Editing Schulze method (section)

=== Beatpath explanation ===
The idea behind Schulze's method is that if [[Alice and Bob|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 all of Bob's strongest beatpaths to Alice. The winner is the candidate who has a beatpath-win over every other candidate.

Markus Schulze proved that this definition of a beatpath-win is [[Transitive relation|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.<ref name="schulze201122">Markus Schulze, "[[doi:10.1007/s00355-010-0475-4|A new monotonic, clone-independent, reversal symmetric, and Condorcet-consistent single-winner election method]]", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in ''Voting Matters'', 17:9-19, 2003.</ref>{{rp|§4.1}} As a result, the Schulze method is a [[Condorcet method]], providing a full extension of the [[majority rule]] to any set of ballots.