1.	A vote using Condorcet's Method is	
	A)  never manipulable.    B)  sometimes manipulable.    C)  always manipulable.	

2.	A vote using majority rule is	
	A)  never manipulable.    B)  sometimes manipulable.    C)  always manipulable.	

3.	A vote among two candidates is	
	A)  never manipulable.    B)  sometimes manipulable.    C)  always manipulable.	

4.	A vote using the Borda Count method is	
	A)  never manipulable.    B)  sometimes manipulable.    C)  always manipulable.	

5.	A vote among four or more candidates using the Borda Count method is	
	A)  never manipulable.    B)  sometimes manipulable.    C)  always manipulable.	

6.	Agenda manipulation is a technique to impact an outcome using	
A)	the Hare method.	C)	the Borda Count method.	
B)	the plurality runoff method.	D)	the sequential pairwise method.	

7.	A vote using plurality is	
A)	never manipulable.	
B)	manipulable by individuals only.	
C)	manipulable by groups only.	
D)	manipulable by both individuals and groups.	

8.	Which of these voting methods never results in a tie?	
A)	the Hare method	C)	Condercet's Method	
B)	sequential runoff	D)	plurality runoff	

9.	Which of the following is NOT a property of the Condercet Method of voting?	
A)	satisfies the Pareto condition	C)	not a dictatorship	
B)	nonmanipulable	D)	always produces a winner	

10.	After considering all possible one-on-one contests, Copeland's rule chooses as the winner	
A)	the candidate who wins every contest in which he or she participates.	
B)	the candidate with the best win-loss record.	
C)	the candidate who wins the longest sequence of contests.	
D)	the candidate who wins more contests than he or she loses.	

11.	The Chair's paradox is the fact that the chair, who can break ties, can	
A)	always end up with his or her preferred candidate.	
B)	sometimes end up with his or her preferred candidate.	
C)	sometimes end up with his or her least preferred candidate.	
D)	never end up with his or her least preferred candidate.	

12.	Which of the following is also known as an “insincere ballot”?	
A)	a disingenuous ballot	C)	a preference ballot	
B)	a strategic ballot	D)	a dispreference ballot	

13.	A person who has tie-breaking power	
A)	always ends up with his or her preferred candidate.	
B)	only votes when there is a tie.	
C)	may vote twice when there is a tie.	
D)	becomes the winning candidate when there is a tie.	

14.	One strategy weakly dominates another if it yields an outcome	
A)	that is no worse than the other.	C)	that is definitely better than the other.	
B)	that is no better than the other.	D)	that is definitely worse than the other.	

15.	If a voter sincerely prefers A over B over C over D, then he or she will prefer a tie between B and C over	
	A)  a tie between B and D.    B)  a tie between A and B.    C)  a tie between A and C.	

16.	Thirty voters with the preference schedules below are to elect a union spokesman from among five candidates: A, B, C, D, and E.  If the Borda count is used, candidate B would win.  Would there be any difference in the result if candidate C withdrew from the race before the ranking?

Number of Voters	

12	
10	
8	

First choice	
A	
B	
D	

Second choice	
D	
C	
B	

Third choice	
B	
A	
A	

Fourth choice	
C	
D	
E	

Fifth choice	
E	
E	
C	

A)	No, B still wins.	C)	Yes, now D wins.	
B)	Yes, now A wins.	D)	Yes, now there is no winner.	

17.	Thirty voters with the preference schedules below are to elect a union spokesman from among five candidates: A, B, C, D, and E.  If the Borda count is used, candidate B would win.  Would there be any difference in the result if candidate D withdrew from the race before the ranking?

Number of Voters	

12	
10	
8	

First choice	
A	
B	
D	

Second choice	
D	
C	
B	

Third choice	
B	
A	
A	

Fourth choice	
C	
D	
E	

Fifth choice	
E	
E	
C	

A)	No, B still wins.	C)	Yes, now C wins.	
B)	Yes, now A wins.	D)	Yes, now there is no winner.	

18.	Thirty voters with the preference schedules below are to elect a union spokesman from among five candidates: A, B, C, D, and E.  If the Borda count is used, candidate B would win.  Would there be any difference in the result if candidate A withdrew from the race before the ranking?

Number of Voters	

12	
10	
8	

First choice	
A	
B	
D	

Second choice	
D	
C	
B	

Third choice	
B	
A	
A	

Fourth choice	
C	
D	
E	

Fifth choice	
E	
E	
C	

A)	No, B still wins.	C)	Yes, now D wins.	
B)	Yes, now C wins.	D)	Yes, now there is no winner.	

19.	Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z.  Their schedule of preferences is shown below.  If the Hare system is used, alternative X wins.  Could the voters who most prefer Z vote insincerely in some way to change the outcome in a way that would benefit them?

