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A refinement of the uncovered set in tournaments

Author

Listed:
  • Weibin Han

    (South China Normal University, Guangzhou Higher Education Mega Center)

  • Adrian Deemen

    (Radboud University Nijmegen)

Abstract

We introduce a new solution for tournaments called the unsurpassed set. This solution lies between the uncovered set and the Copeland winner set. We show that this solution is more decisive than the uncovered set in discriminating among alternatives, and avoids a deficiency of the Copeland winner set. Moreover, the unsurpassed set is more sensitive than the uncovered set but less sensitive than the Copeland winner set to the reinforcement of the chosen alternatives. Besides, it turns out that this solution violates the other standard properties including independence of unchosen alternatives, stability, composition consistency and indempotency.

Suggested Citation

  • Weibin Han & Adrian Deemen, 2019. "A refinement of the uncovered set in tournaments," Theory and Decision, Springer, vol. 86(1), pages 107-121, February.
    • Handle: RePEc:kap:theord:v:86:y:2019:i:1:d:10.1007_s11238-018-9676-6
    DOI: 10.1007/s11238-018-9676-6
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    References listed on IDEAS

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    1. 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.
    2. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    3. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    4. İpek Özkal-Sanver & M. Sanver, 2010. "A new monotonicity condition for tournament solutions," Theory and Decision, Springer, vol. 69(3), pages 439-452, September.
    5. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    6. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    7. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    8. Deb, Rajat, 1977. "On Schwartz's rule," Journal of Economic Theory, Elsevier, vol. 16(1), pages 103-110, October.
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    Cited by:

    1. Yusufcan Demirkan & Boyao Li, 2023. "Individual choice under social influence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 585-606, August.
    2. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    3. Yihao Luo & Jinhui Pang & Weibin Han & Huafei Sun, 2021. "New Solution based on Hodge Decomposition for Abstract Games," Papers 2109.14539, arXiv.org, revised Jan 2024.

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