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A note on the McKelvey uncovered set and Pareto optimality

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  • Felix Brandt
  • Christian Geist
  • Paul Harrenstein

Abstract

We consider the notion of Pareto optimality under the assumption that only the pairwise majority relation is known and show that the set of necessarily Pareto optimal alternatives coincides with the McKelvey uncovered set. As a consequence, the McKelvey uncovered set constitutes the coarsest Pareto optimal majoritarian social choice function. Moreover, every majority relation is induced by a preference profile in which the uncovered alternatives precisely coincide with the Pareto optimal ones. We furthermore discuss the structure of the McKelvey covering relation and the McKelvey uncovered set. Copyright Springer-Verlag Berlin Heidelberg 2016

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  • Felix Brandt & Christian Geist & Paul Harrenstein, 2016. "A note on the McKelvey uncovered set and Pareto optimality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 81-91, January.
    • Handle: RePEc:spr:sochwe:v:46:y:2016:i:1:p:81-91
    DOI: 10.1007/s00355-015-0904-5
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    References listed on IDEAS

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    1. Bordes, Georges, 1983. "On the possibility of reasonable consistent majoritarian choice: Some positive results," Journal of Economic Theory, Elsevier, vol. 31(1), pages 122-132, October.
    2. Josep E. Peris & BegoÓa Subiza, 1999. "Condorcet choice correspondences for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 217-231.
    3. Gaertner, Wulf, 2009. "A Primer in Social Choice Theory: Revised Edition," OUP Catalogue, Oxford University Press, number 9780199565306.
    4. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
    5. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
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    Cited by:

    1. Costa, Matheus & Riella, Gil, 2022. "King-chicken choice correspondences," Mathematical Social Sciences, Elsevier, vol. 120(C), pages 113-118.
    2. Florian Brandl & Felix Brandt & Christian Stricker, 2022. "An analytical and experimental comparison of maximal lottery schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 5-38, January.
    3. Weibin Han & Adrian Deemen, 2019. "A refinement of the uncovered set in tournaments," Theory and Decision, Springer, vol. 86(1), pages 107-121, February.
    4. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    5. Horan, Sean & Sprumont, Yves, 2022. "Two-stage majoritarian choice," Theoretical Economics, Econometric Society, vol. 17(2), May.

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