EXAMPLE 6 The Corporation with Four Shareholders

A corporation has four shareholders, , , , and , with 49, 48, 2, and 1 shares, respectively. it uses the weighted voting system .

The permutations of the shareholders are shown in Table 11.3. (The arrangement is the same as in Table 11.2, which lists permutations and finds their pivotal voters in a three-voter system.) in 10 of the permutations, is the pivotal voter; and are each pivotal voters in 6; and is the pivotal voter in 2 permutations. Therefore, the Shapley–Shubik power index for this weighted voting system is