1.	What would be the quota for a voting system that has a total of 15 votes and uses a simple majority quota?	
	A)  7    B)  8    C)  9    D)  15	

2.	What would be the quota for a voting system that has a total of 16 votes and uses a simple majority quota?	
	A)  7    B)  8    C)  9    D)  16	

3.	What would be the quota for a voting system that has a total of 30 votes and uses a simple majority quota?	
	A)  14    B)  15    C)  16    D)  30	

4.	Which of the following describe legitimate weighted voting systems?
I	
[16: 13, 8, 6, 4]	

II	
[15: 10, 8, 7, 5]	

	A)  I only    B)  II only    C)  I and II    D)  Neither I nor II	

5.	Which of the following describe legitimate weighted voting systems?
I	
[27: 20, 15, 12, 5]	

II	
[30: 20, 17, 10, 5]	

	A)  I only    B)  II only    C)  I and II    D)  Neither I nor II	

6.	Which of the following describe legitimate weighted voting systems?
I	
[20: 16, 12, 8]	

II	
[24: 20, 15, 10]	

	A)  I only    B)  II only    C)  I and II    D)  Neither I nor II	

7.	Which of the following describe legitimate weighted voting systems?
I	
[20: 30, 10, 6]	

II	
[34: 30, 18, 6]	

	A)  I only    B)  II only    C)  I and II    D)  Neither I nor II	

8.	In a weighted voting system, all winning coalitions would become blocking coalitions if each voter switched his/her vote from YES to NO.	
	A)  True    B)  False	

9.	In a weighted voting system, all blocking coalitions would become winning coalitions if each voter switched his/her vote from NO to YES.	
	A)  True    B)  False	

10.	In a weighted voting system, any voter with veto power is a dictator.	
	A)  True    B)  False	

11.	A weighted voting system can have a dictator without dummy voters.	
	A)  True    B)  False	

12.	A weighted voting system can have dummy voters without a dictator.	
	A)  True    B)  False	

13.	In the weighted voting system [9: 10, 5, 3], voter A is a dictator.	
	A)  True    B)  False	

14.	Which voters in the system [30: 20, 17, 10, 5] have veto power?	
	A)  A only    B)  A and B    C)  A, B, and C    D)  None	

15.	Which voters in the system [38: 20, 15, 12, 5] have veto power?	
	A)  A only    B)  A and B    C)  A, B, and C    D)  None	

16.	Given the weighted voting system [38: 20, 15, 12, 5], which is a winning coalition?	
	A)  {A, B}    B)  {B, C, D}    C)  {A, B, D}    D)  {A}	

17.	Given the weighted voting system [38: 20, 15, 12, 5], which of the coalitions listed is/are blocking coalitions?
	
I  {A}	
II  {C, D}	
III  {A, B, C}	

	A)  III only    B)  I and II only    C)  I, II, and III    D)  None	

18.	Given the weighted voting system [38: 20, 15, 12, 5], which voter(s) is/are dummy voters.	
	A)  D only    B)  D and C    C)  D, C, and B    D)  There are no dummy voters.	

19.	Given the weighted voting system [51: 45, 43, 7, 5], which of the following is a winning coalition?	
	A)  {A}    B)  {A, D}    C)  {A, C}    D)  {B, D}	

20.	Given the weighted voting system [52: 45, 43, 7, 5], which of the following is a minimal winning coalition?
	
I  {A, B}	
II  {A, C}	
III  {A, B, C}	

	A)  I only    B)  I and II    C)  I, II, and III    D)  None	

21.	Given the weighted voting system [51: 45, 43, 7, 5], which of the following is a blocking coalition?
	
I  {A}	
II  {B, C}	
III  {C}	

	A)  II only    B)  I and II    C)  I, II, and III    D)  None	

22.	Given the weighted voting system [9: 6, 4, 2], which of the voters are dummy voters?	
	A)  C only    B)  B and C    C)  B only    D)  None	

23.	Given the weighted voting system [8: 5, 4, 3], which of the coalitions given are minimal winning coalitions?	
A)	{A, B, C}	
B)	{A, B}	
C)	{B, C}	
D)	There are no minimal winning coalitions.	

24.	Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are winning?
	
I  {A, B}	
II  {A, C}	
III  {B, C, D}	

	A)  I only    B)  I and II    C)  I and III    D)  I, II, and III	

25.	Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions?
	
