ABSTRACT
The idea of computing a power index in a weighted voting system originated with Lionel Penrose in 1946 [36]. Lloyd Shapley and Martin Shubik proposed a competing index in 1954 [40]. John Banzhaf [6] invented his index to analyze the distribution of power on the county board of Nassau County, New York in the early 1960s. The index is named after Banzhaf, although it is the same as the index proposed earlier by Penrose. Other indices to measure power were introduced in [15] and [28]. In [20], Dan Felsenthal and Moshe Machover review these indices and make a case for the Shapley-Shubik index as the one that best avoids paradoxes.
