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Single-Peakedness and Disconnected Coalitions

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Author Info
Brams, S. J.
Jones, M. A.
Kilgour, M. D.

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Abstract

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.

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Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 01-06.

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Length: 37 pages
Date of creation: 2001
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Handle: RePEc:cvs:starer:01-06

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Related research
Keywords: COALITION FORMATION SINGLE-PEAKEDNESS LEGISLATURES ALLIANCES

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Find related papers by 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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416. [Downloadable!] (restricted)
  2. William Zwicker & Nadia Burani, 2001. "Coalition Formation Games with Separable Preferences," Grand Coalition 22, Grand Coalition Web Site. [Downloadable!]
  3. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January. [Downloadable!] (restricted)
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  4. Jackson, Matthew O. & Moselle, Boaz, 1998. "Coalition and Party Formation in a Legislative Voting Game," Working Papers 1036, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  5. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Greenberg, J. & Weber, S., 1991. "Stable Coalition Structures with Unidimensional Set of Alternatives," Papers 9133, Tilburg - Center for Economic Research.
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  8. Brams, S.J. & Kilgour, D.M., 1998. "Fallback Bargaining," Working Papers 98-10, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  9. Igal Milchtaich & Eyal Winter, 2000. "Stability and Segregation in Group Formation," Discussion Paper Series dp263, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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  10. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Juan Perote-Peña & Javier Perote, 2003. "The impossibility of strategy-proof clustering," Economics Bulletin, Economics Bulletin, vol. 4(23), pages 1-9. [Downloadable!]
    Other versions:
  2. Steven J. Brams & Michael A. Jones & D.Marc Kilgour, 2003. "Forming Stable Coalitions: The Process Matters," Working Papers 2003.97, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  3. Anna Bogomolnaia & Michel Breton & Alexei Savvateev & Shlomo Weber, 2008. "Stability of jurisdiction structures under the equal share and median rules," Economic Theory, Springer, vol. 34(3), pages 525-543, March. [Downloadable!] (restricted)
  4. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, vol. 35(4), pages 505-519, April. [Downloadable!] (restricted)
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