Deck 12: Electing the President

Question 1

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively.
Which candidate would be elected for the position based on the ideal points?

Answer 1

B

Question 2

Use the following information to answer Questions
Suppose that 17 voters have ideal points as given in the following table. Candidate A announces a policy position of 1 and Candidate B announces a policy position of 5.
Suppose that a voter is added with ideal points of 3. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

Answer 2

Yes. There are 12 voters between 1 and 5 which is 2/3 of 18. For example, if Candidate C has a policy position of 2.5, then Candidate C would get 9 votes and win the election.

Question 3

Describe the composition of the Electoral College.

Answer 3

Each state gets one electoral vote for each of its two senators and for each of its representatives in the House of Representatives. The District of Columbia is given three electoral votes.

Question 4

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively.
Find the midpoint of the two policy positions.

Question 5

Use the following information to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming Candidate A and Candidate B's policy positions are 2.7 and 3.3, determine whether Candidate C can enter and win the election.

Question 6

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively.
Find the number of board members who would vote for A based on ideal points.

Question 7

Use the following information to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming that Candidate A's policy position is 4 and Candidate B announces a policy position of 2.5, describe which voters vote for Candidate B.

Question 8

Use the following information to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Explain why the bent solid line describes a continuous distribution.

Question 9

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively.
Find the number of board members who would vote for B based on ideal points.

Question 10

Use the following information to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming that Candidate A's policy position is 4, if Candidate B announces a policy position between 1 and 2, then who will be the winner of the election?

Question 11

Explain the justification for the Electoral College.

Question 12

Find the range of values that make up the extended median if the voters' ideal points are 2, 3, 4, 4, 6, 8, 8, 8, 9, 10.

Question 13

Use the following information to answer Questions.
Consider the following distribution of 33 voters at eight different positions over the interval [0,1].
What is the equilibrium position in a two-candidate election?

Question 14

Use the following information to answer Questions.
Consider the following distribution of 33 voters at eight different positions over the interval [0,1].
For two candidates A and B with distinct policy positions 0.3 and 0.75, respectively, find the number of votes for the candidate B based on voter's ideal positions.

Question 15

Use the following information to answer Questions
Suppose that 17 voters have ideal points as given in the following table. Candidate A announces a policy position of 1 and Candidate B announces a policy position of 5.
Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

Question 16

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively.
Find the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A.

Question 17

Give an example of a voter distribution over the interval [0,1] that is skewed to the left.

Question 18

Use the following information to answer Questions.
Consider the following distribution of 33 voters at eight different positions over the interval [0,1].
For two candidates A and B with distinct policy positions 0.3 and 0.75, respectively, find the number of votes for the candidate A based on voter's ideal positions.

Question 19

Use the following information to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming Candidate A and Candidate B's policy positions are 2 and 4, determine whether Candidate C can enter and win the election.

Question 20

Use the following information to answer Questions.
Consider the following distribution of 33 voters at eight different positions over the interval [0,1].
What is the median of the distribution?

Question 21

What is

A) 2
B) 3
C) 10
D) 20

Question 22

Explain the median of a continuous voter distribution.

Question 23

Describe the spoiler problem.

Question 24

Use the following distribution of 33 voters at eight different positions over the interval [0, 1] to answer Questions
What is the median of the distribution?

A) 0.5
B) 0.55
C) 0.56
D) 0.6

Question 25

Describe the 1/3-separation obstacle.

Question 26

Describe the National Popular Vote law.

Question 27

Explain the median-voter theorem.

Question 28

Use the following distribution of 33 voters at eight different positions over the interval [0, 1] to answer Questions
For two candidates A and B with distinct policy positions 0.3 and 0.8, respectively, find the number of votes for the candidate A based on voter's ideal positions.

A) 16
B) 17
C) 23
D) 25

Question 29

Use the following distribution of 32 voters at eight different positions over the interval [0, 1] to answer Questions
For two candidates A and B with distinct policy positions 0.2 and 0.7, respectively, find the number of votes for the candidate A based on voter's ideal positions.

A) 11
B) 16
C) 19
D) 23

Question 30

Describe the 2/3-separation opportunity.

