1.	Consider the following distribution of 31 voters at 7 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	

Location li 
   of position i	
0.1	
0.2	
0.3	
0.4	
0.5	
0.7	
0.8	

Number of voters 
   at position i	
1	
4	
5	
6	
5	
6	
4	

The equilibrium position is	
	A)  0.3    B)  0.35    C)  0.4    D)  0.47	

2.	Consider the following distribution of 31 voters at 7 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	

Location li 
   of position i	
0.1	
0.2	
0.3	
0.4	
0.5	
0.7	
0.8	

Number of voters 
   at position i	
1	
4	
5	
6	
5	
6	
4	

The mean position is	
	A)  0.3    B)  0.35    C)  0.4    D)  0.47	

3.	Consider the following distribution of 31 voters at 7 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	

Location li 
   of position i	
0.1	
0.2	
0.3	
0.4	
0.5	
0.7	
0.8	

Number of voters 
   at position i	
1	
4	
5	
6	
5	
6	
4	

The median position is	
	A)  0.3    B)  0.35    C)  0.4    D)  0.47	

4.	Consider the following distribution of 33 voters at 8 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	
8	

Location li 
   of position i	
0.1	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

Number of voters 
   at position i	
1	
4	
6	
6	
6	
2	
5	
3	

The equilibrium position is	
	A)  0.5    B)  0.55    C)  0.56    D)  0.6	

5.	Consider the following distribution of 33 voters at 8 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	
8	

Location li 
   of position i	
0.1	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

Number of voters 
   at position i	
1	
4	
6	
6	
6	
2	
5	
3	

The mean position is	
	A)  0.5    B)  0.55    C)  0.56    D)  0.6	

6.	Consider the following distribution of 33 voters at 8 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	
8	

Location li 
   of position i	
0.1	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

Number of voters 
   at position i	
1	
4	
6	
6	
6	
2	
5	
3	

The median position is	
	A)  0.5    B)  0.55    C)  0.56    D)  0.6	

7.	Consider the following distribution of 32 voters at 8 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	
8	

Location li 
   of position i	
0.1	
0.2	
0.3	
0.5	
0.6	
0.7	
0.8	
0.9	

Number of voters 
   at position i	
6	
5	
5	
3	
4	
6	
2	
1	

The equilibrium position is	
	A)  0.3    B)  0.4    C)  0.5    D)  0.6	

8.	Consider the following distribution of 32 voters at 8 different positions over the interval [0, 1].
 
Position i	
1	
2	
3	
4	
5	
6	
7	
8	

Location li 
  of position i	
0.1	
0.2	
0.3	
0.5	
0.6	
0.7	
0.8	
0.9	

Number of voters
  at position i	

6	

5	

5	

3	

4	

6	

2	

1	

The mean position is	
	A)  0.4    B)  0.43    C)  0.47    D)  0.5	

9.	The point on the horizontal axis of a voter distribution where half of the voters have attitudes that lie to the left and half of the voters have attitudes that lie to the right is the	
	A)  median.    B)  mean.    C)  mode.    D)  maximin position.	

10.	The positions of voters on a voter distribution are weighted by the fraction of voters at that position. This is used to find the	
	A)  median.    B)  mean.    C)  mode.    D)  maximin position.	

11.	A candidate selects a point on the horizontal axis of a voter distribution where no position can guarantee a better outcome, no matter what position another candidate adopts. This position is the	
	A)  median.    B)  mean.    C)  mode.    D)  maximin position.	

12.	A peak of a voter distribution is a	
	A)  median.    B)  mean.    C)  mode.    D)  maximin position.	

13.	A poll has identified Candidates A and B as the top two candidates in an election. Candidate A is the Condorcet winner. We know that A will win because of the	
A)	Condorcet rule.	C)	median-voter theorem.	
B)	poll sssumption.	D)	proportional rule.	

14.	A distribution of voters is symmetric and unimodal, and the first two candidates have chosen different positions A and B that are equidistant from the median. A is below the median and B is above the median. No more than 1/3 of the voters lie between A and B. To win the election, a third candidate should take a position C that lies	
	A)  below A.    B)  between A and B.    C)  above B.    D)  nowhere; C cannot win.	

15.	A distribution of voters is symmetric and unimodal, and the first two candidates have chosen different positions A and B that are equidistant from the median. A is below the median and B is above the median, and 2/3 of the voters lie between A and B. To win the election, a third candidate should take a position C that lies	
	A)  below A.    B)  between A and B.    C)  above B.    D)  nowhere; C cannot win.	

