Chapter 2, Problem 14E

Find the Banzhaf power distribution of a weighted voting system with five players in which the winning coalitions (with critical players underlined) are

$\begin{array}{l}\left\{P\underset{\_}{1},P\underset{\_}{2},P\underset{\_}{3}\right\},\left\{P\underset{\_}{1},P\underset{\_}{2},P\underset{\_}{4}\right\},\left\{P\underset{\_}{1},P\underset{\_}{2},P3,P4\right\},\\ \left\{P\underset{\_}{1},P\underset{\_}{2},P\underset{\_}{3},P5\right\},\left\{P\underset{\_}{1},P\underset{\_}{2},P\underset{\_}{4},P5\right\},\left\{P\underset{\_}{1},P\underset{\_}{3},P\underset{\_}{4},P5\right\},\\ \left\{P\underset{\_}{1},P2,P3,P4,P5\right\}.\end{array}$