WHEN IS SIZE A LIABILITY - BARGAINING POWER IN MINIMAL WINNING COALITIONS

Riker's 'size principle' predicts that only minimal winning coalitions (MWCs) will form in n-person zero-sum games that satisfy certain cond itions. After summarizing the logic of this principle, a model is prop osed in which n players can be ordered from most to least weighty. Two different kinds of MWCs are distinguished: those in which every membe r is 'critical' (member-MWCs); and member-MWCs that have the smallest weight (weight-MWCs). A member is critical when its defection causes a n 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 qua ntitative 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 a nd bargaining power in parliamentary coalitions and international poli tics are discussed.