Chapter 2, Problem 38E

Table 2-16 shows the 24 sequential coalitions in a weighted voting system with four players. In some cases the pivotal player is underlined, and in some cases it isn’t. Find the Shapley-Shubik power distribution of this weighted voting system.(Hint: First find the pivotal player in the remaining sequential coalitions.)

Table 2-16

$\langle P_1,{\underset{\_}{P}}_2,P_3,P_4\rangle$	$\langle P_2\text{, }{P}_1,P_3,P_4\rangle$	$\langle P_3,P_1,P_2,P_4\rangle$	$\langle P_4,P_1,P_2,P_3\rangle$
$\langle P_1,P_2,P_4,P_3\rangle$	$\langle P_2,P_1,P_4,P_3\rangle$	$\langle P_3,P_1,P_4,P_2\rangle$	$\langle P_4,P_1,P_3,P_2\rangle$
$\langle P_1,P_3,\underset{\_}{P_2},P_4\rangle$	$\langle P_2,P_3,\underset{\_}{P_1},P_{\text{4 }}\rangle$	$\langle P_3,P_2,P_1,P_{\text{4 }}\rangle$	$\langle P_4,P_2,P_1,P_3\rangle$
$\langle P_1,P_3,\underset{\_}{P_4},P_2\rangle$	$\langle P_2,P_3,P_4,\underset{\_}{P_1}\rangle$	$\langle P_3,P_2,P_4,P_1\rangle$	$\langle P_4,P_2,P_3,P_1\rangle$
$\langle P_1,P_4,\underset{\_}{P_2},P_3\rangle$	$\langle P_2,P_4,{\underset{\_}{P}}_1,P_3\rangle$	$\langle P_3,P_4,\underset{\_}{P_1},P_2\rangle$	$\langle P_4,P_3,P_1,P_2\rangle$
$\langle P_1,P_4,\underset{\_}{P_3},P_2\rangle$	$\langle P_2,P_4,P_3,P_1\rangle$	$\langle P_3,P_4,P_2,P_1\rangle$	$\langle P_4,P_3,P_2,P_1\rangle$