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Majority rule on rhombus tilings and Condorcet super-domains

We deal with the problem of aggregation of rhombus tilings with the help of a certain natural majority rule. As a 2-dimensional counterpart of the well-known problem of aggregation of linear orders and related Condorcet domains, in this paper we introduce a Condorcet super-domain to be a collection...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2021-03, Vol.292, p.85-96
Main Authors: Danilov, Vladimir I., Karzanov, Alexander V., Koshevoy, Gleb A.
Format: Article
Language:English
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Summary:We deal with the problem of aggregation of rhombus tilings with the help of a certain natural majority rule. As a 2-dimensional counterpart of the well-known problem of aggregation of linear orders and related Condorcet domains, in this paper we introduce a Condorcet super-domain to be a collection of rhombus tilings on a zonogon Z(n;2) satisfying the property that whenever the voting designs (ballots) belong to this collection, then the majority rule produces a rhombus tiling as well. A study of Condorcet super-domains and methods of constructing them form the main subject of this paper.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.12.029