5 research outputs found

    A tournament of order 24 with two disjoint TEQ-retentive sets

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    Brandt et al. (2013) have recently disproved a conjecture by Schwartz (1990) by non-constructively showing the existence of a counterexample with about 10 136 alternatives. We provide a concrete counterexample for Schwartz’s conjecture with only 24 alternatives

    Minimal Stable Sets in Tournaments

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    We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, which encompasses the top cycle, the uncovered set, the Banks set, the minimal covering set, the tournament equilibrium set, the Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.Comment: 29 pages, 4 figures, changed conten
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