set below all others, with this holding recursively for all candidates ranked between them; in essence, this guarantees that when the candidates can be split into two groups, such that every candidate in the first group beats every candidate in the second group head-to-head, then all candidates in the first group are ranked higher than all candidates in the second group.<ref>{{cite web|url=https://core.ac.uk/download/pdf/7227054.pdf|title=AN EXTENSION OF THE CONDORCET CRITERION AND KEMENY ORDERS |date=October 1998|first=Michel |last=Truchon |quote=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.}}</ref> Because the Smith set and Smith loser set are equivalent to the Condorcet winner and Condorcet loser when they exist, methods that always produce Smith set rankings also always produce Condorcet rankings.