Schulze method: Difference between revisions
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The Schulze method then says to drop the weakest defeat, so we drop C > A and are left with
* A > B 72% (as C has been removed from the Schwartz set and thus eliminated, since they no longer beat or tie anyone in the set)
Therefore, A is the winner.
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Because Schulze, like [[Ranked Pairs]], is equivalent to [[Minimax]] when there are 3 or fewer candidates with no pairwise ties, and passes [[Independence of Smith-dominated Alternatives]], it is possible to eliminate all candidates not in the Smith set before running Schulze and get the same result, potentially making computation easier, and when the Smith set has 3 or fewer members with no pairwise ties between them, Minimax can then be used instead after eliminating non-Smith candidates to find the Schulze winner.
[[File:Smith based Schulze example.png|thumb|An example of the Smith set-based variation of the Schulze method.]]
A variation of Schulze which is only Smith-efficient and not Schwartz-efficient (see the image to the right for an example) can be described as "Iteratively repeat the following two steps until there are no more pairwise defeats, at which point all of the remaining candidates are tied to win: Eliminate all candidates not in the Smith set, and then turn the weakest pairwise defeat into a pairwise victory for both candidates in the matchup." This can be argued to be simpler than regular Schulze, since the Smith set is easier to understand than the Schwartz set. It will return the same result as regular Schulze when there are no pairwise ties between any members of the Smith set. (Unverified) It may be the case that this variation of Schulze can be described by changing the definition of a path in the Schulze description from a [[beatpath]] to a [[beat-or-tie path]] (i.e. changing the third property of a path from <blockquote>For all i = 1,...,(n-1): d[C(i),C(i+1)] > d[C(i+1),C(i)] </blockquote>to <blockquote>For all i = 1,...,(n-1): d[C(i),C(i+1)] '''>=''' d[C(i+1),C(i)] </blockquote>in which case this variation could be called the '''beat-or-tie path method''' or '''cloneproof Smith sequential dropping''' (though instead of dropping defeats, they are "flipped" to victories for both candidates in the matchup). It may be possible when using this variation to pretend a particular pairwise matchup simply didn't happen, rather than to say that both candidates in the matchup got a pairwise victory, when flipping or dropping defeats.
== Use of the Schulze method ==
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