IDEAS home Printed from
   My bibliography  Save this paper

Single-Peakedness and Disconnected Coalitions


  • Brams, S. J.
  • Jones, M. A.
  • Kilgour, M. D.


Ordinally single-peaked preferences are distinguished from cardinally singlepeaked preferences, in which all players have a similar perception of distances in some one-dimensional ordering. While ordinal single-peakedness can lead to disconnected coalitions that have a "hole" in the ordering, cardinal single-peakedness precludes this possibility, based on two models of coalition formation: ¥ Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until a majority coalition forms. ¥ Build-Up (BU): Similar to FB, except that when nonmajority subcoalitions form, they fuse into composite players, whose positions are defined cardinally and who are treated as single players in the convergence process. FB better reflects the unconstrained, or nonmyopic, possibilities of coalition formation, whereas BU-because all subcoalition members must be included in any majority coalition that forms-restricts combinatorial possibilities and tends to produce less compact majority coalitions. The "strange bedfellows" frequently observed in legislative coalitions and military alliances suggest that even when players agree on, say, a left-right ordering, their perceptions of exactly where players stand in this ordering may differ substantially. If so, a player may be acceptable to a coalition but may not find every member in it acceptable, causing that player not to join and possibly creating a disconnected coalition.

Suggested Citation

  • Brams, S. J. & Jones, M. A. & Kilgour, M. D., 2001. "Single-Peakedness and Disconnected Coalitions," Working Papers 01-06, C.V. Starr Center for Applied Economics, New York University.
  • Handle: RePEc:cvs:starer:01-06

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    2. Greenberg Joseph & Weber Shlomo, 1993. "Stable Coalition Structures with a Unidimensional Set of Alternatives," Journal of Economic Theory, Elsevier, vol. 60(1), pages 62-82, June.
    3. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, March.
    4. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416-416.
    5. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
    6. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    7. Geoffrey Garrett & George Tsebelis, 1999. "Why Resist the Temptation to Apply Power Indices to the European Union?," Journal of Theoretical Politics, , vol. 11(3), pages 291-308, July.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Anna Bogomolnaia & Michel Breton & Alexei Savvateev & Shlomo Weber, 2008. "Stability of jurisdiction structures under the equal share and median rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 525-543, March.
    2. Steven Brams & D. Kilgour, 2013. "Kingmakers and leaders in coalition formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 1-18, June.
    3. Francesco Giovannoni & Daniel Seidmann, 2014. "Corruption and power in democracies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 707-734, March.
    4. Bogomolnaia, Anna & Laslier, Jean-Francois, 2007. "Euclidean preferences," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 87-98, February.
    5. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 505-519, April.
    6. Steven Brams & Michael Jones & D. Kilgour, 2005. "Forming stable coalitions: The process matters," Public Choice, Springer, vol. 125(1), pages 67-94, July.
    7. repec:ebl:ecbull:v:4:y:2003:i:23:p:1-9 is not listed on IDEAS
    8. Steven Brams & Gustavo Camilo & Alexandra Franz, 2014. "Coalition formation on the U.S. Supreme Court: 1969–2009," Public Choice, Springer, vol. 158(3), pages 525-539, March.
    9. Matthias Dahm, 2010. "Free mobility and taste-homogeneity of jurisdiction structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 259-272, March.
    10. Juan Perote-Peña & Javier Perote, 2003. "The impossibility of strategy-proof clustering," Economics Bulletin, AccessEcon, vol. 4(23), pages 1-9.
    11. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    12. Jiehua Chen & Kirk R. Pruhs & Gerhard J. Woeginger, 2017. "The one-dimensional Euclidean domain: finitely many obstructions are not enough," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 409-432, February.

    More about this item



    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cvs:starer:01-06. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Anne Stubing). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.