16.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  7:  A B C D
II.  5:  B D A C
III.  3:  C B A D
IV.  4:  D C B A
 
Which candidate is the plurality winner?	
	A)  A    B)  B    C)  C    D)  D	

17.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  7:  A B C D
II.  5:  B D A C
III.  3:  C B A D
IV.  4:  D C B A
 
Which candidate is the Condorcet winner?	
	A)  A    B)  B    C)  C    D)  D	

18.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  7:  A B C D
II.  5:  B D A C
III.  3:  C B A D
IV.  4:  D C B A
 
Suppose there is a poll that differentiates the top two candidates.  Which candidate will win the election after the poll?	
	A)  A    B)  B    C)  C    D)  D	

19.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  6:  C A B D
II.  4:  D B A C
III.  2:  B C A D
IV.  5:  A D C B
 
Which candidate is the plurality winner?	
	A)  A    B)  B    C)  C    D)  D	

20.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  6:  C A B D
II.  4:  D B A C
III.  2:  B C A D
IV.  5:  A D C B
 
Which candidate is the Condorcet winner?	
	A)  A    B)  B    C)  C    D)  D	

21.	Assume there are four classes of voters that rank four candidates as follows:
 
I.  6:  C A B D
II.  4:  D B A C
III.  2:  B C A D
IV.  5:  A D C B
 
Suppose there is a poll that differentiates the top two candidates.  Which candidate will win the election after the poll?	
	A)  A    B)  B    C)  C    D)  D	

22.	Assume there are three classes of voters that rank three candidates as follows:
 
I.  3:  A B C
II.  7:  C A B
III.  5:  B C A
 
Which candidate is the plurality winner?	
	A)  A    B)  B    C)  C    D)  There is no plurality winner.	

23.	Assume there are three classes of voters that rank three candidates as follows:
 
I.  3:  A B C
II.  7:  C A B
III.  5:  B C A
 
Which candidate is the Condorcet winner?	
	A)  A    B)  B    C)  C    D)  There is no Condorcet winner.	

24.	A distribution of voters is uniform over [0, 1]. Candidates A and B have already entered the election and anticipate a third candidate C to enter the election later. Candidates A and B should choose what positions?	
A)	One at 1/3, the other at 2/3	C)	One at 1/4, the other at 3/4	
B)	Both at 1/2	D)	None of the above	

25.	A distribution of voters is uniform over [0, 1]. Candidates A and B have already entered the election and have chosen positions at 1/4 and 3/4, respectively. If C enters at 1/2, who wins the election?	
	A)  A    B)  B    C)  C    D)  A and B tie	

26.	Assume there are three classes of voters that rank three candidates as follows:
 
I.  1:  A B C
II.  4:  C B A
III.  3:  B A C
 
Which candidate is the Condorcet winner?	
	A)  A    B)  B    C)  C    D)  There is no Condorcet winner.	

27.	Assume there are three classes of voters that rank three candidates as follows:
 
I.  1:  A B C
II.  4:  C B A
III.  3:  B A C
 
According to the Poll Assumption, which candidate will win?	
	A)  A    B)  B    C)  C    D)  No conclusion can be made.	

28.	Suppose there are three classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the five class I voters prefer A and C, between whom they are indifferent, to B and D, between whom they are also indifferent: 
 
I.  5:  (A C) (B D)
II.  3:  (B C D) (A)
III.  4:  (B) (A C D)
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

29.	Suppose there are three classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the six class I voters prefer A and B, between whom they are indifferent, to C and D, between whom they are also indifferent: 
 
I.  6:  (A B) (C D)
II.  3:  (B C D) (A)
III.  4:  (C) (A B D)
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

30.	Suppose there are four classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the five class I voters prefer B and C, between whom they are indifferent, to A and D, between whom they are also indifferent: 
 
I.  5:  (B C) (A D)
II.  3:  (A B C) (D)
III.  3:  (A) (B C D)
IV. 4:  (C D) (A B)
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

31.	Suppose there are four classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the seven class I voters prefer C and D, between whom they are indifferent, to A and B, between whom they are also indifferent: 
 
I.  7:  (C D) (A B)
II.  6:  (A C D) (B) 
III. 1:  (B D) (A C)
IV. 3:  (B C) (A D)
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

