Characterizing the Banzhaf and Shapley values assuming limited linearity

This paper presents characterizations of the Banzhaf-Coleman and Shapley-Shubik indices for monotonic simple games. The characterizations are obtained without explicitly requiring that the indices satisfy the linearity assumptionψ (v∧ w) +ψ (v ∨ w) =ψ (v) + ψ (w). The ideas developed are then used to obtain a characterization of the Banzhaf value for the class of alln-person games in characteristic function form.