Overview
The Schulze method is a ranked-choice, Condorcet-style voting system designed to pick a single winner (or produce a complete ranking) from voters' ordered preferences. Rather than relying on plurality or instant-runoff eliminations, it compares every pair of candidates and selects the option that is preferred by strongest indirect support across the electorate. It is sometimes called Beatpath, Beatpath Winner, Schwartz Sequential Dropping, Cloneproof Schwartz Sequential Dropping (CSSD), or Path Voting.
How it works
At a high level the procedure consists of three steps. First, build a pairwise preference matrix recording how many voters prefer candidate A to candidate B for every ordered pair. Second, compute the strength of the strongest path between every pair of candidates: each path links two candidates through intermediate candidates, and the strength of a path is determined by its weakest (minimum) pairwise link. Third, compare the strongest path from X to Y with the strongest path from Y to X; if the path from X to Y is stronger, X is ranked above Y. The winner is the candidate who beats every other candidate by these comparisons.
- Pairwise counts (preference matrix).
- Compute strongest paths using an all-pairs algorithm (similar in spirit to Floyd–Warshall).
- Determine ordering by comparing path strengths.
History and naming
The method was introduced by Markus Schulze in 1997. It was developed to satisfy desirable properties of voting methods—particularly the Condorcet criterion—while resisting strategic problems such as vote-splitting among similar candidates. Because its decision rule relies on strongest paths, it acquired names like Beatpath and Path Winner; implementations and descriptions occasionally refer to the Schwartz set and variants emphasizing clone resistance.
Use and adoption
Because it is transparent and readily automated, the Schulze method has been adopted by a number of organizations and communities. For general information on voting methods see voting methods. It is appropriate for single-winner elections and for producing full rankings. Notable users include the Wikimedia community (Wikimedia), the Debian project (Debian), Gentoo (Gentoo), and the KDE community (KDE), among others.
Properties, strengths and practical notes
The Schulze method satisfies the Condorcet criterion: if a candidate exists who beats every other candidate in head-to-head comparisons, that candidate will be chosen. It also produces a complete ranking and can be implemented efficiently for typical ballot sizes; the commonly used algorithm for computing strongest paths runs in polynomial time, roughly cubic in the number of candidates. Practical implementations must handle tie-breaking and ballot-format details, and software libraries exist to perform the computation reliably. Because the method uses pairwise comparisons and transitive path strengths, it tends to reduce the impact of vote-splitting and supports more expressive ranked ballots than simple plurality systems.