Theory and Decision

, Volume 86, Issue 1, pp 107–121 | Cite as

A refinement of the uncovered set in tournaments

  • Weibin HanEmail author
  • Adrian Van Deemen


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.


Uncovered set Unsurpassed set Copeland winner set Monotonicity 



We would like to thank the anonymous referees and the editor in charge for their excellent comments and insightful remarks. The authors are also grateful to Dr. Jean Derks whose advices and comments improved the paper substantially. Preliminary results of this paper were presented at the 13th Meeting of the Society for Social Choice and Welfare (Lund, Sweden, June 2016). All mistakes are our responsibility. This research was supported by SCNU under the Project No. 508/8S0253.


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Authors and Affiliations

  1. 1.School of Economics and ManagementSouth China Normal University, Guangzhou Higher Education Mega CenterGuangzhouPeople’s Republic of China
  2. 2.Institute for Management ResearchRadboud University NijmegenNijmegenThe Netherlands

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