Schwartz Woodall

Definition of Schwartz Woodall: Do IRV till there remains un-eliminated only one member of the initial Schwartz set. Elect hir. [end of Schwartz Woodall definition] There are two equivalent definitions of the Schwartz set: X beats Y if more ballots rank X over Y than rank Y over X. The beatpath definition of the Schwartz set: There is a beatpath from X to Y if either X beats Y, or X beats something that has a beatpath to Y. X has a beatpath to Y if there is a beatpath from X to Y. X is in the Schwartz set if there is no Y such that there is a beatpath from Y to X, but not from X to Y. [end of beatpath definition of the Schwartz set] The unbeaten set definition of the Schwartz set: 1. An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set. 2. An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set. 3. The Schwartz set is the set of candidates who are in innermost unbeaten sets. [end of unbeaten set definition of the Schwartz set] For more information, go to the Woodall's method article.

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