This
page enables you
calculate the Banzhaf, Penrose and Coleman
power indices for a large voting body, for
example the hundreds or thousands of ordinary shareholders of a large
public
corporation. The program ipmmle employs a combination of
direct enumeration and approximation
based on a probabilistic voting model.
It
can be applied to large voting bodies of any size (either in terms of
number of players or in terms of votes). The voting weights and quota
are not restricted to being integers.
The program computes the
following for each member:
The algorithm uses the
modification
of
the approximation method of multilinear extensions of Guillermo Owen
(see 1995) described in Leech (2003). It
is necessary to divide the
players into two groups: "major" and "minor". The "major" players
are a small
number including the largest and the "minor" ones are the remainder.
The algorithm trades off speed against accuracy: the larger is the
number of "major" players
assumed the slower but more accurate the algorithm. In practice, in
most
applications, the number of major players need not be greater than 10
in
order to achieve high accuracy. The weights must be entered in
decreasing
size order.
References: Penrose (1946), Banzhaf (1965), Coleman (1971), Owen (1972, 1975a, 1975b, 1995), Leech (2003; see also 2001, 2002b, 2002c for applications). |
Data Input for ipmmleEnter your data in the
boxes below.
(The
numbers
are examples which can be overwritten.) |