Condorcet domains of tiling type |
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Authors: | Vladimir I Danilov Alexander V Karzanov Gleb Koshevoy |
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Institution: | 1. Central Institute of Economics and Mathematics of the RAS; 47, Nakhimovskii Prospect, 117418 Moscow, Russia;2. Institute for System Analysis of the RAS; 9, Prospect 60 Let Oktyabrya, 117312 Moscow, Russia |
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Abstract: | A Condorcet domain (CD) is a collection of linear orders on a set of candidates satisfying the following property: for any choice of preferences of voters from this collection, a simple majority rule does not yield cycles. We propose a method of constructing “large” CDs by use of rhombus tiling diagrams and explain that this method unifies several constructions of CDs known earlier. Finally, we show that three conjectures on the maximal sizes of those CDs are, in fact, equivalent and provide a counterexample to them. |
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