Defeat-dropping Condorcet methods: Difference between revisions
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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.
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