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| Kemeny–Young method | |
|---|---|
| Name | Kemeny–Young method |
| Type | Voting method |
| Introduced | 1959 |
| Inventor | John G. Kemeny, Kenneth Young |
| Usage | Social choice theory, consensus ranking |
Kemeny–Young method is a consensus-based rank aggregation procedure developed in the context of mathematical voting theory and social choice theory in the mid-20th century. It produces a collective ranking by maximizing agreement with individual preferences, combining ideas from Condorcet method debates, metric aggregation, and statistical consensus measures. The method has been discussed in relation to results by Arrow's impossibility theorem, Black's theorem, and the work of H. A. Simon and Kenneth Arrow on preference aggregation.
The method was formalized by John G. Kemeny and later analyzed by Kenneth Young; it seeks a ranking that minimizes discord with ballots in a manner related to pairwise comparison outcomes like those in the Condorcet paradox. It has been compared to aggregation techniques applied in contexts involving Amartya Sen, Kenneth Arrow, Duncan Black, Maurice Allais, and debates around Condorcet-consistent procedures. Scholars in institutions such as Princeton University, Harvard University, Stanford University, and University of Cambridge have examined its theoretical properties and practical implications.
Formally, given a set of candidates and a profile of ballots, the procedure assigns a score to each possible total order equal to the sum of pairwise agreements with ballots, akin to the Kemeny distance used in permutation metrics studied by researchers at Bell Labs, Bell Telephone Laboratories, and in combinatorial optimization literature influenced by Harold Kuhn and John Nash. The winning ranking maximizes this Kemeny score, which can be viewed as minimizing the sum of Kendall tau distances to voter rankings, a concept related to work by Maurice Kendall and Barbara M. Fredrickson. Implementation often uses search, branch-and-bound, or integer programming techniques developed in the style of Richard Karp and Jack Edmonds.
The method is Condorcet-consistent: if a candidate beats every other candidate in pairwise comparison, they top the Kemeny ranking; this links the method to analyses by Marie Jean Antoine Nicolas de Caritat, Marquis de Condorcet and subsequent commentators such as Ronald A. Fisher and John von Neumann. It satisfies neutrality and anonymity akin to desiderata articulated by Kenneth Arrow but confronts Arrow-style impossibility constraints; comparisons to Borda count and plurality voting highlight trade-offs explored by Nobel laureate economists including Amartya Sen and Kenneth Arrow. The method minimizes Kendall tau distance, relating to axiomatic frameworks proposed by Peter C. Fishburn and Saari, Donald G.. It also adheres to reinforcement and consistency properties investigated by Geoffrey Canright and William S. Zwicker.
Computing an exact Kemeny ranking is NP-hard, a complexity result connected to reductions used by Richard Karp and Michael Garey and studied in theoretical computer science communities at MIT and Carnegie Mellon University. Practical algorithms include exact integer linear programming formulations influenced by George Dantzig and branch-and-bound approaches associated with work by Donald Knuth and Elliot Winston. Heuristic and approximation strategies draw on local search, Markov chain Monte Carlo methods reminiscent of algorithms from Alan Turing's probabilistic work, and fixed-parameter tractable algorithms developed in the spirit of research from ETH Zurich and University of Oxford groups.
Extensions introduce weights for voters or pairs, paralleling weighted aggregation in studies by Kenneth Arrow collaborators and applications in information retrieval aligned with work at Google and Bell Labs. Other variants integrate distance metrics beyond Kendall tau, inspired by permutation aggregation research at INRIA and Microsoft Research. Multicriterion and participatory adaptations relate to proposals by scholars at Columbia University and University of California, Berkeley who examined hybrid methods combining Kemeny-like objectives with approval voting and runoff schemes discussed in literature involving Maurice Allais and Vernon L. Smith.
Kemeny rankings have been applied in political science case studies comparing party preferences in contexts like analyses by Condorcet scholars and election analyses at Elections Canada and the United Kingdom Electoral Commission. In sports, ranking teams or players using pairwise match outcomes links to systems used in research by Bill James and analytics groups at ESPN and FiveThirtyEight. Information retrieval and meta-search problems leverage Kemeny aggregation in projects at Stanford University and Google Research, while bioinformatics and phylogenetics use consensus ranking techniques akin to Kemeny methods in studies from Max Planck Society and Broad Institute.
Critics emphasize computational infeasibility for large candidate sets, echoing complexity concerns raised by Michael Garey and David Johnson, and question sensitivity to small changes in ballots similar to instability discussions by Condorcet commentators and analysts at University of Chicago. Debates compare it to simpler methods like Borda count or plurality systems championed in various legislative reform proposals and studied by scholars at Yale University and Princeton University, noting trade-offs between normative appeal and pragmatic deployability. Other critiques focus on strategic vulnerability and normative interpretation issues analyzed in game-theoretic frameworks by John H. Conway and Lloyd S. Shapley.
Category:Voting methods