Woodall's method: Difference between revisions

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Do IRV till only one member of the initial Smiths set remains
Do IRV till only one member of the initial Smiths set remains
un-eliminated. Elect hir.
un-eliminated. Elect hir.
[end of Woodall definition]
[end of Woodall definition]
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The Smith set is the smallest set of candidates such that every
The Smith set is the smallest set of candidates such that every
candidate in the set beats every candidate outside the set.
candidate in the set beats every candidate outside the set.
[end of Smith set definition]
[end of Smith set definition]
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Repeatedly, cross-off or delete from the rankings the candidate who
Repeatedly, cross-off or delete from the rankings the candidate who
tops the fewest rankings.
tops the fewest rankings.
[end of IRV definition for the purpose of Woodall]
[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
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
voters, who all prefer some same set of candidates to all of the other
candidates. That set of candidates is their MM-preferred set.
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.
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
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
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
have allowed hir to vote in addition to the preferences that she
actually does vote.
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 prefer X to Y.
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As with IRV, Woodall's MMC compliance and freedom from chicken dilemma
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
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
ranking sincerely, ensure that the winner will come from their
MM-preferred set. They can assure that, even while fully, freely and sincerely choosing
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
_among_ that MM preferred set by sincere ranking. And freedom from
chicken dilemma means that that MM have no need to not rank sincerely.
chicken dilemma means that that MM have no need to not rank sincerely.
Therefore, IRV and Woodall guarantee automatic majority-rule
Therefore, IRV and Woodall guarantee automatic majority-rule
enforcement for a mutual majority.
enforcement for a mutual majority.
But Woodall additionally, as well as possible, guarantees automatic
But Woodall additionally, as well as possible, guarantees automatic
majority rule to _all_ majorities, however constituted, by always
majority rule to _all_ majorities, however constituted, by always
electing the voted Condorcet winner (CW)
electing the voted Condorcet winner (CW)
The voted CW is the candidate (when there is one) who beats each one
The voted CW is the candidate (when there is one) who beats each one
of the other candidates (as "beat" was defined above).
of the other candidates (as "beat" was defined above).


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Benham is a method similar to Woodall. Benham can be defined a bit
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,
more briefly, because it doesn't mention the Smith set, though Benham,
like Woodall, always chooses from the Smith set. But Woodall is more
like Woodall, always chooses from the Smith set. But Woodall is more
particular than Benham is, regarding which Smith set member it
particular than Benham is, regarding which Smith set member it
chooses.
chooses.
Benham:
Benham:
Do IRV till there is an un-eliminated candidate who beats each one of
Do IRV till there is an un-eliminated candidate who beats each one of
the other un-eliminated candidates. Elect hir.
the other un-eliminated candidates. Elect hir.
[end of Benham definition]
[end of Benham definition]
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It should be pointed out that, of course, if there is a CW, then
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
Woodall and Benham, by their above-stated definitions, will elect that
CW without doing any IRV.
CW without doing any IRV.


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For current conditions (disinformational media and an electorate who
For current conditions (disinformational media and an electorate who
believe those media), [[FBC]] is necessary.
believe those media), [[FBC]] is necessary.


[[Approval]], [[Score]] ("[[Range]]"), and
[[Approval]], [[Score]] ("[[Range]]"), and
[[Symmetrical ICT]] meet FBC, and are good proposals for current
[[Symmetrical ICT]] meet FBC, and are good proposals for current
conditions.
conditions.
FBC is important only for current conditions.
FBC is important only for current conditions.
But, other than for current conditions, FBC would no longer be needed,
But, other than for current conditions, FBC would no longer be needed,
and then the powerful above-described properties-combinations of IRV, Woodall, and
and then the powerful above-described properties-combinations of IRV, Woodall, and
Benham become important and decisive.
Benham become important and decisive.


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Schwartz Woodall is a variation of Woodall, and an improvement for
Schwartz Woodall is a variation of Woodall, and an improvement for
small electorates, such as organizations, meetings or families.
small electorates, such as organizations, meetings or families.
Schwartz Woodall:
Schwartz Woodall:
Do IRV till only one member of the initial Schwartz set remains
Do IRV till only one member of the initial Schwartz set remains
un-eliminated. Elect hir.
un-eliminated. Elect hir.


[end of Schwartz Woodall definition]
[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
There is a beatpath from X to Y if X beats Y, or if X beats something
that has a beatpath to Y.
that has a beatpath to Y.
X has a beatpath to Y if there is a beatpath from X 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
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.
beatpath from Y to X, but not from X to Y.
[end of beatpath definition of the Schwartz set]
[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
1. An unbeaten set is a set of candidates none of whom are beaten by
anyone outside that set.
anyone outside that set.
2. An innermost unbeaten set is an unbeaten set that doesn't contain a
2. An innermost unbeaten set is an unbeaten set that doesn't contain a
smaller unbeaten set.
smaller unbeaten set.
3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.
3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.
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