32.	Suppose there are four classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the four class I voters prefer A and B, between whom they are indifferent, to C and D, between whom they are also indifferent: 
 
I.  4:  (A B) (C D)
II.  2:  (D) (A B C)
III.  1:  (A B C) (D)
IV. 5:  (C D) (A B)
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

33.	Suppose there are four classes of voters that rank four candidates as shown below. For each class of voters, the preferred subset of candidates is enclosed in the first set of parentheses and the non-preferred subset in the second set of parentheses.  Thus, the four class I voters prefer A and B, between whom they are indifferent, to C and D, between whom they are also indifferent: 
 
I.  4: (A B) (C D)
II.  5:  (A B C) (D)
III.  6:  (B C D) (A)
IV. 5:  (A D) (B C) 
 
Assuming that each class of voters chooses its dominant strategy, who wins?	
	A)  A    B)  B    C)  C    D)  D	

34.	Consider the following distribution of 35 voters at 8 different positions over the interval [0, 1]. 
 
location	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

4	

7	

4	

2	

3	

7	

4	

4	

This distribution of voters is best described as	
	A)  skewed left.    B)  skewed right.    C)  symmetric.    D)  bimodal.	

35.	Consider the following distribution of 34 voters at 8 different positions over the interval [0, 1].
 
location	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

3	

3	

2	

5	

7	

8	

4	

This distribution of voters is best described as	
	A)  skewed left.    B)  skewed right.    C)  symmetric.    D)  bimodal.	

36.	Consider the following distribution of 34 voters at 8 different positions over the interval [0, 1].
 
location	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

3	

5	

7	

7	

5	

3	

2	

This distribution of voters is best described as	
	A)  skewed left.    B)  skewed right.    C)  symmetric.    D)  bimodal.	

37.	Consider the following distribution of 34 voters at 8 different positions over the interval [0, 1].
 
location	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

3	

6	

7	

4	

3	

4	

4	

3	

This distribution of voters is best described as	
	A)  skewed left.    B)  skewed right.    C)  symmetric.    D)  bimodal.	

38.	A voter is faced with a dilemma in a three-candidate election. Her favorite candidate does not seem able to win. However, there is a chance that her second choice candidate could win. The election will be determined using approval voting. The voter's most promising strategy would be to	
A)	vote for both her first and second choices.	
B)	vote for her second choice only.	
C)	vote for her first choice only.	
D)	not vote.	

39.	How many votes are available in the electoral college?	
	A)  51    B)  100    C)  538    D)  561	

40.	How many electoral votes are needed to win an election?	
	A)  359    B)  270    C)  136    D)  26	

41.	Assume there are three states with 3, 8, and 14 voters, and they are all toss-up states.  If both the Democratic and Republican candidates choose strategies that maximize their expected popular vote (the proportional rule), and they have the same total resources (D = R = 100), what resources should be allocated for each state?	
	A)  5, 22, and 52    B)  6, 28, and 65    C)  12, 32, and 56    D)  15, 28, and 57	

42.	Assume there are three states with 3, 8, and 14 voters, and they are all toss-up states.  If both the Democratic and Republican candidates choose strategies that maximize their expected electoral vote (the 3/2's rule), and they have the same total resources (D = R = 100), what resources should be allocated for each state?	
	A)  5, 22, and 52    B)  6, 28, and 65    C)  12, 32, and 56    D)  15, 28, and 57	

43.	Assume there are three states with 7, 8, and 21 voters, and they are all toss-up states.  If both the Democratic and Republican candidates choose strategies that maximize their expected popular vote (the proportional rule), and they have the same total resources (D = R = 100), what resources should be allocated for each state?	
	A)  13, 16, and 70    B)  19, 22, and 58    C)  20, 24, and 56    D)  21, 24, and 63	

44.	Assume there are three states with 7, 8, and 21 voters, and they are all toss-up states.  If both the Democratic and Republican candidates choose strategies that maximize their expected electoral vote (the 3/2's rule), and they have the same total resources (D = R = 100), what resources should be allocated for each state?	
	A)  13, 16, and 70    B)  19, 22, and 58    C)  20, 24, and 56    D)  21, 24, and 63	

45.	Voting in such a way that an acceptable candidate can be elected if a first choice is not viable is called	
	A)  sincere voting.    B)  strategic voting.    C)  plurality voting.    D)  approval voting.	

