Minimal retentive sets in tournaments
نویسندگان
چکیده
منابع مشابه
Minimal retentive sets in tournaments
Many problems in multiagent decision making can be addressed using tournament solutions, i.e., functions that associate with each complete and asymmetric relation on a set of alternatives a non-empty subset of the alternatives. For a given tournament solution S, Schwartz calls a set of alternatives S-retentive if it satisfies a natural stability criterion with respect to S. He then recursively ...
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In 2011, Brandt proposed a new tournament solution called the minimal extending set (ME). It was conjectured that ME satisfies a large number of desirable properties. In this paper, we non-constructively show that ME fails to satisfy most of these properties. However, no concrete examples of these violations are known and it appears that ME satisfies these properties for all practical purposes....
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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, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...
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ژورنال
عنوان ژورنال: Social Choice and Welfare
سال: 2013
ISSN: 0176-1714,1432-217X
DOI: 10.1007/s00355-013-0740-4