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Part of the: Politics and Economics series
Electoral systems
Comparison of electoral systems Social choice theory Mechanism design List (By country)
Single-winner methods Single vote-runoff methods Plurality (FPP) Two-round (US: Jungle primary) Partisan primary Alternative vote (US: Ranked-choice) Condorcet-IRV Condorcet methods Ranked pairs Schulze Minimax Kemeny–Young Nanson Condorcet-IRV Maximal lottery Positional voting First-preference plurality Borda count Anti-plurality voting Cardinal / graded methods Score voting Approval voting Majority judgment STAR voting Quadratic voting
Proportional representation Party-list List type Open list Closed list Localized list Spare vote Apportionment Highest averages Largest remainders National remnant Biproportional apportionment Single transferable vote (Quota methods) Hare STV (Gregory · Wright) Schulze STV CPO-STV Single non-transferable vote Single divisible vote Approval-based committee Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Weighted and Fractional social choice Direct representation Interactive representation Liquid democracy Maximal lottery
Mixed systems By type of representation Winner-take-most Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote Scorporo Double simultaneous vote Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Voting system criteria Spoiler-resistance Condorcet criterion Smith independence Spoiler independence Clone independence Strategy-resistance No lesser evil voting IIA Later-no-harm Later-no-help Rational response Participation criterion Monotonicity criterion Reversal symmetry
Social and collective choice Impossibility theorems Arrow's theorem Impossibility of majority-rule Moulin's impossibility theorem Gibbard's theorem Fishburn's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Campbell-Kelly theorem Harsanyi's utilitarian theorem Tournament sets Smith set Landau set Copeland set Split-cycle set Bipartisan set Tournament solution
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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※