# Schwartz Woodall

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**Schwartz Woodall** is a ranked voting method, a variation of Woodall's method.

## Definition[edit | edit source]

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[edit | edit source]

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[edit | edit source]

- 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.