I  {A, B}	
II  {A, C}	
III  {B, C, D}	

	A)  I only    B)  I and II    C)  II and III    D)  I, II, and III	

26.	Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are blocking coalitions?
	
I  {A, B}	
II  {B, C}	
III  {C, D}	

	A)  I only    B)  I and II    C)  II and III    D)  I, II, and III	

27.	If there are four voters in a weighted voting system, how many distinct coalitions of voters can be formed?	
	A)  8    B)  16    C)  24    D)  30	

28.	If there are five voters in a weighted voting system, how may different combinations of YES and NO votes can there be?	
	A)  10    B)  25    C)  32    D)  120	

29.	Calculate C52.	
	A)  5    B)  10    C)  32    D)  25	

30.	Calculate C124.	
	A)  48    B)  20,736    C)  495    D)  11,880	

31.	Calculate C93.	
	A)  27    B)  84    C)  504    D)  729	

32.	In a weighted voting system with eight voters, how many coalitions would there be in which exactly five members voted YES?	
	A)  32    B)  40    C)  56    D)  256	

33.	In a weighted voting system with 20 voters, how many distinct coalitions would there be in which exactly eight members voted YES?	
	A)  12    B)  56    C)  160    D)  125,970	

34.	Given the weighted voting system [27: 20, 15, 12, 5], calculate the Banzhaf power index.	
	A)  (8, 8, 8, 0)    B)  (8, 6, 6, 2)    C)  (6, 6, 6, 1)    D)  (8, 6, 6, 0)	

35.	Given the weighted voting system [34: 30, 18, 6], calculate the Banzhaf power index.	
	A)  (6, 4, 2)    B)  (6, 2, 2)    C)  (6, 6, 6)    D)  (6, 4, 0)	

36.	Given the weighted voting system [30: 20, 17, 10, 5], calculate the Banzhaf power index.	
	A)  (10, 6, 6, 0)    B)  (8, 6, 6, 2)    C)  (10, 6, 6, 2)    D)  (8, 4, 4, 0)	

37.	In a weighted voting system, the Banzhaf power index of each voter is directly proportional to the weight of the vote.	
	A)  True    B)  False	

38.	In a weighted voting system, the Banzhaf power index of a dummy voter is 0.	
	A)  True    B)  False	

39.	In the weighted voting system [8: 5, 2, 2, 2, 2, 2], find the Banzhaf power index for voter A.	
	A)  8    B)  10    C)  15    D)  40	

40.	In the weighted voting system [8: 5, 2, 2, 2, 2, 2], find the Banzhaf power index for voter B.	
	A)  2    B)  16    C)  4    D)  20	

41.	In the weighted voting system [6: 3, 1, 1, 1, 1, 1, 1], find the Banzhaf power index for voter A.	
	A)  6    B)  20    C)  40    D)  82	

42.	Are the weighted voting systems [8: 5, 4, 3] and [34: 30, 18, 6] equivalent?	
	A)  Yes    B)  No	

43.	Are the weighted voting systems [8: 5, 4, 3] and [11: 10, 9, 2] equivalent?	
	A)  Yes    B)  No	

44.	Are the weighted voting systems [18: 10, 9, 8] and [15: 8, 7, 6] equivalent?	
	A)  Yes    B)  No	

45.	Are the weighted voting systems [11: 10, 9, 2] and [2: 1, 1, 1] equivalent?	
	A)  Yes    B)  No	

46.	How many permutations of five voters can be made?	
	A)  14    B)  25    C)  32    D)  120	

47.	Calculate the Shapley-Shubik power index for each voter in the system [8: 5, 4, 3].	
	A)  (4/6, 1/6, 1/6)    B)  (3/6, 3/6, 0/6)    C)  (2/6, 2/6, 2/6)    D)  (4/6, 2/6, 2/6)	

48.	Calculate the Shapley-Shubik power index for each voter in the system [15: 8, 7, 6].	
	A)  (4/6, 1/6, 1/6)    B)  (3/6, 3/6, 0/6)    C)  (2/6, 2/6, 2/6)    D)  (4/6, 2/6, 2/6)	

49.	Calculate the Shapely-Shubik power index for each voter in the weighted voting system [8: 5, 2, 2, 2, 2, 2].	
A)	(7/12, 1/12, 1/12, 1/12, 1/12, 1/12)	C)	(5/6, 1/30, 1/30, 1/30, 1/30, 1/30)	
B)	(5/8, 3/40, 3/40, 3/40, 3/40, 3/40)	D)	(1/3, 2/15, 2/15, 2/15, 2/15, 2/15)	

