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Definitions and important properties of '''Woodall's Method''' and two similar methods:
 
'''Woodall's method''' or '''Smith,IRV''' is a voting method that combines [[instant-runoff voting]] and [[Condorcet]]. It was invented by [[Douglas Woodall]].
 
== Woodall's method: ==
{{definition|Do IRV till only one member of the initial Smiths[[Smith set]] remains un-eliminated. Elect hir.}}
Smith set:
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=== A few properties of Woodall ===
Woodall meets the Mutual[[mutual Majoritymajority Criterion (MMC)criterion]], and [[chicken dilemma criterion|has no chicken dilemma]]. Woodall meets the [[Condorcet criterion]], and the [[Smith set|Smith criterion]].
Meeting Smith always implies meeting MMCthe [[mutual majority criterion]], and [[Condorcet loser criterion|Condorcet Loserloser]] as well.▼
dilemma. Woodall meets the Condorcet Criterion (CC), and the Smith Criterion.
▲Meeting Smith always implies meeting MMC, and Condorcet Loser as well.
 
ConsistencyWoodall criteria:doesn't Woodall,meet like[[FBC]]. Like all Condorcet methods, Woodall fails Consistency, Participation, Mono-Add-Top, and Mono-Add-Unique-Top. Woodall fails Mono-Raise, but passes Mono-Add-Plump and Mono-Append.▼
Woodall doesn't meet [[FBC]]. FBC is necessary only under current conditions (dishonest, disinformational media, and an electorate who believe those media). Woodall isn't proposed for current conditions. Likewise for the similar methods proposed later at this page.
 
Woodall's importance comes from its unmatched freedom from strategy-need, made possible by MMC, freedom from chicken dilemma, and CC. Advantages such as that come at a price. The abovementionedabove-mentioned combination of properties appears to be incompatible with FBC and with Mono-Raise, Participation, Mono-Add-Top and Mono-Add-Unique top. Choice of a voting system always involves choice among properties.▼
▲Consistency criteria: Woodall, like all Condorcet methods, fails Consistency, Participation, Mono-Add-Top, and Mono-Add-Unique-Top. Woodall fails Mono-Raise, but passes Mono-Add-Plump and Mono-Append.
 
▲Woodall's importance comes from its unmatched freedom from strategy-need, made possible by MMC, freedom from chicken dilemma, and CC. Advantages such as that come at a price. The abovementioned combination of properties appears to be incompatible with FBC and with Mono-Raise, Participation, Mono-Add-Top and Mono-Add-Unique top. Choice of a voting system always involves choice among properties.
 
The consistency criteria don't have strategic importance.
----
Definition of MMC:
{{definition|A mutual majority (MM) is a set of voters comprising a majority of the voters, who all prefer some same set of candidates to all of the other candidates. That set of candidates is their MM-preferred set.
If a MM vote sincerely, then the winner should come from their MM-preferred set.
A voter votes sincerely if s/he doesn't vote an unfelt preference, or fail to vote a felt preference that the balloting system in use would have allowed hir to vote in addition to the preferences that she actually does vote.
To vote an unfelt preference is to vote X over Y if you prefer X to Y.
To vote an unfelt preference is to vote X over Y if you don't prefer X to Y.}}
===Consequences of Woodall's properties===
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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.}}
 
----
 
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.
 
----
 
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 ==
{{Merge to|Schwartz Woodall|date=August 2019}}
 
Schwartz Woodall is a variation of Woodall, and an improvement for
small electorates, such as organizations, meetings or families.
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Schwartz Woodall:
{{definition|Do IRV till only one member of the initial [[Schwartz set]] remains un-eliminated. Elect hir.}}
 
== Notes ==
The Schwartz set has two equivalent definitions:
[[Benham's method]] is similar, but always terminates in the same round as Woodall's or earlier. This is because the two methods are identical to [[IRV]] until their algorithms' completion, but Benham's method can potentially terminate in a round where there are still multiple members of the Smith set remaining i.e. a member of the Smith set whose only pairwise loss or tie is to one of the other candidates in the Smith set would become a [[CW]] if that other candidate is eliminated, and be the Benham winner.
 
The beatpath definition of the Schwartz set:
==References==
<references />
{{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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