Editing Condorcet method (section)

===Defeat strength===
{{More citations needed section|date=March 2021}}
Some pairwise methods—including minimax, Ranked Pairs, and the Schulze method—resolve circular ambiguities based on the relative strength of the defeats. There are different ways to measure the strength of each defeat, and these include considering "winning votes" and "margins":

*Winning votes: The number of votes on the winning side of a defeat.
*Margins: The number of votes on the winning side of the defeat, minus the number of votes on the losing side of the defeat.<ref>{{cite web|url=https://principles.liquidfeedback.org/The_Principles_of_LiquidFeedback_1st_edition_online_version.pdf |title=The Principles of Liquid Feedback|edition=1 |first1=Jan |last1=Behrens |first2=Axel |last2=Kistner |first3=Andreas |last3=Nitsche |first4=Bjorn |last4=Swierczek |year= 2014}}</ref>

If voters do not rank their preferences for all of the candidates, these two approaches can yield different results. Consider, for example, the following election:

{| class="wikitable"
|-
!45 voters
!11 voters
!15 voters
!29 voters
|-
|1. A
|1. B
|1. B
|1. C
|-
|
|
|2. C
|2. B
|}

The pairwise defeats are as follows:

*B beats A, 55 to 45 (55 winning votes, a margin of 10 votes)
*A beats C, 45 to 44 (45 winning votes, a margin of 1 vote)
*C beats B, 29 to 26 (29 winning votes, a margin of 3 votes)

Using the winning votes definition of defeat strength, the defeat of B by C is the weakest, and the defeat of A by B is the strongest. Using the margins definition of defeat strength, the defeat of C by A is the weakest, and the defeat of A by B is the strongest.

Using winning votes as the definition of defeat strength, candidate B would win under minimax, Ranked Pairs and the Schulze method, but, using margins as the definition of defeat strength, candidate C would win in the same methods.

If all voters give complete rankings of the candidates, then winning votes and margins will always produce the same result. The difference between them can only come into play when some voters declare equal preferences amongst candidates, as occurs implicitly if they do not rank all candidates, as in the example above.

The choice between margins and winning votes is the subject of scholarly debate. Because all Condorcet methods always choose the Condorcet winner when one exists, the difference between methods only appears when cyclic ambiguity resolution is required. The argument for using winning votes follows from this: Because cycle resolution involves disenfranchising a selection of votes, then the selection should disenfranchise the fewest possible number of votes. When margins are used, the difference between the number of two candidates' votes may be small, but the number of votes may be very large—or not. Only methods employing winning votes satisfy [[plurality criterion|Woodall's plurality criterion]].

An argument in favour of using margins is the fact that the result of a pairwise comparison is decided by the presence of more votes for one side than the other and thus that it follows naturally to assess the strength of a comparison by this "surplus" for the winning side. Otherwise, changing only a few votes from the winner to the loser could cause a sudden large change from a large score for one side to a large score for the other. In other words, one could consider losing votes being in fact disenfranchised when it comes to ambiguity resolution with winning votes. Also, using winning votes, a vote containing ties (possibly implicitly in the case of an incompletely ranked ballot) does not have the same effect as a number of equally weighted votes with total weight equaling one vote, such that the ties are broken in every possible way (a violation of Woodall's symmetric-completion criterion), as opposed to margins.<ref>{{Cite journal |first=D R |last=Woodall |title=Properties of Preferential Election Rules |journal=Voting Matters |issue =3 |pages= 8–15 |url=http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM |access-date=2024-12-14}}</ref>

Under winning votes, if two more of the "B" voters decided to vote "BC", the A->C arm of the cycle would be overturned and Condorcet would pick C instead of B. This is an example of "Unburying" or "Later does harm". The margin method would pick C anyway.

Under the margin method, if three more "BC" voters decided to "bury" C by just voting "B", the A->C arm of the cycle would be strengthened and the resolution strategies would end up breaking the C->B arm and giving the win to B. This is an example of "Burying". The winning votes method would pick B anyway.