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

Authors:
Fuad Aleskerov;Andrey Subochev
Affiliations:
DeCAn Lab and Department of Mathematics for Economics, National Research University Higher School of Economics, Moscow, Russia and Institute of Control Sciences, Russian Academy of Sciences, Mosco ...;DeCAn Lab and Department of Mathematics for Economics, National Research University Higher School of Economics, Moscow, Russia
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

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.