A characterization of the single-crossing domain
We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient way to decide whether a preference profile is single-crossing.
KeywordsSocial Choice Choice Rule Social Choice Function Condorcet Winner Strategic Vote
This research was started and partially conducted during the Schloss Dagstuhl seminar 12101 on “Computation and Incentives in Social Choice”. We are grateful to the organizers of this seminar (Edith Elkind, Christian Klamler, Jeffrey Rosenschein, M. Remzi Sanver) and to the Dagstuhl staff for providing a stimulating atmosphere. Robert Bredereck is supported by the DFG, research project PAWS, NI 369/10. Jiehua Chen is supported by the Studienstiftung des Deutschen Volkes. Gerhard Woeginger acknowledges support by the Netherlands Organization for Scientific Research (NWO), Grant 639.033.403, and by DIAMANT (an NWO mathematics cluster).
- Ballester MA, Haeringer G (2011) A characterization of the single-peaked domain. Soc Choice Welf 36(2):305–322Google Scholar
- Elkind E, Faliszewski P, Slinko A (2012) Clone structures in voters’ preferences. In: Proceedings of the 13th ACM conference on electronic commerce, pp 496–513Google Scholar
- Hoffman AJ, Kolen AWJ, Sakarovitch M (1985) Totally-balanced and greedy matrices. SIAM J Alg Discret Methods 6(4):721–730Google Scholar
- Kuratowski K (1930) Sur le problème des courbes gauches en topologie. Fundamenta Mathematicae 15:271–283Google Scholar
- Lekkerkerker CG, Boland JC (1962) Representation of a finite graph by a set of intervals on the real line. Fundamenta Mathematicae 51:45–64Google Scholar
- Saporiti A (2009) Strategy-proofness and single-crossing. Theor Econ 4(2):127–163Google Scholar