Editing Schulze method (section)

== Satisfied and failed criteria ==
=== Satisfied criteria ===
The Schulze method satisfies the following criteria:
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* [[Monotonicity criterion]]<ref name="schulze2011">Markus Schulze, "[https://doi.org/10.1007/s00355-010-0475-4 A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method]", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in ''Voting Matters'', 17:9-19, 2003.</ref>{{rp|§4.5}}
* [[Majority favorite criterion|Majority criterion]]
* [[Majority loser criterion]]
* [[Condorcet criterion]]
* [[Condorcet loser criterion]]
* [[Smith criterion]]<ref name=schulze2011 />{{rp|§4.7}}
* [[Independence of Smith-dominated alternatives]]<ref name=schulze2011 />{{rp|§4.7}}
* [[Mutual majority criterion]]
* [[Independence of clones criterion|Independence of clones]]<ref name=schulze2011 />{{rp|§4.6}}
* [[Reversal symmetry]]<ref name=schulze2011 />{{rp|§4.4}}
* Mono-append<ref name="woodall1994">Douglas R. Woodall, [http://www.votingmatters.org.uk/ISSUE3/P5.HTM Properties of Preferential Election Rules], ''Voting Matters'', issue 3, pages 8–15, December 1994</ref>
* Mono-add-plump<ref name=woodall1994/>
* [[Resolvability criterion]]<ref name=schulze2011 />{{rp|§4.2}}
* [[Polynomial time|Polynomial runtime]]<ref name=schulze2011 />{{rp|§2.3"}}
* prudence<ref name=schulze2011 />{{rp|§4.9"}}
* MinMax sets<ref name=schulze2011 />{{rp|§4.8"}}
* [[Plurality criterion|Woodall's plurality criterion]] if [[Condorcet method#Defeat strength|winning votes]] are used for d[X,Y]
* Symmetric-completion<ref name=woodall1994/> if [[Condorcet method#Defeat strength|margins]] are used for d[X,Y]
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=== Failed criteria ===
Since the Schulze method satisfies the Condorcet criterion, it automatically fails the following criteria:

* [[Participation criterion|Participation]]<ref name="schulze20113" />{{rp|§3.4}}
* [[Consistency criterion|Consistency]]
* [[Tactical voting#Burying|Invulnerability to burying]]
* [[Later-no-harm criterion|Later-no-harm]]

Likewise, since the Schulze method is not a [[Dictatorship mechanism|dictatorship]] and is a [[ranked voting]] system (not [[Rated voting|rated]]), [[Arrow's Theorem]] implies it fails [[independence of irrelevant alternatives]], meaning it can be vulnerable to the [[spoiler effect]] in some rare circumstances. The Schulze method also fails [[Peyton Young]]'s criterion of [[Local independence of irrelevant alternatives|Local Independence of Irrelevant Alternatives]].

=== Comparison table ===
The following table compares the Schulze method with other single-winner election methods:
{{Comparison of Schulze to preferential voting systems}}

=== Difference from ranked pairs ===
[[Ranked pairs]] is another [[Condorcet method]] which is very similar to Schulze's rule, and typically produces the same outcome. There are slight differences, however. The main difference between the beatpath method and [[ranked pairs]] is that Schulze retains behavior closer to [[Minimax Condorcet method|minimax]]. Say that the [[Minimax Condorcet method|minimax]] score of a set '''X''' of candidates is the strength of the strongest pairwise win of a candidate A ∉ '''X''' against a candidate B ∈ '''X'''. Then the Schulze method, but not ranked pairs, guarantees the winner is always a candidate of the set with minimum minimax score.<ref name="schulze20113" />{{rp|§4.8}} This is the sense in which the Schulze method minimizes the largest majority that has to be reversed when determining the winner.

On the other hand, Ranked Pairs minimizes the largest majority that has to be reversed to determine the order of finish.<ref>Tideman, T. Nicolaus, "Independence of clones as a criterion for voting rules", Social Choice and Welfare vol 4 #3 (1987), pp. 185–206.</ref> In other words, when Ranked Pairs and the Schulze method produce different orders of finish, for the majorities on which the two orders of finish disagree, the Schulze order reverses a larger majority than the Ranked Pairs order.