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 criterion3
- Majority loser criterion3
- Condorcet loser criterion3
- Reversal symmetry3
- Resolvability criterion
- Polynomial time
Failed criteria
Black's method does not satisfy the following criteria:
- Mutual majority criterion2
- Smith criterion3
- Participation3
- Consistency3
- Independence of Smith-dominated alternatives
- Independence of clones
- Independence of irrelevant alternatives
- Local independence of irrelevant alternatives
- Sincere favorite criterion
References
References
- Black, Duncan (1958). The theory of committees and elections. Cambridge: University Press.
- 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.
- 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.