Chapter 2, Problem 27E

Table 2-13 shows the 24 sequential coalitions (with pivotal players underlined) in a weighted voting system with four players. Find the Shapley-Shubik power distribution of this weighted voting system.

Table 2-13

$\langle P_1,P_2,\underset{\_}{P_3},P_4\rangle$	$\langle P_1\text{, }{P}_2,\underset{\_}{P_4},P_3\rangle$	$\langle P_1,P_3,\underset{\_}{P_2},P_4\rangle$	$\langle P_1,P_3,P_4,\underset{\_}{P_2}\rangle$
$\langle P_1,P_4,\underset{\_}{P_2},P_3\rangle$	$\langle P_1,P_4,P_3,\underset{\_}{P_2}\rangle$	$\langle P_2,P_1,\underset{\_}{P_3},P_4\rangle$	$\langle P_2,P_1,\underset{\_}{P_4},P_3\rangle$
$\langle P_2,P_3,{\underset{\_}{P}}_1,P_4\rangle$	$\langle P_2,P_3,P_4,{\underset{\_}{P}}_1\rangle$	$\langle P_2,P_4,\underset{\_}{P_1},P_3\rangle$	$\langle P_2,P_4,P_3,\underset{\_}{P_1}\rangle$
$\langle P_3,P_1,{\underset{\_}{P}}_2,P_4\rangle$	$\langle P_3,P_1,P_4,\underset{\_}{P_2}\rangle$	$\langle P_3,P_2,\underset{\_}{P_1},P_4\rangle$	$\langle P_3,P_2,P_4,\underset{\_}{P_1}\rangle$
$\langle P_3,P_4,P_1,\underset{\_}{P_2}\rangle$	$\langle P_3,P_4,P_2,\underset{\_}{P_1}\rangle$	$\langle P_4,P_1,\underset{\_}{P_2},P_3\rangle$	$\langle P_4,P_1,P_3,\underset{\_}{P_2}\rangle$
$\langle P_4,P_2,\underset{\_}{P_1},P_3\rangle$	$\langle P_4,P_2,P_3,\underset{\_}{P_1}\rangle$	$\langle P_4,P_3,P_1,\underset{\_}{P_2}\rangle$	$\langle P_4,P_3,P_2,\underset{\_}{P_1}\rangle$