This page enables you to
calculate Shapley-Shubik indices exactly and efficiently by the method
of generating functions using the program ssgenf. This method was originally
proposed by
Mann and Shapley (1962, after a suggestion of Cantor). The program
ssgenf is an adaptation of that published by Lambert (1988).
References: Shapley and Shubik (1954), Mann and Shapley (1962),
Lambert (1988), Lucas (1983), Leech (2002e).
This algorithm is very fast and gives exact values for the power
indices. It can be used for any number of members (although this
particular implementation has a limit of 100). It is therefore very
useful
for many applications where the Shapley-Shubik index is desired. Its
two major disadvantages are: (1) that it has exponential storage
complexity
which places a limitation on the total number of votes, and the weight
for each member, that it can handle: it does not work for the IMF
Board of Governors for example where the total number of votes exceeds
2million; and (2) the quota and all the weights must be integers.
|