Majority relations for Condorcet domains of tiling type

Condorcet domains are subsets of permutations arising in voting theory: regarding their permutations as preference orders on a list of candidates, one avoids Condorcet's paradox when aggregating the preferences via a simple majority relation. We use poset theory to show that, for the subclass of Condorcet domains of tiling type, the majority rule has stronger properties. We then develop techniques to predict the majority rule explicitly for the uniform vote tally on Condorcet domains of tiling type, and apply this to several well-known examples.