Journal of Global Optimization

, Volume 56, Issue 2, pp 737–756 | Cite as

Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule

  • Fuad Aleskerov
  • Andrey SubochevEmail author


Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped set, classes of k-stable alternatives and k-stable sets. The main focus of the paper is to construct a unified matrix-vector representation of a tournament solution in order to get a convenient algorithm for its calculation. New versions of some solutions are also proposed.


Solution concept Majority relation Tournament Matrix-vector representation Condorcet winner Core Top cycle Uncovered set Weakly stable set Externally stable set Uncaptured set Untrapped set k-stable alternative k-stable set 


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Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.DeCAn Lab and Department of Mathematics for EconomicsNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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