Minimal Stable Sets in Tournaments

Details Minimal Stable Sets in Tournaments Minimal Stable Sets in Tournaments

2008-03-14

arxiv.org/abs/0803.2138v4

Mathematics

Combinatorics

29 pages, 4 figures, changed content

Scientific paper

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.

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