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Schulze method
The Schulze method (/ˈʃʊltsə/), also known as the beatpath method, is a single winner ranked-choice voting rule developed by Markus Schulze. The Schulze method is a Condorcet completion method, which means it will elect a majority-preferred candidate if one exists. In other words, if most people rank A above B, A will defeat B (whenever this is possible). Schulze's method breaks cyclic ties by using indirect victories. The idea is that if Alice beats Bob, and Bob beats Charlie, then Alice (indirectly) beats Charlie; this kind of indirect win is called a "beatpath".
The Schulze method is used by several organizations including Debian, Ubuntu, Gentoo, Pirate Party political parties and many others. It was also used by Wikimedia prior to their adoption of score voting.
Schulze's method uses ranked ballots with equal ratings allowed. There are two common (equivalent) descriptions of Schulze's method.
The idea behind Schulze's method is that if Alice defeats Bob, and Bob beats Charlie, then Alice "indirectly" defeats Charlie. These chained sequences of "beats" are called 'beatpaths'.
Every beatpath is assigned a particular strength. The strength of a single-step beatpath from Alice to Bob is just the number of voters who rank Alice over Bob. For a longer beatpath, consisting of multiple beats, a beatpath is as strong as its weakest link (i.e. the beat with the smallest number of winning votes).
We say Alice has a "beatpath-win" over Bob if her strongest beatpath to Bob is stronger than Bob's strongest beatpath to Alice (or if Bob has no beatpath to Alice). The winner is any candidate who is not beaten by any other candidate via a beatpath-win.
This definition of a beatpath-win is transitive: in other words, if Alice has a beatpath-win over Bob, and Bob has a beatpath-win over Charlie, Alice has a beatpath-win over Charlie. As a result, the Schulze method is a Condorcet method, providing a full extension of the majority rule to any set of ballots.
The Schulze winner can also be constructed iteratively, using a defeat-dropping method:
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Schulze method AI simulator
(@Schulze method_simulator)
Schulze method
The Schulze method (/ˈʃʊltsə/), also known as the beatpath method, is a single winner ranked-choice voting rule developed by Markus Schulze. The Schulze method is a Condorcet completion method, which means it will elect a majority-preferred candidate if one exists. In other words, if most people rank A above B, A will defeat B (whenever this is possible). Schulze's method breaks cyclic ties by using indirect victories. The idea is that if Alice beats Bob, and Bob beats Charlie, then Alice (indirectly) beats Charlie; this kind of indirect win is called a "beatpath".
The Schulze method is used by several organizations including Debian, Ubuntu, Gentoo, Pirate Party political parties and many others. It was also used by Wikimedia prior to their adoption of score voting.
Schulze's method uses ranked ballots with equal ratings allowed. There are two common (equivalent) descriptions of Schulze's method.
The idea behind Schulze's method is that if Alice defeats Bob, and Bob beats Charlie, then Alice "indirectly" defeats Charlie. These chained sequences of "beats" are called 'beatpaths'.
Every beatpath is assigned a particular strength. The strength of a single-step beatpath from Alice to Bob is just the number of voters who rank Alice over Bob. For a longer beatpath, consisting of multiple beats, a beatpath is as strong as its weakest link (i.e. the beat with the smallest number of winning votes).
We say Alice has a "beatpath-win" over Bob if her strongest beatpath to Bob is stronger than Bob's strongest beatpath to Alice (or if Bob has no beatpath to Alice). The winner is any candidate who is not beaten by any other candidate via a beatpath-win.
This definition of a beatpath-win is transitive: in other words, if Alice has a beatpath-win over Bob, and Bob has a beatpath-win over Charlie, Alice has a beatpath-win over Charlie. As a result, the Schulze method is a Condorcet method, providing a full extension of the majority rule to any set of ballots.
The Schulze winner can also be constructed iteratively, using a defeat-dropping method: