  Several power indices have been introduced in the literature in order to
measure the influence of individual committee members on the aggregated
decision. Here we ask the inverse question and aim to design voting rules for a
committee such that a given desired power distribution is met as closely as
possible. We present an exact algorithm for a large class of different power
indices based on integer linear programming. With respect to negative
approximation results we generalize the approach of Alon and Edelman who
studied power distributions for the Banzhaf index, where most of the power is
concentrated on few coordinates. It turned out that each Banzhaf vector of an
n-member committee that is near to such a desired power distribution, has to be
also near to the Banzhaf vector of a k-member committee. We show that such
Alon-Edelman type results are possible for other power indices like e.g. the
Public Good index or the Coleman index to prevent actions, while they are
principally impossible for e.g. the Johnston index.
