Chapter 2, Problem 67E

a. Verify that the weighted voting systems $\left[12:7,4,3,2\right]$ and $\left[24:14,8,6,4\right]$ result in exactly the same Banzhaf power distribution. (If you need to make calculations, do them for both systems side by side and look for patterns.).

b. Based on your work in (a), explain why the two proportional weighted voting systems $\left[q:w_1,w_2,\mathrm{...},w_N\right]$ and $\left[cq:c{w}_1,c{w}_2,\mathrm{...},c{w}_N\right]$ always have the same Banzhaf power distribution.