Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Power in Weighted Voting Systems

Peter Tannenbaum
Organization: California State University, Fresno
Journal / Anthology

The Mathematica Journal
Year: 1997
Volume: 7
Issue: 1
Page range: 58-63

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.

*Applied Mathematics > Optimization