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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.

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.

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)
• Monotonicity criterion
• Majority loser criterion
• Condorcet loser criterion
• Reversal symmetry
• Resolvability criterion
• Polynomial time

Failed criteria

Black's method does not satisfy the following criteria:

• Mutual majority criterion
• Smith criterion
• Participation
• Consistency
• Independence of Smith-dominated alternatives
• Independence of clones
• Independence of irrelevant alternatives
• Local independence of irrelevant alternatives
• Sincere favorite criterion

References

1. Black, Duncan (1958). The theory of committees and elections. Cambridge: University Press.
2. ^ 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.
3. ^ 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.

• Single-winner electoral systems
• Monotonic Condorcet methods
• Electoral systems
• Preferential electoral systems