Beatpaths are defined for an election in which all candidates are evaluated in pair-wise contests and each such contest results either in a tie or with exactly one of the two candidates beating the other. This often comes into play when for example, voters cast ballots that rank candidates in an ordinal preference.
Definition
editA beatpath from candidate X to candidate Y is a series of candidates, C(0),...,C(n), n>=1, where:
- X = C(0)
- Y = C(n)
- for every k = 0,...,n-1: C(k) ≠ C(k+1) and C(k) beats C(k+1) in their pair-wise contest.