Answer: The explanation is as follows:
Explanation:
(a) [8: 9, 3, 2, 1]
q = 8
Here, coalition is as follows:
[P1, P2, P3, P4] = [9, 3, 2, 1]
for the above coalition, the combined weight is
[P1, P2, P3, P4] = 9+3+2+1 = 15 ⇒ combined weight
For simplified weighted voting system;
q = combined weight ⇒ both the terms have to be equal for a simplified weighted voting system.
But, here 8 ≠ 15
∴ It is not a simplified weighted voting system.
(b) [20: 8, 6, 3, 2, 1]
q = 20
Here, coalition is as follows:
[P1, P2, P3, P4, P5] = [8, 6, 3, 2, 1]
for the above coalition, the combined weight is
[P1, P2, P3, P4, P5] = 8+6+3+2+1 = 20 ⇒ combined weight
For simplified weighted voting system;
q = combined weight
Since, 20 = 20
∴ It is a simplified weighted voting system.