Condorcet domains of tiling type

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.

► We propose a method of constructing large Condorcet domains by use of rhombus tiling diagrams.
► We explain that this method unifies constructions of Condorcet domains known early.
► We show that three conjectures on the maximal size of those Condorcet domains are, in fact, equivalent and provide a counterexample to them.