Chapter 2, Problem 64E

The weighted voting system $\left[27:10,8,6,4,2\right]$ represents a partnership among five people ( $P_1$, $P_2$, $P_3$, $P_4$ and $P_5$). You are $P_5$ the one with two votes. You want to increase your power in the partnership and are prepared to buy one share (one share equals one vote) from any of the other partners. Partners $P_1$, $P_2$ and $P_3$ are each willing to sell cheap ($1000 for one share), but $P_4$ is not being quite as cooperative-she wants $5000 for one of her shares. Given that you still want to buy one share, from whom should you buy it? Use the Banzhaf power index for your calculations. Explain your answer.