Summary: A Survey of Algorithms for Calculating Power Indices of
Weighted Majority Games
Tomomi Matsui University of Tokyo,
Bunkyo-ku, Tokyo 113, Japan.
Yasuko Matsui Tokai University,
Hiratsuka-shi, Kanagawa, 259-1292, Japan.
Received December 1998;revised August 1999
In 1944, John von Neumann and Oskar Morgenstern studied the distribution of power in
voting systems in their book Theory of Games and Economic Behavior . They dealt
with a \simple game" in which the only goal is \winning". This is an abstraction of the
constitutional political machinery for voting. This paper deals with the weighted majority
game, which is a familiar example of voting systems.
In 1960s, U.S. Supreme Court handed down a series of \one person one vote" decisions.
After that, calculations of power indices using real data were carried out and presented
as evidence in the courtroom. For example, the courts in New York State have accepted
the Banzhaf index (also called the Coleman value or Chow parameters) as an appropriate
measure for weighted voting systems. The calculation normally requires the aid of a