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(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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Line 8:
Do IRV till only one member of the initial Smiths set remains
un-eliminated. Elect hir.
[end of Woodall definition]
Line 15:
The Smith set is the smallest set of candidates such that every
candidate in the set beats every candidate outside the set.
[end of Smith set definition]
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Repeatedly, cross-off or delete from the rankings the candidate who
tops the fewest rankings.
[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
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.
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As with IRV, Woodall's MMC compliance and freedom from chicken dilemma
mean that a MM have no need to not rank sincerely. They can, by merely
ranking sincerely, ensure that the winner will come from their
MM-preferred set. They can assure that, even while fully, freely and sincerely choosing
_among_ that MM preferred set by sincere ranking. And freedom from
chicken dilemma means that that MM have no need to not rank sincerely.
Therefore, IRV and Woodall guarantee automatic majority-rule
enforcement for a mutual majority.
But Woodall additionally, as well as possible, guarantees automatic
majority rule to _all_ majorities, however constituted, by always
electing the voted Condorcet winner (CW)
The voted CW is the candidate (when there is one) who beats each one
of the other candidates (as "beat" was defined above).
 
Line 93:
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:
Do IRV till there is an un-eliminated candidate who beats each one of
the other un-eliminated candidates. Elect hir.
[end of Benham definition]
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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.
 
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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.
 
Line 136:
Schwartz Woodall is a variation of Woodall, and an improvement for
small electorates, such as organizations, meetings or families.
Schwartz Woodall:
Do IRV till only one member of the initial Schwartz set remains
un-eliminated. Elect hir.
 
[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
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.
[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
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.
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