Power Indices Calculated by Generating Functions

Program ipgenf

(Go straight to data input screen.)

This page enables you to run the program called ipgenf to find power indices exactly by the method of generating functions. The indices computed are those that measure what Felsenthal and Machover (1998) called I-power (power as influence) based on counting all possble voting outcomes or coalitions equally.

The program computes the following for each member:
Penrose index or Absolute Banzhaf index:  the number of swings divided by the number of possible voting outcomes among the other members.

Normalised Banzhaf index:  the number of swings as a proportion of the total number of swings for all members. The indices sum to 1 over all members.

Power to Prevent Action (Coleman):  the number of swings divided by the number of voting outcomes that lead to a decision. A measure of a member's  blocking power. The Coleman indices are useful when the decision rule requires a supermajority.

Power to Initiate Action (Coleman):  the number of swings divided by the number of outcomes that do not produce a decision. A measure of the member's power to get its proposals accepted.

References: Penrose (1946), Banzhaf (1965), Coleman (1971). The method of generating functions for computing these indices is described in Brams and Affuso (1986); see also Leech (2002e).

This algorithm is very fast and gives exact values for the power indices. It can be used for voting bodies with any number of members and is therefore very powerful. (This particular implementation has a limit of 200 members for convenience.) It has two limitations which make it unsuitable for some situations. (1) It has exponential storage complexity which places limitations on the total voting weight that it can  handle: for example it cannot be applied to the IMF Board of Governors where the total weight exceeds 2 million votes.  (2) The quota and all the weights must be integers; in some voting bodies where these are percentages or fractions this is a real limitation.

Data Input for ipgenf

Enter your data in the boxes below.

All numbers must be integers.

(The numbers are an example and can be overwritten.)

Number of Members or Players:


Weights: (Enter the values of the weights with no punctuation, and separated by spaces.)

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