Power measures derived from the sequential query process

We study a basic sequential model for the formation of winning coalitions in a simple game, well known from its use in defining the Shapley–Shubik power index. We derive in a uniform way a family of measures of collective and individual decisiveness in simple games, and show that, as for the Shapley–Shubik index, they extend naturally to measures for TU-games. These individual measures, which we call weighted semivalues, form a class whose intersection with that of the class of weak semivalues yields the class of all semivalues.