Schulze method: Difference between revisions

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'''Cloneproof Schwartz Sequential Dropping''' ('''CSSD''') is a [[voting system]] developed by Markus Schulze that selects a single winner using votes that express preferences. CSSD can also be used to create a sorted list of winners. CSSD is also known as "Schwartz Sequential Dropping", "Beatpath Method", "Beatpath Winner", "Path Voting", "Path Winner", and "Schulze Method".
The '''Schulze method''' is a [[voting system]] developed by Markus Schulze that selects a single winner using votes that express preferences. The Schulze method can also be used to create a sorted list of winners. The Schulze method is also known as "cloneproof Schwartz sequential dropping" (CSSD), "Schwartz sequential dropping" (SSD), "beatpath method", "beatpath winner", "path voting", and "path winner".


If there is a candidate who is preferred over the other candidates,
If there is a candidate who is preferred over the other candidates,
when compared in turn with each of the others, CSSD guarantees that that candidate will win.
when compared in turn with each of the others, the Schulze method guarantees that that candidate will win.
Because of this property, CSSD is (by definition) a '''[[Condorcet method]]'''.
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
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.
[[Instant-runoff voting]], which do not make this guarantee.
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== The Schwartz Set ==
== The Schwartz Set ==


The definition of a [[Schwartz set]], as used in CSSD, is as follows:
The definition of a [[Schwartz set]], as used in the Schulze method, is as follows:


# An unbeaten set is a set of candidates of whom none is beaten by anyone outside that set.
# An unbeaten set is a set of candidates of whom none is beaten by anyone outside that set.
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The voters cast their ballots by ranking the candidates according to their preferences, just like for any other Condorcet election.
The voters cast their ballots by ranking the candidates according to their preferences, just like for any other Condorcet election.


CSSD uses [[Condorcet method|Condorcet]] pairwise matchups between the candidates and a winner is chosen in each of the matchups.
The Schulze method uses [[Condorcet method|Condorcet]] pairwise matchups between the candidates and a winner is chosen in each of the matchups.


From there, CSSD operates as follows to select a winner (or create a ranked list):
From there, the Schulze method operates as follows to select a winner (or create a ranked list):


# Calculate the Schwartz set based only on undropped defeats.
# Calculate the Schwartz set based only on undropped defeats.
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In this situation the Schwartz set is A, B, and C as they all beat someone.
In this situation the Schwartz set is A, B, and C as they all beat someone.


CSSD then says to drop the weakest defeat, so we drop C > A and are left with
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)
* A > B 72% (as C has been removed)
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== History ==
== History ==


The Schulze method has been proposed by Markus Schulze in 1997. See e.g. [http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-August/001958.html here], [http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-August/002044.html here], and [http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-November/002771.html here]!
See http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-December/011477.html


== Satisfied Criteria ==
== Satisfied Criteria ==
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== External Resources ==
== External Resources ==

* [http://groups.yahoo.com/group/election-methods-list/ A mailing list containing technical discussions about election methods]
* [http://groups.yahoo.com/group/election-methods-list/ A mailing list containing technical discussions about election methods]
* [http://electionmethods.org/ electionmethods.org] where CSSD is also called "Schwartz Sequential Dropping" and "Beatpath Winner"
* [http://electionmethods.org/ electionmethods.org] where CSSD is also called "Schwartz Sequential Dropping" and "Beatpath Winner"
Retrieved from "https://electowiki.org/wiki/Schulze_method"