Majority rule on rhombus tilings and Condorcet super-domains

Abstract: In this paper we consider a Condorcet domain (CD) formed by a rhombus tiling as a voting design and consider a problem of aggregation of voting designs using majority rule. A Condorcet super-domain is a collection of CDs obtained from rhombus tilings on a zonogone Z(n; 2) with the property that if voting designs (ballots) belong to this collection, then the simple majority rule does not yield cycles. A study of Condorcet super-domains and methods of constructing them form the main subject of this paper.