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A characterization of the single-crossing domain

Social Choice and Welfare volume 41, pages 989–998 (2013)Cite this article

Abstract

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.

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References

  • Abello J (1991) The weak Bruhat order of \(\text{ S}_\Sigma, \) consistent sets, and Catalan numbers. SIAM J Discrete Math 4(1):1–16

    Article  Google Scholar 

  • Ballester MA, Haeringer G (2011) A characterization of the single-peaked domain. Soc Choice Welf 36(2):305–322

    Google Scholar 

  • Barberà S, Jackson MO (2004) Choosing how to choose: self-stable majority rules and constitutions. Quart J Econ 119(3):1011–1048

    Article  Google Scholar 

  • Barberà S, Moreno B (2011) Top monotonicity: a common root for single peakedness, single crossing and the median voter result. Games Econ Behav 73(2):345–359

    Article  Google Scholar 

  • Black D (1948) On the rationale of group decision-making. J Politic Econ 56(1):23–34

    Article  Google Scholar 

  • Bóna M (2004) Combinatorics of permutations. Chapman and Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Booth KS, Lueker GS (1976) Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J Comput Syst Sci 13(3):335–379

    Article  Google Scholar 

  • Demange G (1994) Intermediate preferences and stable coalition structures. J Math Econ 23(1):45–58

    Article  Google Scholar 

  • Elkind E, Faliszewski P, Slinko A (2012) Clone structures in voters’ preferences. In: Proceedings of the 13th ACM conference on electronic commerce, pp 496–513

  • Epple D, Platt GJ (1998) Equilibrium and local redistribution in an urban economy when households differ in both preferences and incomes. J Urban Econ 43(1):23–51

    Article  Google Scholar 

  • Galambos Á, Reiner V (2008) Acyclic sets of linear orders via the Bruhat orders. Soc Choice Welf 30(2):245–264

    Article  Google Scholar 

  • Gans JS, Smart M (1996) Majority voting with single-crossing preferences. J Public Econ 59(2):219–237

    Article  Google Scholar 

  • Grandmont JM (1978) Intermediate preferences and the majority rule. Econometrica 46(2):317–330

    Article  Google Scholar 

  • Hoffman AJ, Kolen AWJ, Sakarovitch M (1985) Totally-balanced and greedy matrices. SIAM J Alg Discret Methods 6(4):721–730

    Google Scholar 

  • Inada K (1969) The simple majority decision rule. Econometrica 37(3):490–506

    Article  Google Scholar 

  • Kung FC (2006) An algorithm for stable and equitable coalition structures with public goods. J Public Econ Theory 8(3):345–355

    Article  Google Scholar 

  • Kuratowski K (1930) Sur le problème des courbes gauches en topologie. Fundamenta Mathematicae 15:271–283

    Google Scholar 

  • Lekkerkerker CG, Boland JC (1962) Representation of a finite graph by a set of intervals on the real line. Fundamenta Mathematicae 51:45–64

    Google Scholar 

  • Meltzer AH, Richard SF (1981) A rational theory of the size of government. J Politic Econ 89(5):914–927

    Article  Google Scholar 

  • Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35(4):437–455

    Article  Google Scholar 

  • Roberts KWS (1977) Voting over income tax schedules. J Public Econ 8(3):329–340

    Article  Google Scholar 

  • Rothstein P (1990) Order restricted preferences and majority rule. Soc Choice Welf 7(4):331–342

    Article  Google Scholar 

  • Saporiti A (2009) Strategy-proofness and single-crossing. Theor Econ 4(2):127–163

    Google Scholar 

  • Saporiti A, Tohmé F (2006) Single-crossing, strategic voting and the median choice rule. Soc Choice Welf 26(2):363–383

    Article  Google Scholar 

  • Westhoff F (1977) Existence of equilibria in economies with a local public good. J Econ Theory 14(1):84–112

    Article  Google Scholar 

Download references

Acknowledgments

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).

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Authors and Affiliations

  1. Institut fuer Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Robert Bredereck & Jiehua Chen

  2. Department of Mathematics and Computer Science, TU Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Robert Bredereck
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  2. Jiehua Chen
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  3. Gerhard J. Woeginger
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Correspondence to Jiehua Chen.

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Bredereck, R., Chen, J. & Woeginger, G.J. A characterization of the single-crossing domain. Soc Choice Welf 41, 989–998 (2013). https://doi.org/10.1007/s00355-012-0717-8

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  • DOI: https://doi.org/10.1007/s00355-012-0717-8

Keywords

  • Social Choice
  • Choice Rule
  • Social Choice Function
  • Condorcet Winner
  • Strategic Vote