Question 31

Give an example of a set of five data that is bimodal.

Question 32

Use the following distribution of 31 voters at seven different positions over the interval [0, 1] to answer Questions
What is the median of the distribution?

A) 0.3
B) 0.35
C) 0.4
D) 0.47

Question 33

Suppose voters are distributed so that they are only located at certain positions along the left-right continuum. What is this type of distribution called?

Question 34

Use the following distribution of 31 voters at seven different positions over the interval [0, 1] to answer Questions
For two candidates A and B with distinct policy positions 0.3 and 0.75, respectively, find the number of votes for the candidate A based on voter's ideal positions.

A) 5
B) 10
C) 16
D) 21

Question 35

Use the following distribution of 32 voters at eight different positions over the interval [0, 1] to answer Questions
What is the equilibrium position in a two-candidate election?

A) 0.3
B) 0.4
C) 0.5
D) 0.6

Question 36

Give an example of five data that is unimodal.

Question 37

Use the following distribution of 31 voters at seven different positions over the interval [0, 1] to answer Questions
What is the equilibrium position in a two-candidate election?

A) 0.3
B) 0.35
C) 0.4
D) 0.47

Question 38

Use the following distribution of 33 voters at eight different positions over the interval [0, 1] to answer Questions
What is the equilibrium position in a two-candidate election?

A) 0.5
B) 0.55
C) 0.56
D) 0.6

Question 39

Explain the extended median of a discrete distribution.

Question 40

Define an equilibrium position.

Question 41

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
What is the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A?

A) QUOTE
B)
C)
D) QUOTE

Question 42

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
What is the midpoint of the two policy positions?

A) (7/2, 5/2)
B) (3, 4)
C) (7/2, 3)
D) (5/2, 3/2)

Question 43

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
How many board members would vote for B based on ideal points?

A) 2
B) 3
C) 4
D) 5

Question 44

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 two thirds 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.

Question 45

Use the following information to answer Questions
Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively.
What is the midpoint of the two policy positions?

A) (2, 2)
B) (2, 3)
C) (3, 3)
D) (3, 4)

Question 46

Use the following information to answer Questions
Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively.
Which candidate would win the election?

A) A
B) B

Question 47

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.

Question 48

Use the following information to answer Questions
Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively.
How many board members would vote for B based on ideal points?

A) 1
B) 2
C) 3
D) 4

Question 49

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.

Question 50

Use the following information to answer Questions
Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively.
What is the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A?

A)
B) QUOTE
C)
D)

Question 51

Use the following information to answer Questions
Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively.
What is the equation of the line passing through candidates' policy positions?

A) 7?? = 5??+2
B) 3?? = −5??+7
C) 5?? = 3??+2
D) 5?? = −7??+12

Question 52

What is the smallest value of the extended median if the voters' ideal points are 2, 2, 4, 4, 6, 8, 8, 8, 10, 10?

A) 2
B) 4
C) 6
D) 8

Question 53

What is

A) 4
B) 8
C) 10
D) 12

Question 54

What is the largest value of the extended median if the voters' ideal points are 2, 2, 4, 4, 6, 8, 8, 8, 10, 10?

A) 4
B) 6
C) 8
D) 10

Question 55

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
Which candidate would win the election based on ideal points?

A) A
B) B

Question 56

Use the following information to answer Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
What is the equation of the line passing through candidates' policy positions?

A) QUOTE
B) QUOTE
C) QUOTE
D) QUOTE

Question 57

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 one third 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.

Question 58

A peak of a voter distribution is a:

A) median.
B) mean.
C) mode.
D) maximin position.

Question 59

Which statement is correct for the bent solid line given below?

A) It describes a continuous distribution because the bent line is continuous.
B) It does not describe a continuous distribution because the area beneath the bent line is not 1.
C) It describes a continuous distribution because the area beneath the bent line is 1.
D) None of the above.

Question 60

Which statement is correct for the curve given below?

A) It describes a continuous distribution because the area beneath the curve is 1.
B) It does not describe a continuous distribution because the area beneath the curve is not 1.
C) It does not describe a continuous distribution because the curve is not continuous.
D) None of the above.

