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Regular version of the site

Article

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

Journal of Global Optimization. 2013. Vol. 56. No. 2. P. 737-756.

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.