A Comparison of Power Indices and a Nonsymmetric Generalization

The first half of this paper describes and contrasts two well known measures of power in voting systems, introduced by Shapley and Shubik and by Banzhaf and Coleman, respectively. The second half develops an explanatory model for a generalization of the Shapley-Shubik measure, first proposed by Owen in a slightly different form, in which ideological differences among the voters can be taken into account. The purpose of the paper is mainly expository, but a number of new results and interpretations are included.