Permutation-Based Randomised Tournament Solutions
Airiau, Stéphane; Kruger, Justin (2017), Permutation-Based Randomised Tournament Solutions, Multi-Agent Systems and Agreement Technologies - 15th European Conference, EUMAS 2017, and 5th International Conference, AT 2017, Evry, France, December 14-15, 2017, Revised Selected Papers, 2017
TypeCommunication / Conférence
Conference titleMulti-Agent Systems and Agreement Technologies - 15th European Conference, EUMAS 2017, and 5th International Conference, AT 2017, Evry, France, December 14-15, 2017, Revised Selected Papers
Book authorFrancesco Belardinelli and Estefania Argente
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Abstract (EN)Voting rules that are based on the majority graph typically output large sets of winners. In this full original paper our goal is to investigate a general method which leads to randomized version of such rules. We use the idea of parallel universes, where each universe is connected with a permutation over alternatives. The permutation allows us to construct resolute voting rules (i.e. rules that always choose unique winners). Such resolute rules can be constructed in a variety of ways: we consider using binary voting trees to select a single alternative. In turn this permits the construction of neutral rules that output the set the possible winners of every parallel universe. The question of which rules can be constructed in this way has already been partially studied under the heading of agenda implementability. We further propose a randomised version in which the probability of being the winner is the ratio of universes in which the alternative wins. We also briefly consider (typically novel) rules that elect the alternatives that have maximal winning probability. These rules typically output small sets of winners, thus provide refinements of known tournament solutions.
Subjects / KeywordsTournament; Probabilistic rules; Refinements; Condorcet consistency
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