When is size a liability? Bargaining power in minimal winning coalitions

Steven J. Brams, Peter C. Fishburn

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)301-316
    Number of pages16
    JournalJournal of Theoretical Politics
    Issue number3
    StatePublished - Jul 1995


    • bargaining
    • coalitions
    • game theory
    • power

    ASJC Scopus subject areas

    • Sociology and Political Science


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