Defeat-dropping 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 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:
| A | B | C | D | E | F | G | |
|---|---|---|---|---|---|---|---|
| A | Win | F-Win | Win | Win | Win | Win | |
| B | Win | Win | Win | Win | Win | ||
| C | Win | Win | Win | Win | |||
| D | Win | F-Win | Win | ||||
| E | Win | Win | |||||
| F | 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.