Consider the weighted voting system q12 10 6 3 2 a What is t

Consider the weighted voting system [q:12, 10, 6, 3, 2). (a) What is the smallest value that the quota q can take? (b) What is the largest value that the quota q can take? (c) What is the value of the quota if at least two-thirds of the votes are required to pass a motion? (d) What is the value of the quota if more than two-thirds of the votes are required to pass a motion? (a) The smallest value that the quota q can take is. (b) The largest value that the quota q can take is. (c) The quota if at least two-thirds of the votes are required is. (d) The quota if more than two-thirds of the votes are required is.

Solution

Answer a: 2 (As shown below)

Answer b: 33 (As shown below)

Answer c: 22 (As shown below)

Answer d: 23 (As shown below)

Smallest value that quota q can take = 2, since minimum wieght in the given set is 2.

Largest value that quota q can take = v = 12 + 10 + 6 + 3 + 2 = 33

Quota if at least 2/3rds of votes are required = 33 x 2/3 = 22

Quota if more than 2/3rds of votes are required >22 = 23