Schulze method: Difference between revisions

If there is a candidate who is preferred over the other candidates, when [[Pairwise counting|compared]] in turn with [[pairwise matchup|each of the others]], the Schulze method guarantees that that candidate will win. Because of this property, the Schulze method is (by definition) a [[Condorcet method]]. Note that this is different from some other preference voting systems such as [[Borda count|Borda]] and [[Instant-runoff voting]], which do not make this guarantee.

A possible variation of Schulze (caution;: not proposed, endorsed, or seriously analyzed by Markus 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: 1) Eliminate all candidates not in the [[Smith set]], and then 2) turn the weakest pairwise defeat into a [[pairwise beat|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 thisThis variation could be called the '''beat-or-tie path method''' or '''cloneproof Smith sequential dropping method''' (though instead ofwhen dropping defeats, they are "flipped" to victories for both candidates in the matchup, rather than turned into a pairwise tie). 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.