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| Minimax (electoral system) | |
|---|---|
| Name | Minimax |
| Type | Single-winner, Condorcet-consistent |
| Introduced | 1980s |
| Designer | Multiple proponents |
| Used in | Academic studies |
Minimax (electoral system) is a single-winner voting method that selects the candidate whose worst pairwise defeat is minimal, forming a Condorcet-consistent approach related to pairwise comparison methods. It is situated among Condorcet methods that include Condorcet method, Schulze method, Ranked Pairs, and Copeland's method, and has been discussed in contexts involving electoral reform advocates such as FairVote, scholars connected to Arrow's impossibility theorem, and theoreticians citing work by figures like Kenneth Arrow, William Vickrey, and John H. Smith (mathematician).
Minimax emerged in the late 20th century in literature debating alternatives to plurality systems used in jurisdictions like United Kingdom general election, United States presidential election, and municipal contests examined by Institute for Politics. It operates on ballots similar to those used in Instant-runoff voting and approval voting studies, relying on pairwise tallies as in analyses by researchers from institutions such as Massachusetts Institute of Technology, Stanford University, and University of California, Berkeley. Discussions of Minimax often reference normative frameworks developed by scholars associated with Kenneth Arrow, Amartya Sen, and committees such as the Constitutional Convention in comparative electoral design debates.
Voters rank candidates on ballots analogous to systems taught in courses at Harvard University, Princeton University, and London School of Economics. Ballots are aggregated into pairwise contest matrices similar to those used in examinations of the Condorcet paradox and publications from American Political Science Association. For each candidate, Minimax computes the margin of defeat in every head-to-head contest—metrics comparable to scoring approaches evaluated by researchers at Yale University and University of Oxford. The winner is the candidate with the smallest maximum pairwise loss, a decision rule analyzed alongside methods like Borda count and Kemeny–Young method in journals such as those of American Statistical Association and presentations at conferences like International Symposium on Voting Theory.
Multiple Minimax variants arise by choosing different measures of pairwise defeat: largest margin by votes, largest margin by percentage, or largest losing pair measured by raw pair counts—variants paralleling distinctions studied by groups at Carnegie Mellon University and University of Toronto. Tie-breaking mechanisms include using smallest mean defeat, secondary comparisons akin to the tie procedures in Ranked Pairs, or fallback to Plurality voting counts, mirroring practices debated in reports by Electoral Reform Society and committees such as House of Commons Procedure Committee. Scholarly treatments compare tie rules in papers presented at venues like European Consortium for Political Research and workshops at University of Cambridge.
Minimax satisfies the Condorcet criterion by electing a Condorcet winner when one exists, placing it alongside methods like Schulze method and unlike Plurality voting or First-past-the-post. It fails criteria such as monotonicity in certain configurations examined by researchers influenced by Gibbard–Satterthwaite theorem and analyses by Martin Osborne and Aaron Bramson. The method's behavior under clone independence, reinforcement, and participation criteria has been compared to Kemeny–Young method and Copeland's method in studies from University of Michigan and institutions publishing in Social Choice and Welfare.
Strategic incentives under Minimax have been modeled in game-theoretic work referencing Gibbard–Satterthwaite theorem and equilibrium analyses from scholars at London School of Economics and New York University. Voters may attempt tactical ranking or burying strategies as described in theoretical examples published by researchers affiliated with Princeton University and Duke University. Comparative experiments, including those run by labs at Stanford University and Columbia University, evaluate susceptibility to manipulation relative to Alternative vote and Approval voting, often invoking analytical tools used in studies of Arrow's impossibility theorem and Median voter theorem.
Academic case studies apply Minimax to historical datasets such as preference surveys from Iowa caucuses simulations, party primaries in analyses referencing Democratic National Committee and Republican National Committee data, and public opinion datasets compiled by Pew Research Center and Gallup. Computational experiments by teams at Massachusetts Institute of Technology and University of California, San Diego compare Minimax outcomes with those from Schulze method and Ranked Pairs on synthetic electorates and empirical ballots derived from contests like Australian federal election preference data. Policy reports by Electoral Reform Society and think tanks such as Rand Corporation and Brookings Institution discuss potential impacts for municipal adoption scenarios.
Critics note that Minimax can be sensitive to ballot noise and minor preference shifts, as highlighted in critiques circulated through outlets like The Economist and academic rebuttals from scholars at Yale University and University of Chicago. The method's violation of some voting axioms—such as certain monotonicity and participation variants studied in Social Choice and Welfare—is often raised alongside practical concerns about ballot complexity and voter understanding in contexts like local government referendums and national reform debates framed by Constitutional Court proceedings. Implementation challenges, including public education and administrative counting procedures, mirror issues encountered in transitions to systems such as Instant-runoff voting in jurisdictions studied by FairVote.
Category:Electoral systems