Number of Voters	

5	
4	
2	

First choice	
Z	
X	
Y	

Second choice	
Y	
Y	
X	

Third choice	
X	
Z	
Z	

A)	Yes, switch ranking of X and Y.	C)	Yes, switch ranking of X and Z.	
B)	Yes, switch ranking of Y and Z.	D)	No, X would always win.	

20.	Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z.  Their schedule of preferences is shown below.  If the Hare system is used, alternative X wins.  Could the voters who most prefer Y vote insincerely in some way to change the outcome in a way that would benefit them?

Number of Voters	

5	
4	
2	

First choice	
Z	
X	
Y	

Second choice	
Y	
Y	
X	

Third choice	
X	
Z	
Z	

A)	Yes, switch ranking of X and Y.	C)	Yes, switch ranking of X and Z.	
B)	Yes, switch ranking of Y and Z.	D)	No, X would always win.	

21.	Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z.  Their schedule of preferences is shown below.  Is there an agenda for which X would win under sequencial pairwise voting?  

Number of Voters	

5	
4	
2	

First choice	
Z	
X	
Y	

Second choice	
Y	
Y	
X	

Third choice	
X	
Z	
Z	

	A)  Yes, X Y Z.    B)  Yes, Y Z X.    C)  Yes, Z Y X.    D)  No.	

22.	Consider an 11-member committee that must choose one of three alternatives: X, Y, or Z.  Their schedule of preferences is shown below.  Is there an agenda for which Z would win under sequencial pairwise voting?  

Number of Voters	

5	
4	
2	

First choice	
Z	
X	
Y	

Second choice	
Y	
Y	
X	

Third choice	
X	
Z	
Z	

	A)  Yes, X Y Z.    B)  Yes, Y Z X.    C)  Yes, Z Y X.    D)  No.	

23.	Twenty-nine voters must choose from among three alternatives: A, B, and C.  The voters' preference schedules are shown below.  C wins in a Borda count. Can the six voters in the third column change their preference list to produce an outcome they like better?

Number of Voters	

12	
8	
6	
3	

First choice	
B	
C	
A	
C	

Second choice	
C	
A	
B	
B	

Third choice	
A	
B	
C	
A	

A)	No, C will always win.	C)	Yes, they can rank B, A, C.	
B)	Yes, they can rank A, C, B.	D)	Yes, they can rank C, A, B.	

24.	Twenty-nine voters must choose from among three alternatives: A, B, and C.  The voters' preference schedules are shown below.  C wins in a Borda count. Can the 12 voters in the first column change their preference list to produce an outcome they like better?

Number of Voters	

12	
8	
6	
3	

First choice	
B	
C	
A	
C	

Second choice	
C	
A	
B	
B	

Third choice	
A	
B	
C	
A	

A)	No, C will always win.	C)	Yes, they can rank B, A, C.	
B)	Yes, they can rank A, C, B.	D)	Yes, they can rank C, A, B.	

25.	Twenty-nine voters must choose from among three alternatives: A, B, and C.  The voters' preference schedules are shown below.  Using the agenda A, B, C, and sequential pairwise voting, alternative B wins.  Is there an agenda that produces C as a winner?

Number of Voters	

12	
8	
6	
3	

First choice	
B	
C	
A	
C	

Second choice	
C	
A	
B	
B	

Third choice	
A	
B	
C	
A	

A)	No, B always wins.	C)	Yes, the agenda C, B, A.	
B)	Yes, the agenda A, C, B.	D)	Yes, the agenda B, A, C.	

26.	Twenty-nine voters must choose from among three alternatives: A, B, and C.  The voters' preference schedules are shown below.  Using the agenda A, B, C, and sequential pairwise voting, alternative B wins.  Is there an agenda that produces A as a winner?

Number of Voters	

12	
8	
6	
3	

First choice	
B	
C	
A	
C	

Second choice	
C	
A	
B	
B	

Third choice	
A	
B	
C	
A	

A)	No, B always wins.	C)	Yes, the agenda C, B, A.	
B)	Yes, the agenda A, C, B.	D)	Yes, the agenda B, A, C.	

27.	A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip.  Their preference rankings are summarized in the table below, and the decision will be made using a Borda count.  Can the four voters in the last column change the results of the vote to their favor by changing their preference rankings?

Number of Voters	

10	
8	
4	

First choice	
B	
M	
Z	

Second choice	
M	
B	
M	

Third choice	
Z	
Z	
B	

	A)  No.    B)  Yes.	

28.	A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip.  Their preference rankings are summarized in the table below, and the decision will be made using a Borda count.  Can the 10 voters in the first column change the results of the vote to their favor by changing their preference rankings?

Number of Voters	

10	
8	
4	

First choice	
B	
M	
Z	

Second choice	
M	
B	
M	

Third choice	
Z	
Z	
B	

	A)  No.    B)  Yes.	

