  Decisions in a shareholder meeting or a legislative committee are often
modeled as a weighted game. Influence of a member is then measured by a power
index. A large variety of different indices has been introduced in the
literature. This paper analyzes how power indices differ with respect to the
largest possible power of a non-dictatorial player. It turns out that the
considered set of power indices can be partitioned into two classes. This may
serve as another indication which index to use in a given application.
