56 research outputs found
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
Logics of preference when there is no best
Well-behaved preferences (e.g., total pre-orders) are a cornerstone of several areas in artificial intelligence, from knowledge representation, where preferences typically encode likelihood comparisons, to both game and decision theories, where preferences typically encode utility comparisons. Yet weaker (e.g., cyclical) structures of comparison have proven important in a number of areas, from argumentation theory to tournaments and social choice theory. In this paper we provide logical foundations for reasoning about this type of preference structures where no obvious best elements may exist. Concretely, we compare and axiomatize a number of ways in which the concepts of maximality and optimality can be lifted to this general class of preferences. In doing so we expand the scope of the long-standing tradition of the logical analysis of preference
10101 Abstracts Collection -- Computational Foundations of Social Choice
From March 7 to March 12, 2010, the Dagstuhl Seminar 10101
``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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