The one-dimensional Euclidean domain: finitely many obstructions are not enough
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We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.
This research has been supported by COST Action IC1205 on Computational Social Choice. Jiehua Chen acknowledges support by the Studienstiftung des Deutschen Volkes. Kirk Pruhs is supported in part by NSF Grants CCF-1115575, CNS-1253218, CCF-1421508, and an IBM Faculty Award. Gerhard Woeginger acknowledges support by the Zwaartekracht NETWORKS grant of NWO, and by the Alexander von Humboldt Foundation, Bonn, Germany.
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