Woodall's method: Difference between revisions
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Definitions and important properties of '''Woodall's Method''' and |
Definitions and important properties of '''Woodall's Method''' and a similar method: |
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== Woodall's method: == |
== Woodall's method: == |
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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 |
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of the other candidates (as "beat" was defined above). |
of the other candidates (as "beat" was defined above). |
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== Benham's method: == |
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Benham is a method similar to Woodall. Benham can be defined a bit |
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more briefly, because it doesn't mention the Smith set, though Benham, |
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like Woodall, always chooses from the Smith set. But Woodall is more |
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particular than Benham is, regarding which Smith set member it |
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chooses. |
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Benham: |
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{{definition|Do IRV till there is an un-eliminated candidate who beats each one of |
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the other un-eliminated candidates. Elect hir.}} |
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---- |
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It should be pointed out that, of course, if there is a CW, then |
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Woodall and Benham, by their above-stated definitions, will elect that |
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CW without doing any IRV. |
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---- |
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For current conditions (disinformational media and an electorate who |
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believe those media), [[FBC]] is necessary. |
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[[Approval]], [[Score]] ("[[Range]]"), and |
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[[Symmetrical ICT]] meet FBC, and are good proposals for current |
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conditions. |
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FBC is important only for current conditions. |
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But, other than for current conditions, FBC would no longer be needed, |
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and then the powerful above-described properties-combinations of IRV, Woodall, and |
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Benham become important and decisive. |
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== Schwartz Woodall == |
== Schwartz Woodall == |
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Schwartz Woodall: |
Schwartz Woodall: |
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{{definition|Do IRV till only one member of the initial Schwartz set remains un-eliminated. Elect hir.}} |
{{definition|Do IRV till only one member of the initial [[Schwartz set]] remains un-eliminated. Elect hir.}} |
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==References== |
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The Schwartz set has two equivalent definitions: |
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<references /> |
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The beatpath definition of the Schwartz set: |
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{{definition|There is a beatpath from X to Y if X beats Y, or if X beats something that has a beatpath to Y. |
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X has a beatpath to Y if there is a beatpath from X to Y. |
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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.}} |
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Unbeaten set definition of the Schwartz set: |
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{{definition|1. An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set. |
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2. An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set. |
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3. The Schwartz set is the set of candidates who are in innermost unbeaten sets.}} |
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[[Category:Smith-efficient Condorcet methods]] |
[[Category:Smith-efficient Condorcet methods]] |