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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

Type
Communication / Conférence
Date
2017
Conference title
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
Conference date
2017
Book author
Francesco Belardinelli and Estefania Argente
Publisher
Springer International Publishing
Published in
Berlin Heidelberg
ISBN
978-3-030-01712-5
Pages
235-250
Publication identifier
10.1007/978-3-030-01713-2_17
Metadata
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Author(s)
Airiau, Stéphane cc
Kruger, Justin
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 / Keywords
Tournament; Probabilistic rules; Refinements; Condorcet consistency

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