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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.

AbstractStochastic dominance concerns conditions on outcome probabilities that are necessary and sufficient for one act to be (strictly) preferred to another according to all preference relations that share certain properties, one of which customarily is an Archimedean property sufficient to entail existence of real‐valued representations. We relax this assumption to permit linear lexicographic utility of finite and known dimensionality. In some situations, levels of the lexicographic hierarchy could correspond to explicit criteria or attributes. In our model, subjective probabilities emerge as matrix premultipliers of the outcome utility vectors. We thus obtain matrix probability generalizations of the familiar cumulative probability conditions for stochastic dominance.