Abstract
A Condorcet domain is a subset of the set of linear orders on a finite set of candidates (alternatives to vote), such that if voters preferences are linear orders belonging to this subset, then the simple majority rule does not yield cycles. It is well-known that the set of linear orders is the Bruhat lattice. We prove that a maximal Condorcet domain is a distributive sublattice in the Bruhat lattice. An explicit lattice formula for the simple majority rule is given. We introduce the notion of a symmetric Condorcet domain and characterize symmetric Condorcet domains of maximal size.
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Danilov, V.I., Koshevoy, G.A. Maximal Condorcet Domains. Order 30, 181–194 (2013). https://doi.org/10.1007/s11083-011-9235-z
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DOI: https://doi.org/10.1007/s11083-011-9235-z