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.