Woodall's method: Difference between revisions
Content added Content deleted
Psephomancy (talk | contribs) No edit summary |
Psephomancy (talk | contribs) (add definition template, update formatting) |
||
Line 2: | Line 2: | ||
== Woodall's method: == |
== Woodall's method: == |
||
Do IRV till only one member of the initial Smiths set remains |
{{definition|Do IRV till only one member of the initial Smiths set remains |
||
un-eliminated. Elect hir. |
un-eliminated. Elect hir.}} |
||
[end of Woodall definition] |
|||
Smith set: |
Smith set: |
||
The Smith set is the smallest set of candidates such that every |
{{definition|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] |
|||
IRV definition (for the purpose of Woodall): |
IRV definition (for the purpose of Woodall): |
||
Repeatedly, cross-off or delete from the rankings the candidate who |
{{definition|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] |
|||
Definition of "beats": |
Definition of "beats": |
||
X beats Y if more ballots rank X over Y than rank Y over X. |
{{definition|X beats Y if more ballots rank X over Y than rank Y over X.}} |
||
[end of "beats" definition] |
|||
---- |
|||
=== A few properties of Woodall === |
=== A few properties of Woodall === |
||
Line 49: | Line 37: | ||
Definition of MMC: |
Definition of MMC: |
||
A mutual majority (MM) is a set of voters comprising a majority of the |
{{definition|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. |
||
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. |
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 have allowed hir to vote in addition to the preferences that she actually does vote. |
||
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. |
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 don't prefer X to Y. |
To vote an unfelt preference is to vote X over Y if you don't prefer X to Y.}} |
||
⚫ | |||
[end of MMC definition] |
|||
---- |
|||
⚫ | |||
As with IRV, Woodall's MMC compliance and freedom from chicken dilemma |
As with IRV, Woodall's MMC compliance and freedom from chicken dilemma |
||
Line 74: | Line 53: | ||
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 |
|||
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. |
||
Line 81: | Line 60: | ||
But Woodall additionally, as well as possible, guarantees automatic |
But Woodall additionally, as well as possible, guarantees automatic |
||
majority rule to |
majority rule to ''all'' majorities, however constituted, by always |
||
electing the voted Condorcet winner (CW) |
electing the voted Condorcet winner (CW) |
||
Line 87: | Line 66: | ||
of the other candidates (as "beat" was defined above). |
of the other candidates (as "beat" was defined above). |
||
---- |
|||
== Benham's method: == |
== Benham's method: == |
||
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 |
||
Line 99: | Line 75: | ||
Benham: |
Benham: |
||
Do IRV till there is an un-eliminated candidate who beats each one of |
{{definition|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] |
|||
Line 129: | Line 103: | ||
Benham become important and decisive. |
Benham become important and decisive. |
||
---- |
|||
== Schwartz Woodall == |
== Schwartz Woodall == |
||
{{Merge to|Schwartz Woodall|date=August 2019}} |
{{Merge to|Schwartz Woodall|date=August 2019}} |
||
Line 140: | Line 111: | ||
Schwartz Woodall: |
Schwartz Woodall: |
||
Do IRV till only one member of the initial Schwartz set remains |
{{definition|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] |
|||
The Schwartz set has two equivalent definitions: |
The Schwartz set has two equivalent definitions: |
||
The beatpath definition of the Schwartz set: |
The beatpath definition of the Schwartz set: |
||
There is a beatpath from X to Y if X beats Y, or if X beats something |
{{definition|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] |
|||
Unbeaten set definition of the Schwartz set: |
Unbeaten set definition of the Schwartz set: |
||
1. An unbeaten set is a set of candidates none of whom are beaten by |
{{definition|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 |
|||
smaller unbeaten 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.}} |
|||
[end of unbeaten set definition of the Schwartz set] |
|||
End of page |
|||
[[Category:Condorcet methods]] |
[[Category:Condorcet methods]] |