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]].
== Woodall's method: ==
{{definition|Do IRV till only one member of the initial
Smith set:
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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
Meeting Smith always implies meeting
▲Meeting Smith always implies meeting MMC, and Condorcet Loser as well.
Woodall doesn't meet [[FBC]].
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.
===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).
== Schwartz Woodall ==
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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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