Black's method
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Black's method is an election method proposed by Duncan Black in 1958 as a compromise between the Condorcet method and the Borda count. This method selects a Condorcet winner. If a Condorcet winner does not exist, then the candidate with the highest Borda score is selected.[1]
Properties
Among methods satisfying the majority criterion, Black's method gives the minimum power to the majority and hence the method is best at protecting minorities.[2]
Satisfied criteria
Black's method satisfies the following criteria:
- Unrestricted domain
- Non-imposition (a.k.a. citizen sovereignty)
- Non-dictatorship
- Homogeneity
- Condorcet criterion
- Majority criterion
- Pareto criterion (a.k.a. unanimity)[3]
- Monotonicity criterion[3]
- Majority loser criterion[3]
- Condorcet loser criterion[3]
- Reversal symmetry[3]
- Resolvability criterion
- Polynomial time
Failed criteria
Black's method does not satisfy the following criteria:
- Mutual majority criterion[2]
- Smith criterion[3]
- Participation[3]
- Consistency[3]
- Independence of Smith-dominated alternatives
- Independence of clones
- Independence of irrelevant alternatives
- Local independence of irrelevant alternatives
References
- ^ Black, Duncan (1958). The theory of committees and elections. Cambridge: University Press.
- ^ a b Kondratev, Aleksei Y.; Nesterov, Alexander S. (2020). "Measuring Majority Power and Veto Power of Voting Rules". Public Choice. 183 (1–2): 187–210. arXiv:1811.06739. doi:10.1007/s11127-019-00697-1. S2CID 53670198.
- ^ a b c d e f g h Felsenthal, Dan S; Nurmi, Hannu (2018). Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes. Cham, Switzerland: Springer. ISBN 978-3-319-74033-1.
