5 research outputs found
A tournament of order 24 with two disjoint TEQ-retentive sets
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
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