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Definitions and important properties of '''Woodall's Method''' and a similar method:
 
'''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.
 
Woodall doesn't meet [[FBC]]. FBCLike isall necessaryCondorcet onlymethods, underWoodall currentfails conditionsConsistency, (dishonestParticipation, disinformational mediaMono-Add-Top, and an electorate who believe those media)Mono-Add-Unique-Top. Woodall isn'tfails proposedMono-Raise, forbut currentpasses conditions.Mono-Add-Plump Likewise for the similar methods proposed later at thisand pageMono-Append.
 
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 above-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.
 
The consistency criteria don't have strategic importance.
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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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{{definition|Do IRV till only one member of the initial [[Schwartz set]] remains un-eliminated. Elect hir.}}
 
== Notes ==
[[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.
 
==References==
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