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 Duncan Black).^[1]

Example:

 25 A>B>C
 40 B>C>A
 35 C>A>B

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.

Note that the winner of the Borda count is not necessarily in the Smith set.^[2]

A Smith-efficient variant of Black's method could be used instead, to ensure someone in the Smith set will win.

References

↑ Black, Duncan (1987). The Theory of Committees and Elections. p. 66. ISBN 978-94-009-4225-7. Retrieved 2020-03-31.
↑ di Fenizio, Pietro Speroni (March 12, 2014). "Is there formal proof that Duncan Black's Electoral System is a Condorcet System?". ResearchGate. Retrieved 2020-03-31.

[1] Black, Duncan (1987). The Theory of Committees and Elections. p. 66. ISBN 978-94-009-4225-7. Retrieved 2020-03-31.

[2] Fenizio, Pietro Speroni (March 12, 2014). "Is there formal proof that Duncan Black's Electoral System is a Condorcet System?". ResearchGate. Retrieved 2020-03-31.

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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>
 Example:
 A>B>C
 B>C>A
 C>A>B
 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.
+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>
-Note that a [[Smith-efficient]] variant of Black's method could be used instead, to ensure someone in the [[Smith set]] will win.
+A [[Smith-efficient]] variant of Black's method could be used instead, to ensure someone in the [[Smith set]] will win.
+== References ==
+<references />
 [[Category:Condorcet methods]]
 [[Category:Preferential voting methods]]