Schulze method: Difference between revisions
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== Notes ==
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 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 be used instead to find the Schulze winner.
A variation of Schulze which is only Smith-efficient and not Schwartz-efficient 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." 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) If 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 "For all i = 1,...,(n-1): d[C(i),C(i+1)] > d[C(i+1),C(i)]" to "For all i = 1,...,(n-1): d[C(i),C(i+1)] '''>=''' d[C(i+1),C(i)]") in which case this variation could be called the '''beat-or-tie path method''' or '''cloneproof Smith sequential dropping'''.
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