46.	When voters may vote for as many candidates as they like, the selection method is called	
	A)  sincere voting.    B)  strategic voting.    C)  plurality voting.    D)  approval voting.	

47.	Suppose 36 voters are distributed at 9 different positions over the interval [0, 1], as suggested by this incomplete table.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

?	

?	

?	

?	

?	

?	

?	

?	

?	

Which situation below would result in a bimodal distribution?	
A)	18 voters at 0.3 and 18 voters at 0.7	
B)	3 voters at each of the nine positions	
C)	all 36 voters at 0.1	
D)	9 voters at each of these four positions:  0.2, 0.4, 0.6, 0.8	

48.	Suppose 36 voters are distributed at 9 different positions over the interval [0, 1], as suggested by this incomplete table.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

?	

?	

?	

?	

?	

?	

?	

?	

?	

Which situation below would result in a skewed distribution?	
A)	18 voters at 0.3 and 18 voters at 0.7	
B)	3 voters at each of the nine positions	
C)	all 36 voters at 0.1	
D)	9 voters at each of these four positions:  0.2, 0.4, 0.6, 0.8	

49.	Suppose 36 voters are distributed at 9 different positions over the interval [0, 1], as suggested by this incomplete table.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

?	

?	

?	

?	

?	

?	

?	

?	

?	

Which situation below would result in a symmetric distribution?	
A)	12 voters at each of 0.3 and 0.7, 6 voters at each of 0.4 and 0.6	
B)	6 voters at each of the first 6 positions	
C)	all 36 voters at 0.1	
D)	9 voters at each of these four positions:  0.2, 0.4, 0.8, 0.9	

50.	Suppose 16 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

4	

0	

0	

1	

4	

7	

0	

0	

0	

What can you say about the distribution?	
	A)  it is bimodal    B)  it is unimodal    C)  it is symmetric    D)  it is sincere	

51.	Suppose 16 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

0	

4	

5	

4	

1	

0	

0	

0	

What can you say about the distribution?	
A)	it is symmetric	C)	it is skewed to the right	
B)	it is skewed to the left	D)	it reflects strategic voting	

52.	Suppose 16 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

0	

4	

5	

0	

5	

0	

0	

0	

What is the mean position of the voters?	
	A)  0.3    B)  0.4    C)  0.6    D)  none of these	

53.	Suppose 16 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

0	

4	

5	

0	

5	

0	

0	

0	

What is the median position of the voters?	
	A)  0.3    B)  0.4    C)  0.6    D)  none of these	

54.	Suppose 20 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

0	

4	

3	

0	

7	

2	

0	

2	

What is the mean position of the voters?	
	A)  0.4    B)  0.5    C)  0.6    D)  none of these	

55.	Suppose 20 voters are distributed at different positions over the interval [0, 1], as shown below.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

2	

0	

4	

3	

0	

7	

2	

0	

2	

What is the median position of the voters?	
	A)  0.4    B)  0.5    C)  0.6    D)  none of these	

56.	Suppose 20 voters are distributed at 9 different positions over the interval [0, 1], as suggested by this incomplete table.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

?	

?	

?	

?	

?	

?	

?	

?	

?	

If the distribution is symmetric, which of the following conditions would be true?	
A)	the mean and the median are equal	C)	the mean is greater than the median	
B)	the mean is less than the median			

57.	Suppose 20 voters are distributed at 9 different positions over the interval [0, 1], as suggested by this incomplete table.
 
location	
0.1	
0.2	
0.3	
0.4	
0.5	
0.6	
0.7	
0.8	
0.9	

number of
  voters	

?	

?	

?	

?	

?	

?	

?	

?	

?	

If the distribution is skewed to the left, which of the following conditions would be true?	
A)	the mean and the median are equal	C)	the mean is greater than the median	
B)	the mean is less than the median			

58.	If state A has three times the population of state B then	
A)	A will have about three times the Electoral College members as B	
B)	A will have about two times the Electoral College members as B	
C)	A will have the same number of Electoral College members as B	

59.	A toss-up state is	
A)	a state where the outcome is close.	
B)	a state where the outcome is easily determined.	
C)	a state whose Electoral College votes do not make a difference in the result.	
D)	a state whose Electoral College members are free to vote their individual choice.	

60.	The Electoral College is designed to enable the most popular candidate to win an election.	
	A)  True    B)  False	

Answer Key

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