Black's method

Part of the Politics series
Electoral systems
Single-winner/majoritarian Plurality First-past-the-post Plurality at-large (plurality block voting) General ticket (party block voting) Multi-round voting Two-round Exhaustive ballot Primary election Nonpartisan unified top-four Majority at-large (two-round block voting) Ranked / preferential systems Instant-runoff (alternative vote) Contingent vote Coombs' method Condorcet methods (Copeland's, Dodgson's, Kemeny–Young, Minimax, Nanson's, ranked pairs, Schulze, Alternative Smith) Positional voting (Borda count, Nauru/Dowdall method) Bucklin voting Oklahoma primary electoral system Preferential block voting Cardinal / graded systems Score voting Approval voting Combined approval voting Unified primary Usual judgment Satisfaction approval voting Majority judgment STAR voting
Proportional representation Party-list Electoral list open list closed list local lists Apportionment Sainte-Laguë D'Hondt Huntington–Hill Hare Droop Imperiali Hagenbach-Bischoff National remnant Highest averages Largest remainder Proportional forms of ranked voting Single transferable vote Gregory Wright Schulze STV CPO-STV Ranked party list PR Spare vote Proportional forms of cardinal voting Proportional approval voting Sequential proportional approval voting Method of Equal Shares Phragmen's voting rules Biproportional apportionment Fair majority voting Weighted voting Direct representation Interactive representation Liquid democracy
Mixed systems By type of representation Mixed-member majoritarian Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote (positive vote transfer) Scorporo (negative vote transfer) Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Other systems and related theory Semi-proportional representation Single non-transferable vote Limited voting Cumulative voting Binomial voting Other systems Multiple non-transferable vote Double simultaneous vote Proxy voting Delegated voting Indirect STV Liquid democracy Random selection (sortition, random ballot) Supermajority Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Public choice theory Veto Players List of electoral systems List of electoral systems by country Comparison of electoral systems Effects of electoral systems Political fragmentation Political efficacy Voter turnout
Politics portal
v t e

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]

The method is rarely-used compared to Nanson's method, another compromise that blends Condorcet and Borda methods, as Black's method is extremely vulnerable to burial strategy.^{[citation needed]}

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

This page was last edited on 24 February 2024, at 03:39