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Definitions and important properties of '''Woodall's Method''' and twoa similar methodsmethod:
== Woodall's method: ==
The voted CW is the candidate (when there is one) who beats each one
of the other candidates (as "beat" was defined above).
== Benham's method: ==
Benham is a method similar to Woodall. Benham can be defined a bit
more briefly, because it doesn't mention the Smith set, though Benham,
like Woodall, always chooses from the Smith set. But Woodall is more
particular than Benham is, regarding which Smith set member it
chooses.
Benham:
{{definition|Do IRV till there is an un-eliminated candidate who beats each one of
the other un-eliminated candidates. Elect hir.}}
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It should be pointed out that, of course, if there is a CW, then
Woodall and Benham, by their above-stated definitions, will elect that
CW without doing any IRV.
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For current conditions (disinformational media and an electorate who
believe those media), [[FBC]] is necessary.
[[Approval]], [[Score]] ("[[Range]]"), and
[[Symmetrical ICT]] meet FBC, and are good proposals for current
conditions.
FBC is important only for current conditions.
But, other than for current conditions, FBC would no longer be needed,
and then the powerful above-described properties-combinations of IRV, Woodall, and
Benham become important and decisive.
== Schwartz Woodall ==
Schwartz Woodall:
{{definition|Do IRV till only one member of the initial [[Schwartz set]] remains un-eliminated. Elect hir.}}
==References==
The Schwartz set has two equivalent definitions:
<references />
The beatpath definition of the Schwartz set:
{{definition|There is a beatpath from X to Y if X beats Y, or if 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 of the Schwartz set:
{{definition|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.}}
[[Category:Smith-efficient Condorcet methods]]
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