The Schulze method () is an
electoral system
An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political ...
developed in 1997 by Markus Schulze that selects a
single winner using votes that express
preferences
In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision the ...
. The method can also be used to create a sorted list of winners. The Schulze method is also known as Schwartz Sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), the beatpath method, beatpath winner, path voting, and path winner. The Schulze method is a
Condorcet method
A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...
, which means that if there is a candidate who is preferred by a majority over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied.
The output of the Schulze method gives an ordering of candidates. Therefore, if several positions are available, the method can be used for this purpose without modification, by letting the ''k'' top-ranked candidates win the ''k'' available seats. Furthermore, for
proportional representation
Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divis ...
elections, a
single transferable vote
Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
(STV) variant known as
Schulze STV
Schulze STV is a draft single transferable vote (STV) ranked voting system designed to achieve proportional representation.Markus SchulzeFree Riding and Vote Management under Proportional Representation by Single Transferable Vote/ref> It was in ...
has been proposed. The Schulze method is used by several organizations including
Wikimedia
The Wikimedia Foundation, Inc., or Wikimedia for short and abbreviated as WMF, is an American 501(c)(3) nonprofit organization headquartered in San Francisco, California and registered as a charitable foundation under local laws. Best know ...
,
Debian,
Ubuntu
Ubuntu ( ) is a Linux distribution based on Debian and composed mostly of free and open-source software. Ubuntu is officially released in three editions: '' Desktop'', ''Server'', and ''Core'' for Internet of things devices and robots. All ...
,
Gentoo,
Pirate Party political parties and
many others
Many may refer to:
* grammatically plural in number
*an English quantifier used with count nouns indicating a large but indefinite number of; at any rate, more than a few
;Place names
* Many, Moselle, a commune of the Moselle department in Franc ...
.
Description of the method
Ballot
The input for the Schulze method is the same as for other
ranked
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second.
In mathematics, this is known as a weak order or total preorder of ...
single-winner electoral systems: each voter must furnish an ordered preference list on candidates where
ties TIES may refer to:
* TIES, Teacher Institute for Evolutionary Science
* TIES, The Interactive Encyclopedia System
* TIES, Time Independent Escape Sequence
* Theoretical Issues in Ergonomics Science
The ''Theoretical Issues in Ergonomics Science' ...
are allowed (
a strict weak order).
One typical way for voters to specify their preferences on a
ballot
A ballot is a device used to cast votes in an election and may be found as a piece of paper or a small ball used in secret voting. It was originally a small ball (see blackballing) used to record decisions made by voters in Italy around the 16 ...
is as follows. Each ballot lists all the candidates, and each voter ranks this list in order of preference using numbers: the voter places a '1' beside the most preferred candidate(s), a '2' beside the second-most preferred, and so forth. Each voter may optionally:
* give the same preference to more than one candidate. This indicates that this voter is indifferent between these candidates.
* use non-consecutive numbers to express preferences. This has no impact on the result of the elections, since only the order in which the candidates are ranked by the voter matters, and not the absolute numbers of the preferences.
* keep candidates unranked. When a voter doesn't rank all candidates, then this is interpreted as if this voter (i) strictly prefers all ranked to all unranked candidates, and (ii) is indifferent among all unranked candidates.
Computation
Let