English

Condorcet domains of tiling type

Combinatorics 2011-08-19 v2

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.

Keywords

Cite

@article{arxiv.1011.2888,
  title  = {Condorcet domains of tiling type},
  author = {Vladimir I. Danilov and Alexander V. Karzanov and Gleb A. Koshevoy},
  journal= {arXiv preprint arXiv:1011.2888},
  year   = {2011}
}

Comments

16 pages. To appear in Discrete Applied Mathematics

R2 v1 2026-06-21T16:42:51.119Z