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

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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.

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Authors and Affiliations

  1. DeCAn Lab and Department of Mathematics for Economics, National Research University Higher School of Economics, Moscow, Russia

    Fuad Aleskerov & Andrey Subochev

  2. Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Fuad Aleskerov

Authors
  1. Fuad Aleskerov
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  2. Andrey Subochev
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Correspondence to Andrey Subochev.

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Aleskerov, F., Subochev, A. Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule. J Glob Optim 56, 737–756 (2013). https://doi.org/10.1007/s10898-012-9907-2

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  • DOI: https://doi.org/10.1007/s10898-012-9907-2

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