Woodall's method: Difference between revisions
add definition template, update formatting
Psephomancy (talk | contribs) No edit summary |
Psephomancy (talk | contribs) (add definition template, update formatting) |
||
Line 2:
== Woodall's method: ==
{{definition|Do IRV till only one member of the initial Smiths set remains
un-eliminated. Elect hir.}}
Smith set:
{{definition|The Smith set is the smallest set of candidates such that every
candidate in the set beats every candidate outside the set.}}
IRV definition (for the purpose of Woodall):
{{definition|Repeatedly, cross-off or delete from the rankings the candidate who
tops the fewest rankings.}}
Definition of "beats":
{{definition|X beats Y if more ballots rank X over Y than rank Y over X.}}
=== A few properties of Woodall ===
Line 49 ⟶ 37:
Definition of MMC:
{{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.
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.
To vote an unfelt preference is to vote X over Y if you don't prefer X to Y.}}
▲Consequences of Woodall's properties:
As with IRV, Woodall's MMC compliance and freedom from chicken dilemma
Line 74 ⟶ 53:
ranking sincerely, ensure that the winner will come from their
MM-preferred set. They can assure that, even while fully, freely and sincerely choosing
chicken dilemma means that that MM have no need to not rank sincerely.
Line 81 ⟶ 60:
But Woodall additionally, as well as possible, guarantees automatic
majority rule to
electing the voted Condorcet winner (CW)
Line 87 ⟶ 66:
of the other candidates (as "beat" was defined above).
== Benham's method: ==
Benham is a method similar to Woodall. Benham can be defined a bit
Line 99 ⟶ 75:
Benham:
{{definition|Do IRV till there is an un-eliminated candidate who beats each one of
the other un-eliminated candidates. Elect hir.}}
Line 129 ⟶ 103:
Benham become important and decisive.
== Schwartz Woodall ==
{{Merge to|Schwartz Woodall|date=August 2019}}
Line 140 ⟶ 111:
Schwartz Woodall:
{{definition|Do IRV till only one member of the initial Schwartz set remains un-eliminated. Elect hir.}}
The Schwartz set has two equivalent definitions:
The beatpath definition of the Schwartz set:
{{definition|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.}}
Unbeaten set definition of the Schwartz set:
{{definition|1. An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set.
3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.}}
[[Category:Condorcet methods]]
| |||