Schwartz Woodall: Difference between revisions

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== Definition ==

Do [[Instant-runoff voting|IRV]] until there remains un-eliminated only one member of the initial

{{definition|Do [[Instant-runoff voting|IRV]] until there remains un-eliminated only one member of the initial

[[Schwartz set]]. Elect hir.

[[Schwartz set]]. Elect hir.}}

There are two equivalent definitions of the Schwartz set:

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=== Beatpath definition ===

There is a beatpath from X to Y if either X beats Y, or X beats

{{definition|There is a beatpath from X to Y if either X beats Y, or X beats something that has a beatpath to Y.

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.

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.

# The Schwartz set is the set of candidates who are in innermost unbeaten sets.}}

[[Category:Single-winner voting methods]]