Answer to Question #246236 in Discrete Mathematics for help

Question

ASAP

Determine all the winning coalitions and find the Banzhaf power distribution

[16:5,5,11,6,3]

SHOW ALL WORK

Answer 1

Weighed voting system $[16:5,5,11,6,3] \iff [7:5,4,3]$

$P_1=5; P_2=4; P_3=3$

Critical count

To determine a voter's power using the Banzhaf index, first list all of the winning coalitions, then count the crucial voters. A crucial voter is one whose vote, if altered from yes to no, would cause the proposition to fail. The proportion of all swing votes that a voter could cast is used to calculate his voting power.

Number of coalitions for which the players are critical (Banzhaf power distribution)

Critical count for P₁ =3

Critical count for P₂ =1

Critical count for P₃ =1