50.	Calculate the Shapely-Shubik power index for each voter in the weighted voting system [6: 3, 1, 1, 1, 1, 1, 1].	
A)	(3/7, 2/21, 2/21, 2/21, 2/21, 2/21, 2/21)	
B)	(1/2, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12)	
C)	(1/3, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9)	
D)	(2/3, 1/18, 1/18, 1/18, 1/18, 1/18, 1/18)	

51.	A committee has four voters and the system [30: 20, 17, 10, 5].  How many extra votes does the coalition {A, C, D} have?	
	A)  1    B)  5    C)  10    D)  35	

52.	A committee has six voters with the system [8: 5, 2, 2, 2, 2, 2].  How many extra votes does the coalition {B, C, E, F} have?	
	A)  0    B)  1    C)  2    D)  8	

53.	A committee has four voters with the system [30: 20, 17, 10, 5].  Which voters are critical in the coalition {A, C, D}?	
	A)  A only    B)  A and C    C)  C and D    D)  D only	

54.	A committee has six members with the system [8: 5, 2, 2, 2, 2, 2].  Which voters are critical in the coalition {A, C, D}?	
	A)  A only    B)  C and D    C)  A, C, and D    D)  No voter is critical.	

55.	Calculate .	
	A)  10    B)  96    C)  4960    D)  29,760	

56.	What would be the quota for a voting system that has a total of 41 votes and uses a simple majority quota?	
	A)  20    B)  21    C)  31    D)  41	

57.	Which of the following describe legitimate weighted voting systems?

I. [10: 5, 4, 3, 8]
II. [9: 5, 8, 3]	
	A)  I only    B)  II only    C)  I and II    D)  Neither I or II	

58.	Which voters in the system [19: 9, 7, 5, 3, 1] have veto power?	
	A)  A only    B)  A and B    C)  A, B, and C    D)  None	

59.	Given the weighted voting system [12: 1, 3, 5, 7], which is a winning coalition?	
	A)  {B}    B)  {B, C}    C)  {B, C, D}    D)  {D}	

60.	Given the weighted voting system [8: 3, 5, 2, 4], which is a blocking coalition?	
	A)  {A, B}    B)  {A, C}    C)  {A}    D)  {B}	

61.	Given the weighted voting system [19: 9, 7, 5, 3, 1], which of the voters are dummy voters?	
	A)  D only    B)  D and E    C)  E only    D)  None	

62.	Given the weighted voting system [6: 4, 3, 2, 1], calculate the Banzhaf power index.	
	A)  (11, 6, 2, 2)    B)  (5, 4, 4, 1)    C)  (10, 6, 2, 2)    D)  (10, 6, 6, 2)	

63.	Calculate the Shapley-Shubik power index for each voter in the weighted voting system [6: 5, 3, 1].	
	A)  (1, 0, 0)    B)  (2/3, 1/6, 1/6)    C)  (1/3, 1/3, 1/3)    D)  (1/2, 1/2, 0)	

64.	A committee has three members with the system [10: 5, 4, 3, 2, 1]. Which voters are critical in the coalition {A, B, C, E}?	
	A)  A only    B)  A and B    C)  A and E    D)  E only	

Answer Key

1.	B	
2.	C	
3.	C	
4.	A	
5.	C	
6.	C	
7.	D	
8.	A	
9.	B	
10.	B	
11.	B	
12.	A	
13.	A	
14.	D	
15.	B	
16.	C	
17.	C	
18.	D	
19.	C	
20.	B	
21.	A	
22.	A	
23.	B	
24.	D	
25.	D	
26.	B	
27.	B	
28.	C	
29.	B	
30.	C	
31.	B	
32.	C	
33.	D	
34.	A	
35.	B	
36.	C	
37.	B	
38.	A	
39.	D	
40.	B	
41.	D	
42.	A	
43.	B	
44.	B	
45.	A	
46.	D	
47.	A	
48.	B	
49.	D	
50.	A	
51.	B	
52.	A	
53.	B	
54.	C	
55.	C	
56.	B	
57.	B	
58.	B	
59.	C	
60.	A	
61.	C	
62.	D	
63.	B	
64.	B