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Power in Weighted Voting Systems

Volume 7, Issue 1
Winter 1997
Peter Tannenbaum, California State University, Fresno

Traditional algorithms for computing either the Banzhaf or the Shapley-Shubik power index of a voter in a n-voter weighted voting system are based on some type of search through the subsets of an n-set or the permutations of an n-set, respectively, and only work for small values of n. This paper presents an approach based on generating functions, with which the Banzhaf and Shapley-Shubik power distributions can be computed even when the value of n is large. To illustrate the computations, the power distributions of the U.S. Electoral College are examined.

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