Question 61

Use the following to answer Questions
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, what fraction of the vote does the winner receive?

A) 1/3
B) 1/2
C) 11/24
D) 7/12

Question 62

Consider the following distribution of 34 voters at eight different positions over the interval [0, 1]. This distribution of voters is best described as:

A) skewed left.
B) skewed right.
C) symmetric.
D) bimodal.

Question 63

Use the following information to answer Questions
Consider the following distribution of 34 voters at eight different positions over the interval [0, 1].
Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.8. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

A) Yes
B) No

Question 64

Use the following information to answer Questions
Consider the following distribution of 35 voters at eight different positions over the interval [0, 1].
What is the median position of the voters?

A) 0.45
B) 0.5
C) 0.55
D) 0.6

Question 65

Use the following to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assume that Candidate A and Candidate B's policy positions are 1.5 and 2.5. If Candidate C enters at 1, what fraction of the vote does the winner receive?

A) 9/32
B) 7/16
C) 1/2
D) 9/16

Question 66

Use the following to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming that Candidate A's policy position is 1.5 and Candidate B announces a policy position of 2.3, which voters would vote for Candidate B?

A) Voters with ideal points between 1.5 and 2.3
B) Voters with ideal points between 1.5 and 3
C) Voters with ideal points between 2 and 2.3
D) Voters with ideal points between 1.9 and 3

Question 67

Use the following information to answer Questions
Consider the following distribution of 34 voters at eight different positions over the interval [0, 1].
Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.8. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

A) Yes
B) No

Question 68

Use the following to answer Questions
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 1/3, what fraction of the vote does the winner receive?

A) 2/3
B) 3/4
C) 11/24
D) 7/12

Question 69

Use the following to answer Questions
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, who receives a plurality?

A) A
B) B
C) C
D) None of the candidates

Question 70

Use the following to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assume that Candidate A and Candidate B's policy positions are 1.5 and 2.5. If Candidate C enters at 2, what fraction of the vote does the winner receive?

A) 9/32
B) 7/16
C) 1/2
D) 9/16

Question 71

Consider the following distribution of 35 voters at eight different positions over the interval [0, 1]. This distribution of voters is best described as:

A) skewed left.
B) skewed right.
C) symmetric.
D) bimodal.

Question 72

Use the following information to answer Questions
Consider the following distribution of 35 voters at eight different positions over the interval [0, 1].
This distribution of voters is best described as:

A) skewed left.
B) skewed right.
C) symmetric.
D) bimodal.

Question 73

Use the following to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assume that Candidate A and Candidate B's policy positions are 1.5 and 2.5. If Candidate C enters at 2, who would win the election?

A) A
B) B
C) C
D) A and B tie.

Question 74

Use the following information to answer Questions
Consider the following distribution of 34 voters at eight different positions over the interval [0, 1].
This distribution of voters is best described as:

A) skewed left.
B) skewed right.
C) symmetric.
D) bimodal.

Question 75

Use the following to answer Questions
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 1/3, who receives a plurality?

A) A
B) B
C) C
D) D

Question 76

Use the following information to answer Questions
Consider the following distribution of 35 voters at eight different positions over the interval [0, 1].
Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.7. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

A) Yes
B) No

Question 77

Use the following information to answer Questions
Consider the following distribution of 34 voters at eight different positions over the interval [0, 1].
This distribution of voters is best described as:

A) skewed left.
B) skewed right.
C) symmetric.
D) bimodal.

Question 78

Use the following to answer Questions
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.

Question 79

Use the following to answer Questions
Suppose that the continuous distribution of voters' ideal points is the bent solid line below.
Assuming that Candidate A's policy position is 2.5, if Candidate B announces a policy position between 1 and 1.5, then who will be the winner of the election?

A) A
B) B
C) A and B tie.
D) No conclusion can be made.

Question 80

Use the following information to answer Questions
Consider the following distribution of 34 voters at eight different positions over the interval [0, 1].
Assume that Candidate A and Candidate B's policy positions are 0.3 and 0.8. If Candidate C enters at 0.55, what fraction of the vote does the winner receive?

A) 6/17
B) 7/17
C) 19/34
D) 12/17