Woodall's method: Difference between revisions
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'''Woodall's method''' or '''Smith,IRV''' is a voting method that combines [[instant-runoff voting]] and [[Condorcet]]. It was invented by [[Douglas Woodall]].
{{definition|Do IRV till only one member of the initial [[Smith set]] remains un-eliminated. Elect hir.}}
Smith set:
{{definition|The Smith set is the smallest set of candidates such that every candidate in the set beats every candidate outside the set.}}
IRV definition (for the purpose of Woodall):
{{definition|Repeatedly, cross-off or delete from the rankings the candidate who tops the fewest rankings.}}
Definition of "beats":
{{definition|X beats Y if more ballots rank X over Y than rank Y over X.}}An alternative (but equivalent) definition of Woodall's used in James Green-Armytage's Condorcet-IRV paper<ref>http://www.votingmatters.org.uk/ISSUE29/I29P1.PDF</ref>:<blockquote>Score candidates according to their elimination scores, and choose the Smith set candidate with best score. That is, define each candidate’s elimination score as the round in which he is eliminated by AV [IRV].</blockquote>
=== A few properties of Woodall ===
Woodall meets the [[mutual majority 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 the [[mutual majority criterion]], and [[Condorcet loser criterion|Condorcet loser]] as well.
Woodall doesn't meet [[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'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
The consistency criteria don't have strategic importance.
===Consequences of Woodall's properties===
As with IRV, Woodall's MMC compliance and freedom from chicken dilemma
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ranking sincerely, ensure that the winner will come from their
MM-preferred set. They can assure that, even while fully, freely and sincerely choosing
chicken dilemma means that that MM have no need to not rank sincerely.
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But Woodall additionally, as well as possible, guarantees automatic
majority rule to
electing the voted Condorcet winner (CW)
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of the other candidates (as "beat" was defined above).
== Schwartz Woodall ==
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 ==
[[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==
<references />
[[Category:Smith-efficient Condorcet methods]]
[[Category:Condorcet-IRV hybrid methods]]
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