29.	A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip.  Their preference rankings are summarized in the table below, and the decision will be made using a Borda count.  Can the eight voters in the middle column change the results of the vote to their favor by changing their preference rankings?

Number of Voters	

10	
8	
4	

First choice	
B	
M	
Z	

Second choice	
M	
B	
M	

Third choice	
Z	
Z	
B	

	A)  No.    B)  Yes.	

30.	Consider the following preference table:

Number of voters	

4	
6	
8	
4	

First choice	
D	
C	
A	
B	

Second choice	
C	
B	
D	
A	

Third choice	
B	
D	
C	
C	

Fourth choice	
A	
A	
B	
D	

Using plurality, A wins. Could the four voters who most prefer D (and prefer A least) vote insincerely to change the outcome in a way that would benefit them?	
A)	No, they cannot change the outcome.	C)	Yes, they could get C to win.	
B)	Yes, they could get B to win.	D)	Yes, they could get D to win.	

31.	Consider the following preference table:

Number of voters	

4	
6	
8	
4	

First choice	
D	
C	
A	
B	

Second choice	
C	
B	
D	
A	

Third choice	
B	
D	
C	
C	

Fourth choice	
A	
A	
B	
D	

Using plurality, A wins. Could the six voters who most prefer C (and prefer A least) vote insincerely to change the outcome in a way that would benefit them?	
A)	No, they cannot change the outcome.	C)	Yes, they could get C to win.	
B)	Yes, they could get B to win.	D)	Yes, they could get D to win.	

32.	Consider the following preference table:

Number of voters	

4	
6	
8	
4	

First choice	
D	
C	
A	
B	

Second choice	
C	
B	
D	
A	

Third choice	
B	
D	
C	
C	

Fourth choice	
A	
A	
B	
D	

Using plurality, A wins. Could the four voters who most prefer B vote insincerely to change the outcome in a way that would benefit them?	
A)	No, they cannot change the outcome.	C)	Yes, they could get C to win.	
B)	Yes, they could get B to win.	D)	Yes, they could get D to win.	

33.	Consider the following preference table for two voters:
 
First choice	
D	
B	

Second choice	
C	
A	

Third choice	
B	
C	

Fourth choice	
A	
D	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

34.	Consider the following preference table for two voters:
 
First choice	
D	
B	

Second choice	
C	
A	

Third choice	
B	
C	

Fourth choice	
A	
D	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

35.	Consider the following preference table for two voters:
 
First choice	
C	
B	

Second choice	
B	
A	

Third choice	
D	
C	

Fourth choice	
A	
D	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

36.	Consider the following preference table for two voters:
 
First choice	
C	
B	

Second choice	
B	
A	

Third choice	
D	
C	

Fourth choice	
A	
D	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

37.	Consider the following preference table for two voters:
 
First choice	
C	
D	

Second choice	
B	
A	

Third choice	
D	
B	

Fourth choice	
A	
C	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

38.	Consider the following preference table for two voters:
 
First choice	
C	
D	

Second choice	
B	
A	

Third choice	
D	
B	

Fourth choice	
A	
C	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

39.	Consider the following preference table for three voters:
 
First choice	
C	
D	
A	

Second choice	
B	
A	
B	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

40.	Consider the following preference table for three voters:
 
First choice	
C	
D	
A	

Second choice	
B	
A	
B	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

41.	Consider the following preference table for three voters:
 
First choice	
C	
D	
A	

Second choice	
B	
A	
B	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter in the middle manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

42.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
A	
A	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

43.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
A	
A	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

44.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
A	
A	

Third choice	
D	
B	
D	

Fourth choice	
A	
C	
C	

If a Borda Count is used, can the voter on the right manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

45.	Consider the following preference table for three voters:
 
First choice	
C	
D	
D	

Second choice	
B	
B	
A	

Third choice	
D	
C	
B	

Fourth choice	
A	
A	
C	

If a Borda Count is used, can the voter on the left manipulate the outcome to his or her benefit?	
	A)  No    B)  Yes	

46.	Consider the following preference table for three voters:
 
First choice	
C	
D	
D	

Second choice	
B	
B	
A	

Third choice	
D	
C	
B	

Fourth choice	
A	
A	
C	

If a Borda Count is used, can the voter on the right or in the middle manipulate the outcome to his or her benefit?	
A)	Neither can.	C)	Only the voter in the middle can.	
B)	Only the voter on the right can.	D)	Both can.	

