Power Indices by Direct Enumeration

Program ipdirect

(Go straight to data input.)

This page enables you to run the program called ipdirect to evaluate power indices  using the fundamental definitions directly. 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.

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 way within the voting body.

References: Penrose (1946), Banzhaf (1965), Coleman (1971)

The algorithm ipdirect has the advantage that it is simple and gives exact values for the power indices. Its major disadvantage is that it has exponential time complexity because the computing time required doubles each time an extra member is added. In practice this means that it works well for small voting bodies but is realistically infeasible for n>30. The web implementation here will in practice only work for voting bodies with fewer than 26 members because of system restrictions.

Data Input for ipdirect

Enter your data in the boxes below.
(The numbers are merely an example and can be overwritten.)

Number of Members or Players:                 Quota:   

: type or paste the weights with spaces between.

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