We study the inverse power index problem for weighted voting games: the
problem of finding a weighted voting game in which the power of the players is
as close as possible to a certain target distribution. Our goal is to find
algorithms that solve this problem exactly. Thereto, we study various
subclasses of simple games, and their associated representation methods. We
survey algorithms and impossibility results for the synthesis problem, i.e.,
converting a representation of a simple game into another representation.