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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. Copyright Springer Science+Business Media, LLC. 2013

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  • Fuad Aleskerov & Andrey Subochev, 2013. "Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule," Journal of Global Optimization, Springer, vol. 56(2), pages 737-756, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:737-756
    DOI: 10.1007/s10898-012-9907-2
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    1. Alvin E. Roth, 1976. "Subsolutions and the Supercore of Cooperative Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 43-49, February.
    2. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 491-506, April.
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    6. Subochev, Andrey, 2008. "Dominant, weakly stable, uncovered sets: properties and extensions," MPRA Paper 53421, University Library of Munich, Germany.
    7. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
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    Cited by:

    1. Subochev, Andrey & Zakhlebin, Igor, 2014. "Alternative versions of the global competitive industrial performance ranking constructed by methods from social choice theory," MPRA Paper 67462, University Library of Munich, Germany.
    2. Fuad Aleskerov & Sergey Shvydun, 2019. "Allocation of Disputable Zones in the Arctic Region," Group Decision and Negotiation, Springer, vol. 28(1), pages 11-42, February.
    3. Subochev, A., 2016. "How Different Are the Existing Ratings of Russian Economic Journals and How to Unify Them?," Journal of the New Economic Association, New Economic Association, vol. 30(2), pages 181-192.
    4. Fuad T. Aleskerov & Vladimir V. Pislyakov & Andrey N. Subochev, 2014. "Ranking Journals In Economics, Management And Political Science By Social Choice Theory Methods," HSE Working papers WP BRP 27/STI/2014, National Research University Higher School of Economics.
    5. Aleskerov, F., 2013. "Game-Theoretic Modeling: An Attempt of Brief Discussion and a Forecast of Development," Journal of the New Economic Association, New Economic Association, vol. 17(1), pages 181-184.
    6. Scott Moser, 2015. "Majority rule and tournament solutions," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 6, pages 83-101, Edward Elgar Publishing.
    7. Subochev, Andrey & Aleskerov, Fuad & Pislyakov, Vladimir, 2018. "Ranking journals using social choice theory methods: A novel approach in bibliometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 416-429.

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