Schwartz Woodall: Difference between revisions

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+#REDIRECT[[Woodall's method#Schwartz Woodall]]
-'''Schwartz Woodall''' is a ranked voting method, a variation of [[Woodall's method]].
-== Definition ==
-Do [[Instant-runoff voting|IRV]] until there remains un-eliminated only one member of the initial
-[[Schwartz set]]. Elect hir.
-There are two equivalent definitions of the Schwartz set:
-X beats Y if more ballots rank X over Y than rank Y over X.
-=== Beatpath definition ===
-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.
-=== Unbeaten set definition ===
-# An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set.
-# An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set.
-# The Schwartz set is the set of candidates who are in innermost unbeaten sets.
-[[Category:Single-winner voting methods]]
-[[Category:Preferential voting methods]]