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| Tideman's method | |
|---|---|
| Name | Tideman's method |
| Other names | Ranked Pairs |
| Inventor | Nicolaus Tideman |
| Introduced | 1987 |
| Type | Condorcet method |
| Uses | Preferential voting |
Tideman's method is a Condorcet voting method devised by Nicolaus Tideman that selects a winner by considering pairwise preferences and locking in the strongest victories without creating cycles. It is also known as Ranked Pairs and has been discussed in contexts involving electoral reform debates in United Kingdom, United States, Canada, Australia, and New Zealand. The method has been compared with systems championed by figures associated with Arrow's impossibility theorem, Kenneth Arrow, and with practical trials such as those by the Ministry of Justice (United Kingdom) and organizations like the Electoral Reform Society.
Tideman's method is a sequential procedure operating on pairwise majority comparisons among alternatives, drawing on ideas from Condorcet, Marquis de Condorcet, and later formalizations by scholars linked to Kenneth Arrow and Amartya Sen. It constructs a directed graph of candidates akin to analyses in work by Harold Hotelling and game-theoretic treatments by John Nash, then resolves cycles by locking pairwise edges in order of decreasing strength similar to rankings studied in research by Duncan Black and in analyses published in journals like those of American Political Science Association and The Journal of Economic Theory.
The process begins with computing pairwise tallies between each pair of candidates, a calculation routine comparable to tabulations done in Australian Electoral Commission reports and referenced in manuals from institutions like the Federal Election Commission (United States). Each pairwise margin is then ordered from largest to smallest; ties are treated according to predefined tie-breaking rules often modeled after protocols used by bodies such as Organisation for Economic Co-operation and Development panels. Edges representing victories are "locked in" sequentially if and only if adding the edge does not create a directed cycle, echoing cycle-avoidance techniques explored in graph theory by Paul Erdős and Alfred Rényi. The final locked graph yields a ranking from which the top candidate is declared winner, a mechanism discussed alongside other protocols promoted by FairVote and analyzed in studies at universities like Harvard University, Stanford University, and Massachusetts Institute of Technology.
Tideman's method satisfies the Condorcet criterion, meaning it elects a candidate who would beat each other candidate in head-to-head contests; this property is central to works by Condorcet and commentators such as Richard F. Fenno and Maurice Duverger. It also meets monotonicity in many practical cases and resists certain strategic manipulation compared to plurality systems criticized in analyses by Anthony Downs and Ronald D. Lee. However, it does not satisfy all criteria simultaneously, as framed in discussions of Arrow's impossibility theorem and counterexamples presented by scholars like Kenneth Arrow and Amartya Sen. Its ability to produce a complete ranking has been used in comparative constitutional studies by institutions such as United Nations research bodies and by electoral commissions exemplified by the Civil Service Commission (United Kingdom).
Simplified examples illustrating Ranked Pairs often reference hypothetical contests among candidates named after public figures used in case studies conducted at institutions such as Yale University, University of Oxford, and London School of Economics. Empirical demonstrations include analyses of party primaries in contexts like the United States presidential primaries and of municipal contests referenced by the City of Cambridge election reports. Classroom demonstrations sometimes adapt scenarios from historic elections like the 1824 United States presidential election to show Condorcet cycles and how Ranked Pairs resolves them, similar to pedagogical examples used at Princeton University and Columbia University.
Ranked Pairs is compared frequently with the Schulze method, Borda count, Instant-runoff voting, Approval voting, and Plurality voting. Unlike Borda count—which uses point weights as in systems analyzed by Jean-Charles de Borda—Ranked Pairs relies strictly on pairwise strengths. Its approach to cycles contrasts with the path-based resolution in the Schulze method, a distinction debated in comparative studies by scholars at University of California, Berkeley and London School of Economics. Discussions in governmental reports from bodies like the Electoral Commission (United Kingdom) and scholarly reviews in Public Choice (journal) often weigh Ranked Pairs' adherence to Condorcet principles against criteria failures highlighted by researchers at Princeton University and University of Michigan.
Practical implementations of Ranked Pairs appear in software packages developed by academic projects at MIT Media Laboratory, open-source communities such as GitHub, and electoral reform organizations like FairVote and Electoral Reform Society. Some political organizations and professional associations have modeled internal decision rules on Ranked Pairs during nominations and committee selections, similar to procedures employed by groups including Democratic National Committee and Labour Party (UK). Implementations in online voting platforms often incorporate tie-breaking heuristics inspired by conventions from international institutions such as European Union working groups.
Critiques of Tideman's method highlight computational complexity for large candidate sets—an issue addressed in algorithmic research at Carnegie Mellon University and University of Toronto—and potential sensitivity to tie-breaking rules documented in analyses by Oxford University and Cambridge University scholars. Strategic vulnerabilities exist in specific contexts, paralleling concerns raised in literature by Kenneth Arrow and Amartya Sen about impossibility results. Practical barriers to adoption include voter education challenges observed in referendums like those advocated by the Electoral Reform Society and resistance noted in reports by national bodies such as the Australian Electoral Commission and the Federal Election Commission (United States).