# 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[edit]

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[edit]

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[edit]

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
- Peyton Young's criterion Local independence of irrelevant alternatives.

## References[edit]

**^**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.