Schwartz Woodall: Difference between revisions
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== Definition ==
{{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:
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=== Beatpath definition ===
{{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 ===
{{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]]
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Revision as of 14:45, 23 August 2019
 | It has been suggested that this article be merged into Woodall's method. (Discuss) Proposed since August 2019. |
Schwartz Woodall is a ranked voting method, a variation of Woodall's method.
Definition
Do 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.