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| Black's method | |
|---|---|
| Name | Black's method |
| Inventor | Walter L. Black |
| Introduced | 1958 |
| Type | Condorcet-compliant, Condorcet–Hare hybrid |
| Uses | single-winner elections, committee selection |
Black's method is a single-winner voting procedure that combines elements of the Condorcet method and the Borda count. It selects a Condorcet winner when one exists and otherwise elects the Borda count winner, integrating ideas related to Kenneth Arrow, Condorcet paradox, Charles Dodgson, and Jean-Charles de Borda. Designed to balance majority rule tendencies and consensus aggregation, it appears in comparative analyses alongside methods such as Instant-runoff voting, Kemeny–Young method, and plurality voting.
Black's method was proposed by Walter L. Black in 1958 and has been discussed in literature alongside figures and institutions like Kenneth Arrow, Amartya Sen, Harvard University, Princeton University, Stanford University, and the Institute of Mathematical Statistics. Its formulation draws on the historical lineage of voting theory including Marquis de Condorcet, Jean-Charles de Borda, and later formalizers such as Lewis Carroll (Charles Dodgson) and researchers at Bell Labs and RAND Corporation. Debates about Black's method occur in venues such as American Political Science Association conferences, European Consortium for Political Research meetings, and publications from MIT Press and Cambridge University Press.
Black's method is defined by two sequential rules rooted in concepts from the work of Condorcet and Borda: - If a Condorcet winner exists—an option preferred pairwise against every other option—the method selects that candidate, invoking the pairwise comparison framework associated with Condorcet and analyzed by scholars at University of Oxford and University of Cambridge. - If no Condorcet winner exists, the method elects the Borda count winner, using the rank-aggregation scoring originally proposed by Jean-Charles de Borda and studied by researchers affiliated with Columbia University and Yale University.
Practically, the procedure requires ballots that provide complete rankings as in elections studied by Electoral Reform Society analysts and polling organizations like Pew Research Center and Gallup. Implementation may use algorithms developed by teams at Google, Microsoft Research, or academic groups at Carnegie Mellon University and ETH Zurich.
Black's method satisfies several normative and mathematical properties discussed by theorists such as Kenneth Arrow, Amartya Sen, and Donald Saari: - Condorcet criterion: satisfies when a Condorcet winner exists, aligning with analyses from Nobel Memorial Prize laureates in economics who study social choice. - Pareto efficiency: typically considered in evaluations by scholars at London School of Economics and University of Chicago. - Monotonicity and independence properties: researched in contexts involving Arrow's impossibility theorem and Gibbard–Satterthwaite theorem, with commentary from Douglas Hofstadter and methodologists at RAND Corporation.
Mathematical critiques and proofs have been published by academics at Princeton University, University of Michigan, and University of California, Berkeley, linking to combinatorial and game-theoretic frameworks advanced by John Nash and Robert Aumann.
Black's method is often compared to other systems: - Against Condorcet methods like the Kemeny–Young method and Smith/Minimax, Black favors a fallback to Borda count rather than ranking aggregation by distance metrics studied at INRIA and Max Planck Institute. - Versus Instant-runoff voting and plurality voting, Black generally produces more consensus-oriented outcomes, a contrast highlighted in analyses by FairVote and scholars at University of Oxford and Australian National University. - Relative to Approval voting, which was promoted by advocates such as Steven Brams and Peter Fishburn, Black requires full rankings and thus interacts differently with strategic considerations examined by Nobel laureate critics.
Empirical comparisons have been conducted in studies from Massachusetts Institute of Technology, University of Toronto, and University of Melbourne.
Black's method has been proposed for use in academic committees, professional societies, and organizational elections where complete preference rankings are feasible, including bodies like the American Mathematical Society, American Physical Society, IEEE, and university senates at Harvard University and University of California campuses. It has seen theoretical application in multi-agent decision scenarios studied at Cornell University and in algorithmic choice frameworks developed by teams at Stanford University and Imperial College London.
Simulation studies by researchers at University of Minnesota, University of Pennsylvania, and Duke University examine Black's performance in political primary contexts, corporate board selections, and award committees such as those at Royal Society and Nobel Committee-style panels.
Critiques stem from both normative and practical concerns: - Vulnerability to strategic ranking and tactical voting, discussed by Gibbard and Satterthwaite, with applied critiques in work from Yale University and Princeton University. - Dependence on complete rankings makes it less practical for large-scale public elections studied by Electoral Reform Society and Brennan Center for Justice. - Possible violations of monotonicity or other desirable axioms noted in analyses from University of Chicago and London School of Economics analysts.
Comparative performance under realistic voter behavior has been questioned in studies by RAND Corporation, Pew Research Center, and academic teams at University of California, Berkeley.
Extensions of Black's method explored by scholars include hybridizations with runoff mechanisms and weighted scoring, proposed in literature from MIT, ETH Zurich, and INRIA. Variants integrate methods like Schulze method head-to-head analysis, adaptations with partial rankings used by Gallup and Pew Research Center, and computational refinements from Microsoft Research and Google Research. These extensions intersect with research on strategic resistance by Amartya Sen-influenced theorists and algorithmic social choice agendas at Carnegie Mellon University and University of Oxford.
Category:Voting methods