Characterization of the Banzhaf–Coleman Index

The Banzhaf–Coleman index has not been greatly studied by game theorists; yet it is the one game-theoretic concept to receive recognition in a court of law. We give here a theoretical study of this power index. This paper consists of five parts. Section 1 gives a definition of the index, and studies several normalizations. Section 2 gives some of the most important properties of the index; § 3 gives a system of axioms which characterize the index over the space of constant-sum games. Section 4 extends this system to the space of general-sum games. Finally, Section 5 discusses the general meaning of the index.