Condorcet domains of tiling type

Details Condorcet domains of tiling type Condorcet domains of tiling type

2010-11-12

arxiv.org/abs/1011.2888v2

Mathematics

Combinatorics

16 pages. To appear in Discrete Applied Mathematics

Scientific paper

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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