# 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 "Schwartz sequential dropping" (SSD), "cloneproof Schwartz sequential dropping" (CSSD), "beatpath method", "beatpath winner", "path voting", and "path winner".

If there is a candidate who is preferred over the other candidates, when compared in turn with 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 and Instant-runoff voting, which do not make this guarantee.

Many different heuristics for the Schulze method have been proposed. The most important heuristics are the path heuristic and the Schwartz set heuristic.

## The path heuristic

Each ballot contains a complete list of all candidates. Each voter ranks these candidates in order of preference. The individual voter may give the same preference to more than one candidate and he may keep candidates unranked. When a given voter does not rank all candidates, then it is presumed that this voter strictly prefers all ranked candidates to all not ranked candidates and that this voter is indifferent between all not ranked candidates.

### Procedure

Suppose d[V,W] is the number of voters who strictly prefer candidate V to candidate W.

A *path* from candidate X to candidate Y of strength z is an ordered set of candidates C(1),...,C(n) with the following four properties:

- C(1) is identical to X.
- C(n) is identical to Y.
- For i = 1,...,(n-1): d[C(i),C(i 1)]