Power indices in a discretely proportional representative system with a large number of voters (Q798549)

To evaluate the power of voters in a political system, indices introduced by Shapley and Shubik as well as Banzhaf are used in the literature. The author applies these indices to a certain representative system, modeling the elections to the Japanese House of Representatives. Having developed a game-theoretic formulation of the representative system, the Shapley- Shubik and the Banzhaf index are computed using Owen's 1972- approximation. Then, a simple example of the representative system is presented. Applied to this example, the Shapley-Shubik and the Banzhaf index are shown to have considerable deficiences. The introduction of an appropriate modification of the indices is put off to a future paper.