Math Help Please

1. Consider the weighted voting system [75: 31, 29, 23, 16, 8, 7]. Find each:

a. The total number of players.

b. The total number of votes.

c. The weight of P3.

d. The minimum percentage of the votes needed to pass a motion (rounded to the next whole percent).

2. Consider the weighted system [q: 12, 8, 7, 6, 5]

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 the motion?

d. What is the value of the quota if more than two-thirds of the votes are required to pass a motion?

3. Consider the weighted voting system [6: 4,3,2]

a. What is the weight of the coalition formed by P1 and P3.

b. Write down all winning coalitions.

c. Which players are critical in the coalition [P1, P2, P3].

d. Find the Banzhof Power distribution.

4. Consider the weighted voting system [8: 7, 6, 2]

a. Write down all the sequential coalitions and in each sequential coalition identify the pivotal player.

b. Find the Shapley-Shubik power distribution of this weighted voting system.