CHAPTER 2 Weighted Voting Practice Multiple Choice
For questions #1 – #8: Use 36: 18, 11, 7, 4, 2
1) What is the quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
2) How many players are in this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
3) How many votes are in this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
4) What is the minimum possible number for quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
5)What is the maximum possible number for quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
6) Which of the following would represent ¾ majority for this weighted voting system?
A) 27B) 31C) 32D) 42E) None of the above
7) What is the total number of possible coalitions?
A) 16B) 24C) 31D) 120E) None of the above
8) What is the total number of sequential coalitions?
A) 16B) 24C) 31D) 120E) None of the above
9) In the weighted voting system 26: 15, 10, 5which of the following is true.
A) P1is a dictator.
B) All have veto power.
C) Only P1and P2 have veto power.
D) P2 and P3 are the dummies.
E) None of the above.
For #10 - 13: Use [12: 8, 6, 5]
10) Which isn’t a winning coalition?
A) {8, 6} B) {5, 8}C) {8, 5, 6}D) {6, 5}E) None of the above
11) Which player is critical in {8, 6, 5}?
A) P1B) P2C) P3D) All of the aboveE) None of the above
12) Which player is pivotal in <8, 5, 6>?
A) P1B) P2C) P3D) All of the aboveE) None of the above
13)Which of the following is true?
A) P1 has veto powerB) P2has veto powerC) P3has veto power
D) All of the aboveE) None of the above
CHAPTER 2 Weighted Voting Practice Multiple Choice
For questions #1 – #8: Use 36: 18, 11, 7, 4, 2
1) What is the quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
2) How many players are in this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
3) How many votes are in this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
4) What is the minimum possible number for quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
5)What is the maximum possible number for quota of this weighted voting system?
A) 5B) 22C) 36D) 42E) None of the above
6) Which of the following would represent ¾ majority for this weighted voting system?
A) 27B) 31C) 32D) 42E) None of the above
7) What is the total number of possible coalitions?
A) 16B) 24C) 31D) 120E) None of the above
8) What is the total number of sequential coalitions?
A) 16B) 24C) 31D) 120E) None of the above
9) In the weighted voting system 26: 15, 10, 5which of the following is true.
A) P1is a dictator.
B) All have veto power.
C) Only P1and P2 have veto power.
D) P2 and P3 are the dummies.
E) None of the above.
For #10 - 13: Use [12: 8, 6, 5]
10) Which isn’t a winning coalition?
A) {8, 6} B) {5, 8}C) {8, 5, 6}D) {6, 5}E) None of the above
11) Which player is critical in {8, 6, 5}?
A) P1B) P2C) P3D) All of the aboveE) None of the above
12) Which player is pivotal in <8, 5, 6>?
A) P1B) P2C) P3D) All of the aboveE) None of the above
13)Which of the following is true?
A) P1 has veto powerB) P2has veto powerC) P3has veto power
D) All of the aboveE) None of the above
HONORS DISCRETE CHAPTER 2 REVIEW
1)What is the number of POSSIBLE coalitions for N players?
2)What is the number of SEQUENTIAL coalitions for N players?
For each of the following weighted voting systems # 3 - 8:
A)Identify which players are dummies, dictator, or veto power
B)What is the maximum and minimum the quota could be?
C)How many possible coalitions exist?
D)How many sequential coalitions exist?
E)For problems #3 – 5, perform Shapley-Shubik and Banzhaf Power.
F)For problems #6 – 8, perform Banzhaf Power only.
3)[10; 7, 5, 4]
4)[13; 11, 8, 1]
5)[15; 7, 6, 5]
6)[14; 8, 6, 4, 2]
7)[17; 9, 8, 5, 1]
8)[20; 10, 7, 5, 2]