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Woodall's method: Difference between revisions
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imported>MichaelOssipoff (Created page with " == '''Definitions and Important Properties of Woodall's Method and Two Similar Methods''' == '''Woodall's method:''' Do IRV till only one member of the initial Smiths s...") |
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Do IRV till only one member of the initial Smiths set remains
[end of Woodall definition]
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The Smith set is the smallest set of candidates such that every
[end of Smith set definition]
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Repeatedly, cross-off or delete from the rankings the candidate who
[end of IRV definition for the purpose of Woodall]
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A mutual majority (MM) is a set of voters comprising a majority of the
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
To vote an unfelt preference is to vote X over Y if you prefer X to Y.
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As with IRV, Woodall's MMC compliance and freedom from chicken dilemma
Therefore, IRV and Woodall guarantee automatic majority-rule
But Woodall additionally, as well as possible, guarantees automatic
The voted CW is the candidate (when there is one) who beats each one
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Benham is a method similar to Woodall. Benham can be defined a bit
Benham:
Do IRV till there is an un-eliminated candidate who beats each one of
[end of Benham definition]
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It should be pointed out that, of course, if there is a CW, then
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For current conditions (disinformational media and an electorate who
[[Approval]], [[Score]] ("[[Range]]"), and
FBC is important only for current conditions.
But, other than for current conditions, FBC would no longer be needed,
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Schwartz Woodall is a variation of Woodall, and an improvement for
Schwartz Woodall:
Do IRV till only one member of the initial Schwartz set remains
[end of Schwartz Woodall definition]
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There is a beatpath from X to Y if X beats Y, or if X beats something
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
[end of beatpath definition of the Schwartz set]
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1. An unbeaten set is a set of candidates none of whom are beaten by
2. An innermost unbeaten set is an unbeaten set that doesn't contain a
3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.
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