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Showing papers by "Center for Discrete Mathematics and Theoretical Computer Science published in 2004"


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01 Jan 2004
TL;DR: In this paper, the cardinality and structure of maximal sets of permutations for which majority rule produces transitive results (consistent sets) are studied. But the results are restricted to the weak Bruhat order.
Abstract: The Marquis du Condorcet recognized 200 years ago that majority rule can produce intransitive group preferences if the domain of possible (transitive) individual preference orders is unrestricted. We present results on the cardinality and structure of those maximal sets of permutations for which majority rule produces transitive results (consistent sets). Consistent sets that contain a maximal chain in the Weak Bruhat Order inherit from it an upper semimodular sublattice structure. They are intrinsically related to a special class of hamiltonian graphs called persistent graphs. These graphs in turn have a clean geometric interpretation: they are precisely visibility graphs of staircase polygons. We highlight the main tools used to prove these connections and indicate possible social choice and computational research directions.

6 citations