A note on voting

A framework is presented in which to analyze the power of players in a cooperative game in which only certain coalitions are allowed. The allowable coalitions are characterized by a closure operator that combinatorially abstracts the notion of convexity. The Shapley-Shubik index is extended to this situation, allowing a computation of the power of each player. One example of this framework, voting on a one-dimensional spectrum, is analyzed and it is shown that the powerful players are mid-way between the middle and the extremes. This framework is also applied to an empirical study of power of the Supreme Court. Implications and generalizations are also discussed. (C) 1997 Elsevier Science B.V.