47.	Consider the following preference table for four voters:
 
First choice	
B	
D	
D	
C	

Second choice	
C	
B	
A	
A	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
C	
D	

If a Borda Count is used, can the second voter manipulate the outcome so that D wins?	
	A)  No    B)  Yes	

48.	Consider the following preference table for four voters:
 
First choice	
B	
D	
D	
C	

Second choice	
C	
B	
A	
A	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
C	
D	

If a Borda Count is used, can the fourth voter manipulate the outcome so that C wins?	
	A)  No    B)  Yes	

49.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
D	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
C	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the first voter manipulate the outcome so that B wins?	
	A)  No    B)  Yes	

50.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
D	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
C	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the third voter manipulate the outcome so that A wins?	
	A)  No    B)  Yes	

51.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
D	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
C	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the fourth voter manipulate the outcome so that C wins?	
	A)  No    B)  Yes	

52.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
C	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
D	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the first voter manipulate the outcome so that B wins?	
	A)  No    B)  Yes	

53.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
C	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
D	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the second voter manipulate the outcome so that D wins?	
	A)  No    B)  Yes	

54.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
C	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
D	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the second voter manipulate the outcome so that B wins?	
	A)  No    B)  Yes	

55.	Consider the following preference table for four voters:
 
First choice	
B	
D	
A	
C	

Second choice	
C	
B	
C	
D	

Third choice	
A	
C	
B	
B	

Fourth choice	
D	
A	
D	
A	

Fifth choice	
E	
E	
E	
E	

If a Borda Count is used, can the third voter manipulate the outcome so that A wins?	
	A)  No    B)  Yes	

56.	Consider the following preference table for three voters:
 
First choice	
B	
D	
A	

Second choice	
C	
B	
C	

Third choice	
A	
C	
B	

Fourth choice	
D	
A	
D	

Fifth choice	
E	
E	
E	

Is there an agenda for which D would win a sequencial pairwise election?	
	A)  No    B)  Yes	

57.	Consider the following preference table for three voters:
 
First choice	
B	
D	
A	

Second choice	
C	
B	
C	

Third choice	
A	
C	
B	

Fourth choice	
D	
A	
D	

Fifth choice	
E	
E	
E	

Is there an agenda for which A would win a sequencial pairwise election?	
	A)  No    B)  Yes	

58.	Consider the following preference table for three voters:
 
First choice	
B	
D	
A	

Second choice	
C	
B	
C	

Third choice	
A	
C	
B	

Fourth choice	
D	
A	
D	

Fifth choice	
E	
E	
E	

Is there an agenda for which C would win a sequencial pairwise election?	
	A)  No    B)  Yes	

59.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
C	
D	

Third choice	
A	
A	
C	

Fourth choice	
D	
B	
A	

Fifth choice	
E	
E	
E	

Is there an agenda for which D would win a sequencial pairwise election?	
	A)  No    B)  Yes	

60.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
C	
D	

Third choice	
A	
A	
C	

Fourth choice	
D	
B	
A	

Fifth choice	
E	
E	
E	

Is there an agenda for which C would win a sequencial pairwise election?	
	A)  No    B)  Yes	

61.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
C	
D	

Third choice	
A	
A	
C	

Fourth choice	
D	
B	
A	

Fifth choice	
E	
E	
E	

Is there an agenda for which B would win a sequencial pairwise election?	
	A)  No    B)  Yes	

62.	Consider the following preference table for three voters:
 
First choice	
C	
D	
B	

Second choice	
B	
C	
D	

Third choice	
A	
A	
C	

Fourth choice	
D	
B	
A	

Fifth choice	
E	
E	
E	

Is there an agenda for which A would win a sequencial pairwise election?	
	A)  No    B)  Yes	

63.	Consider the following preference table for three voters:
 
First choice	
A	
D	
B	

Second choice	
D	
C	
A	

Third choice	
B	
B	
D	

Fourth choice	
C	
E	
C	

Fifth choice	
E	
A	
E	

Is there an agenda for which A would win a sequencial pairwise election?	
	A)  No    B)  Yes	

64.	Consider the following preference table for three voters:
 
First choice	
A	
D	
B	

Second choice	
D	
C	
A	

Third choice	
B	
B	
D	

Fourth choice	
C	
E	
C	

Fifth choice	
E	
A	
E	

Is there an agenda for which B would win a sequencial pairwise election?	
	A)  No    B)  Yes	

65.	Consider the following preference table for three voters:
 
First choice	
A	
D	
B	

Second choice	
D	
C	
A	

Third choice	
B	
B	
D	

Fourth choice	
C	
E	
C	

Fifth choice	
E	
A	
E	

Is there an agenda for which C would win a sequencial pairwise election?	
	A)  No    B)  Yes	

66.	Consider the following preference table for three voters:
 
First choice	
A	
D	
B	

Second choice	
D	
C	
A	

Third choice	
B	
B	
D	

Fourth choice	
C	
E	
C	

Fifth choice	
E	
A	
E	

Is there an agenda for which D would win a sequencial pairwise election?	
	A)  No    B)  Yes	

Answer Key

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