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When is Size a Liability?

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  • Steven J. Brams
  • Peter C. Fishburn

Abstract

Riker's `size principle' predicts that only minimal winning coalitions (MWCs) will form in n -person zero-sum games that satisfy certain conditions. After summarizing the logic of this principle, a model is proposed in which n players can be ordered from most to least weighty. Two different kinds of MWCs are distinguished: • those in which every member is `critical' (member-MWCs); and • member-MWCs that have the smallest weight (weight-MWCs). A member is critical when its defection causes an MWC to become losing. A listing of the possible categories of member-MWCs indicates that their numbers rapidly increase with the number of players (2, 6, 20, and 116 for n = 3, 4, 5, and 6 players). Three quantitative measures of bargaining power show that less weighty players may, on occasion, be more powerful than more weighty players. Possible empirical manifestations of the inverse relationship between weight and bargaining power in parliamentary coalitions and international politics are discussed.

Suggested Citation

  • Steven J. Brams & Peter C. Fishburn, 1995. "When is Size a Liability?," Journal of Theoretical Politics, , vol. 7(3), pages 301-316, July.
    • Handle: RePEc:sae:jothpo:v:7:y:1995:i:3:p:301-316
    DOI: 10.1177/0951692895007003004
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    References listed on IDEAS

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    1. Fishburns, Peter C. & Brams, Steven J., 1994. "Minimal Winning Coalitions in Weighted-Majority Games," Working Papers 94-28, C.V. Starr Center for Applied Economics, New York University.
    2. Brams, Steven J., 1968. "Measuring the Concentration of Power in Political Systems," American Political Science Review, Cambridge University Press, vol. 62(2), pages 461-475, June.
    3. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    2. Gideon Doron & Martin Sherman, 1995. "A Comprehensive Decision-Making Exposition of Coalition Politics," Journal of Theoretical Politics, , vol. 7(3), pages 317-333, July.
    3. Manfred J. Holler, 1998. "Two Stories, One Power Index," Journal of Theoretical Politics, , vol. 10(2), pages 179-190, April.
    4. Manfred Holler & Rie Ono & Frank Steffen, 2001. "Constrained Monotonicity and the Measurement of Power," Theory and Decision, Springer, vol. 50(4), pages 383-395, June.
    5. Geir Asheim & Carl Claussen & Tore Nilssen, 2006. "Majority voting leads to unanimity," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 91-110, December.
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    7. Manfred Holler & Stefan Napel, 2005. "Local monotonicity of power: Axiom or just a property?," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 637-647, January.
    8. Michela Chessa, 2014. "A generating functions approach for computing the Public Good index efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 658-673, July.

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