Coombs' method | Rich X Wiki Search

Social choice and electoral systems
A joint Politics and Economics series

Social choice Mechanism design Comparative politics Comparison List (By country)
Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Party block voting Plurality block voting Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin, Mdn. Bucklin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery Random ballot Semi-proportional representation Cumulative SNTV Limited voting
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Wasted vote Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem VCG mechanism Quadratic voting
Politics portal Economics portal Mathematics portal
v t e

Coombs' method is a ranked voting system. Like instant-runoff (IRV-RCV), Coombs' method is a sequential-loser method, where the last-place finisher according to one method is eliminated in each round. However, unlike in instant-runoff, each round has electors voting against their least-favorite candidate; the candidate ranked last by the most voters is eliminated.^[1]

The method fails several voting system criteria, including Condorcet's majority criterion, monotonicity, participation, and clone-independence.^[2]^[3] However, it does satisfy Black's single-peaked median voter criterion.^[1]^{: prop. 2}

^ ^a ^b Grofman, Bernard; Feld, Scott L. (2004-12-01). "If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule". Electoral Studies. 23 (4): 641–659. doi:10.1016/j.electstud.2003.08.001. ISSN 0261-3794.
^ Nurmi, Hannu (1983-04-01). "Voting Procedures: A Summary Analysis". British Journal of Political Science. 13 (2). Cambridge University Press: 181–208. doi:10.1017/S0007123400003215. Retrieved 2024-05-19.
^ Nurmi, Hannu (2012-12-06). Comparing Voting systems. Theory and Decision Library A. Vol. 3 (Illustrated ed.). Springer Dordrecht. p. 209. doi:10.1007/978-94-009-3985-1. ISBN 9789400939851.