The Shapley-Shubik index is a measure of a voter's power in a weighted voting system. To calculate the index of a voter we first list all of the permutations of voters. If there are 3 voters there will be 3! = 6 permutations, with 4 voters there will be 4! = 24 permutations, and so forth. In each permutation the order plays an important role. While working from left to right, we add the votes of each of the participants until we reach the individual whose votes cause the total to equal or exceed the quota. This voter is called pivotal, and each permutation will have exactly one pivotal voter. We obtain the Shapley-Shubik index of a voter by dividing the number of times that voter is pivotal by the total number of permutations.
In the applet below you may select a predefined problem by clicking the New vote button. To solve your own problem enter the quota and weights and click the Load vote button. Clicking either of these buttons will load the voter permutations into the mini-spreadsheet.
Your first task in solving a new problem is to enter the pivotal voter for each permutation. When all the pivotal voters have been entered click the Check answer button to check your answers. When all the pivotal voters have been correctly entered, finish the problem by entering the Shapley-Shubik index for each voter. Click Check answer to check your answers.