Black's method explained

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)
• Monotonicity criterion
• Majority loser criterion
• Condorcet loser criterion^[3]
• 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

Notes and References

1. Book: Black . Duncan . The theory of committees and elections . 1958 . University Press . Cambridge.
2. Measuring Majority Power and Veto Power of Voting Rules. 2020. 10.1007/s11127-019-00697-1. 1811.06739. Kondratev. Aleksei Y.. Nesterov. Alexander S.. Public Choice. 183. 1–2. 187–210. 53670198.
3. Book: Felsenthal . Dan S . Nurmi . Hannu . Voting procedures for electing a single candidate : proving their (in)vulnerability to various voting paradoxes . 2018 . Springer . Cham, Switzerland . 978-3-319-74033-1.