Black's method: Difference between revisions
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'''Black's method''' chooses the [[Condorcet winner]] if it exists, but uses the [[Borda count]] instead if there is an ambiguity (the method is named for [[w:Duncan Black|Duncan Black]]). |
'''Black's method''' chooses the [[Condorcet winner]] if it exists, but uses the [[Borda count]] instead if there is an ambiguity (the method is named for [[w:Duncan Black|Duncan Black]]).<ref>{{Cite book| isbn = 978-94-009-4225-7| last = Black| first = Duncan| title = The Theory of Committees and Elections| accessdate = 2020-03-31| date = 1987| url = http://link.springer.com/openurl?genre=book&isbn=978-94-010-8375-1|publisher=|year=|location=|pages=66}}</ref> |
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Example: |
Example: |
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25 A>B>C |
25 A>B>C |
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40 B>C>A |
40 B>C>A |
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35 C>A>B |
35 C>A>B |
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Borda scores are A 185, B 205, C 210. A pairwise beats B beats C beats A, so there is no Condorcet winner (because everyone has at least one defeat). So the Borda winner, C, wins. |
Borda scores are A 185, B 205, C 210. A pairwise beats B beats C beats A, so there is no Condorcet winner (because everyone has at least one defeat). So the Borda winner, C, wins. |
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Note that the winner of the Borda count is not necessarily in the Smith set.<ref>{{Cite web| title = Is there formal proof that Duncan Black's Electoral System is a Condorcet System?| work = ResearchGate| accessdate = 2020-03-31| url = https://www.researchgate.net/post/Is_there_formal_proof_that_Duncan_Blacks_Electoral_System_is_a_Condorcet_System|date=March 12, 2014|last=di Fenizio|first=Pietro Speroni|archive-url=|archive-date=|url-status=live}}</ref> |
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== References == |
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<references /> |
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[[Category:Condorcet methods]] |
[[Category:Condorcet methods]] |
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[[Category:Preferential voting methods]] |
[[Category:Preferential voting methods]] |