University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2014
Views:

16

Pages:

2
Author:

Louis Carson

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) 5 B) 22 C) 36 D) 42 E) None of the above 2) How many players are in this weighted voting system? A) 5 B) 22 C) 36 D) 42 E) None of the above 5 numbers after quota 3) How many votes are in this weighted voting system? A) 5 B) 22 C) 36 D) 42 E) None of the above 18 + 11 + 7 + 4 + 2 4) What is the minimum possible number for quota of this weighted voting system? A) 5 B) 22 C) 36 D) 42 E) None of the above 42/2↑ 5) What is the maximum possible number for quota of this weighted voting system? A) 5 B) 22 C) 36 D) 42 E) None of the above 6) Which of the following would represent ¾ majority for this weighted voting system? A) 27 B) 31 C) 32 D) 42 E) None of the above 3 ( /4) 42↑ 7) What is the total number of possible coalitions? A) 16 B) 24 C) 31 D) 120 E) None of the above 25 – 1 = 32 – 1 = 31 8) What is the total number of sequential coalitions? A) 16 B) 24 C) 31 D) 120 E) None of the above 5! = 120 9) In the weighted voting system [26: 15, 10, 5], which of the following is true. A) P1 is a dictator. B) All have veto power. 15+10+5 only winning coalition C) Only P1 and 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) P1 B) P2 C) P3 D) All of the above E) None of the above 12) Which player is pivotal in <8, 5, 6>? A) P1 B) P2 C) P3 D) All of the above E) None of the above 13) Which of the following is true? A) P1 has veto power B) P2 has veto power D) All of the above E) None of the above C) P3 has veto power HONORS DISCRETE CHAPTER 2 REVIEW MATERIAL 1) What is the number of TOTAL possible coalitions for N players? 2N – 1 2) What is the number of sequential coalitions for N players? N! For each of the following weighted voting systems # 3 - 8: A) B) C) D) E) Identify which players are dummies, dictator, or veto power What is the maximum and minimum the quota could be? How many possible coalitions exist? How many sequential coalitions exist? For problems #3 – 5, perform Shapley-Shubik and Banzhaf Power. 3) [10; 7, 5, 4] A) Dummy = None Dictator = None Veto Power = P1 B) Min = 9 and Max = 16 C) 23 – 1 = 7 D) 3! = 6 E) Banzhaf: 3/5, 1/5, 1/5 7+5; 7+4; 7+5+4 SS: 4/6, 1/6, 1/6 4) [13; 11, 8, 1] A) Dummy = None Dictator = P3 Veto Power = P1 and P2 B) Min = 11 and Max = 20 C) 23 – 1 = 7 D) 3! = 6 E) Banzhaf: 1/2, 1/2, 0 11+8; 11+8+1 SS: 1/2, 1/2, 0 5) [15; 7, 6, 5] A) Dummy = None Dictator = None Veto Power = All B) Min = 10 and Max = 18 C) 23 – 1 = 7 D) 3! = 6 E) Banzhaf: 1/3, 1/3, 1/3 7+6+5 SS: 1/3, 1/3, 1/3 6) [14; 8, 6, 4, 2] A) Dummy = None Dictator = None Veto Power = P1 B) Min = 11 and Max = 20 C) 24 – 1 = 15 D) 4! = 24 F) Banzhaf: 5/10, 3/10, 1/10, 1/10 8+6; 8+4+2; 8+6+4; 8+6+2; 8+6+4+2 7) [17; 9, 8, 5, 1] A) Dummy = None Dictator = P3 and P4 Veto Power = P1 and P2 B) Min = 11 and Max = 20 C) 24 – 1 = 15 D) 4! = 24 F) Banzhaf: 1/2, 1/2, 0, 0 9+8; 9+8+5; 9+8+1; 9+8+5+1 8) [20; 10, 7, 5, 2] A) Dummy = None Dictator = P4 Veto Power = P1 , P2, P3 B) Min = 13 and Max = 24 C) 24 – 1 = 15 D) 4! = 24 F) Banzhaf: 1/3, 1/3, 1/3, 0 10+7+5; 10+7+5+2