consider the weighted - voting system q: 12, 7, 4. assume that this system has no dictators and is not…
consider the weighted - voting system q: 12, 7, 4. assume that this system has no dictators and is not subject to gridlock.\n(a) what is the weight of the coalition formed by p1 and p3?\n(b) for what values of the quota q is the coalition formed by p1 and p3 a winning coalition?\n(c) for what values of the quota q is the coalition formed by p1 and p3 a losing coalition?\n(a) what is the weight of the coalition formed by p1 and p3?\nthe weight of the coalition {p1, p3} is 16.\n(b) for what values of the quota q is the coalition formed by p1 and p3 a winning coalition?\nthe coalition {p1, p3} is a winning coalition for all values of through .
Answer
Explanation:
Step1: Calculate coalition weight
The weights of (P_1 = 12) and (P_3=4). The weight of the coalition ({P_1,P_3}) is (12 + 4=16).
Step2: Determine winning - coalition quota
A coalition is winning if its weight is greater than or equal to the quota (q). So the coalition ({P_1,P_3}) is a winning coalition for (q\leq16). Since there are no dictators and no grid - lock, (q>0). So (q) values range from (1) to (16).
Step3: Determine losing - coalition quota
A coalition is losing if its weight is less than the quota (q). So the coalition ({P_1,P_3}) is a losing coalition for (q > 16).
Answer:
(a) 16 (b) (1\leq q\leq16) (c) (q>16)