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| Ranked Pairs | |
|---|---|
| Name | Ranked Pairs |
| Other names | Tideman method |
| Inventor | Nicolaus Tideman |
| Year | 1987 |
| Genre | Voting system |
| Domain | Elections |
Ranked Pairs is a voting method developed to produce a single collective ranking or winner from individual ranked ballots. It constructs outcomes by examining pairwise contests between alternatives and "locking in" victories in order of decreasing margin, subject to avoiding cycles; the method aims to respect majority preferences while producing a complete ordering. The procedure has been studied in the contexts of social choice theory, electoral reform, and algorithmic decision-making by scholars and practitioners across institutions and commissions.
Ranked Pairs was proposed by Nicolaus Tideman and later discussed in venues involving American Political Science Association meetings, analyses in journals frequented by contributors from Harvard University, Massachusetts Institute of Technology, and Princeton University. It arises amid historical debates traced through work by Kenneth Arrow, Amartya Sen, John Harsanyi, and Kenneth J. Arrow's theorem discussions at conferences like the International Political Science Association. The method is relevant to reform efforts associated with organizations such as FairVote, municipal experiments in Minneapolis, and comparative studies involving systems like Condorcet method, Borda count, Instant-runoff voting, and Approval voting.
The Ranked Pairs algorithm begins by computing pairwise tallies between each pair of alternatives, a process employed in analyses by researchers at Stanford University, Yale University, and University of Oxford. Pairs are sorted by margin magnitude descending, a sorting approach familiar in algorithms discussed at ACM SIGMOD and in textbooks used at Carnegie Mellon University. Each pairwise victory is "locked" into a directed graph unless doing so would create a directed cycle, echoing graph-theoretic concepts from Erdős–Rényi random graph investigations and algorithms from Donald Knuth's corpus. Implementation details reference data structures and complexity analyses taught at Massachusetts Institute of Technology and practiced by engineers at Google and Microsoft.
Ranked Pairs satisfies several normative criteria emphasized by scholars such as Amartya Sen and Kenneth Arrow: it is a Condorcet-consistent method, selecting the Condorcet winner when one exists, a property highlighted in comparative work at Princeton University and University of California, Berkeley. It also meets monotonicity under certain formalizations examined in papers from London School of Economics and Columbia University. However, it fails some other criteria studied by Peter C. Fishburn and analysts associated with Cornell University and University of Michigan, such as certain versions of independence or reinforcement in path-dependent contexts discussed at European Consortium for Political Research conferences.
Empirical and illustrative applications of Ranked Pairs have appeared in municipal adoption debates in Burlington, Vermont, academic course elections at Harvard University and University of Cambridge, and internal selections in organizations like IEEE and ACM. Comparative examples often feature hypothetical contests invoking historical figures and entities from United States presidential elections, such as pairwise comparisons reminiscent of matchups involving Abraham Lincoln, Franklin D. Roosevelt, Theodore Roosevelt, John F. Kennedy, and Ronald Reagan as pedagogical devices in textbooks from Oxford University Press and Cambridge University Press.
Ranked Pairs exhibits resistance to some strategic manipulations studied in game-theoretic work by Kenneth Arrow, Amartya Sen, and John Harsanyi, with computational complexity analyses echoing themes from Leslie Valiant's complexity theory and empirical susceptibility comparisons involving Bohdan Paczyński-style simulations. Nevertheless, research from groups at Stanford University, University of California, Los Angeles, and New York University indicates vulnerabilities to tactical voting and coalition strategies in certain configurations, paralleling insights from studies of Instant-runoff voting and Plurality voting.
Several variants of the Ranked Pairs procedure have been proposed and analyzed by scholars affiliated with University of Warwick, University of Edinburgh, Delft University of Technology, and University of Tokyo. These include tie-breaking rules influenced by proposals from Condorcet-oriented reformers, modifications adapting to multi-winner contexts related to research at Carnegie Mellon University and University of Minnesota, and extensions for participatory budgeting and proportional representation studied by researchers at London School of Economics and European University Institute.
Computational inquiries into Ranked Pairs draw on methods from theoretical computer science communities such as ACM, IEEE, and institutes like Courant Institute of Mathematical Sciences. Determining winners under standard Ranked Pairs implementations is polynomial-time computable using sorting and cycle-detection algorithms familiar from courses at Massachusetts Institute of Technology and Stanford University. Complexity results for strategic manipulation, control, and winner determination under certain generalized or multi-winner variants have been shown to reach NP-hardness in research reported from Cornell University, University of Toronto, and University of Maryland.