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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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Published in: | Discrete Applied Mathematics 2021-03, Vol.292, p.85-96 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/j.dam.2020.12.029 |