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Defeat-dropping Condorcet methods: Difference between revisions
Adding to Category:Defeat-dropping Condorcet methods and putting "*" (asterisk) for the sort order
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[[Category:Condorcet methods]]
The overarching goal of defeat-droppers is to elect a candidate who is "closest" to being a [[Condorcet winner]] i.e. to minimize the number of "overruled" voters. Defeat-droppers are some of the only Condorcet methods that only require the [[Pairwise comparison matrix|pairwise comparison matrix]] to find the results.
These are [[Condorcet methods]] which reduce to [[Minimax]] in situations when there are 3 or fewer candidates (except possibly if there are any pairwise ties). Defeat-dropping Condorcet methods that pass [[Independence of Smith-dominated Alternatives]] are equivalent to [[Smith//Minimax]] with a [[Smith set]] of 3 or fewer candidates (except possibly if there are pairwise ties).
Many defeat-droppers are [[Smith-efficient]] simply because candidates in the Smith set have no defeats to be dropped against candidates not in the Smith set.
All defeat-droppers' final results can be visualized by showing the matchups between the candidates and which matchups the method dropped. For example, with [[Smith-Schulze]], ignoring pairwise losses or ties:
{| class="wikitable"
|+
!
!A
!B
!C
!D
!E
!F
!G
|-
|A
|
|Win
|F-Win
|Win
|Win
|Win
|Win
|-
|B
|
|
|Win
|Win
|Win
|Win
|Win
|-
|C
|<s>Win</s>
|
|
|Win
|Win
|Win
|Win
|-
|D
|
|
|
|
|Win
|F-Win
|Win
|-
|E
|
|
|
|
|
|Win
|Win
|-
|F
|
|
|
|<s>Win</s>
|
|
|Win
|-
|G
|
|
|
|
|
|
|
|}
"F-Win" here refers to a defeat that is "flipped" into a win i.e. the defeat was dropped by Smith-Schulze. Note that, for example, C's pairwise victory over A is crossed out, with A being ranked above C; this is because A's actual loss to C was flipped into a win, giving A pairwise "victories" against every candidate, thus they are a Condorcet winner and are at the top of the table; also, B beats C, and B beats everyone other than A, B, or C, so B is also ranked above C, but below A.
[[Category:Defeat-dropping Condorcet methods|*]]
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