You may use this applet to calculate the Shapley-Shubik and Banzhaf power indices of weighted voting systems. A weighted voting system is specified by giving the quota, that is, the number of votes required to adopt a measure, and the voting weight of each voter.

The applet has preloaded data for several politically important voting systems: the electoral colleges that determined the outcomes of the 2000 and 2004 U.S. presidential elections (the Electoral College will have the same weights and quota in 2008 as it did in 2004), the Council of Ministers of the European Union, and the United Nations Security Council. You may select one of these sets of data from the drop-down menu on the upper right of the screen. Make a choice of the index that you wish to compute, Banzhaf or Shapley-Shubik, and click on COMPUTE.

If you review the pre-loaded data, you will notice a column labeled multiplicity. This gives the option of entering several voters with equal weights on the same line. For example, in the 2004 Electoral College, Pennsylvania and Illinois each had weight 21. Rather than listing them on separate lines, the data indicate that there are 2 voters with weight 21. Similarly, there are 3 voters with 15 votes, and 4 with 11 votes, and so on.

To enter a voting system of your own devising, start by entering the quota. This must be more than half the total of the weights of all of the voters. Then enter the nae(s), the weight weight, and the multiplicity of the first voters. When this is done, click the “Add a new voter” box. An error message “Check data” indicates that something is missing: perhaps you forgot to specify the quota. Continue to enter voters in this way until the system is complete.

The voters don’t have to be given distinct names; you may find it easiest to give all voters with the same weight a common name. For example, a system might have one voter with weight 10, two voters with weight 6, and 28 voters with weight 1. If the quota is 26, start by entering that. Call the weight-10 voter A, put in her weight (10), and her multiplicity (1). Click the “Add a new voter” box. Each 6-vote voter will be called B; put in their weights (6), and their multiplicity (2). Again, click “Add a new voter.” Finally, the voters with only 1 vote are all C; enter their weights (1), and their multiplicity (28). Important: Don’t forget to click “Add a new voter” after entering the last voter(s). Select the power index that you want to compute, and click “Compute.”

Large systems: While the algorithm used by the applet is valid for any weighted voting system, the numbers that it uses when calculating the power indices of systems with large number of voters may be too big for your computer to handle. This is likely to happen if the weighted voting system you are considering has more than 60 participants, and usually results in absurd results (negative poser indices, for example).