Deck 14: Apportionment

Question 1

Explain the population paradox.

Answer 1

The population paradox occurs when one state's apportionment decreases and another state's apportionment increases even though the first state has gained population and the second state has lost population.

Question 2

Use the Jefferson method of apportionment to distribute 15 representatives to the three states with the populations shown below.

Answer 2

A 8
B 5
C 2

Question 3

Given the cities and the populations below, use the Webster method of apportionment to distribute 25 seats on a regional board.

Answer 3

Greenville 9
Riverdale 7
Oceanside 5
Parkview 4

Question 4

Explain the new state paradox.

Question 5

Use the Hamilton method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below.

Question 6

Use the following information to answer Questions 5-7.
A city is divided into three regions for distributing the 20 representatives on a public utility board. The regions and their populations are shown below.
Compute the quota for each region.

Question 7

Use the Webster method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below.

Question 8

Given the cities and the populations below, use the Jefferson method of apportionment to distribute 25 seats on a regional board.

Question 9

A city is divided into four regions for distributing the 20 representatives on a public utility board. The regions and their populations are shown below. The board uses the Hamilton method of apportionment to distribute seats. Find the district population for each region based on this apportionment.

Question 10

Explain the Alabama paradox.

Question 11

Use the Jefferson method of apportionment to distribute representatives.

Question 12

Given the cities and the populations below, use the Hamilton method of apportionment to distribute 25 seats on a regional board.

Question 13

Use the Jefferson method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below.

Question 14

Use the Hill-Huntington method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below.

Question 15

Use the Hamilton method of apportionment to distribute 15 representatives to the three states with the populations shown below.

Question 16

Use the Hill-Huntington method of apportionment to distribute 15 representatives to the three states with the populations shown below.

Question 17

Use the Webster method of apportionment to distribute 15 representatives to the three states with the populations shown below.

Question 18

Use the Hamilton method of apportionment to distribute representatives.

Question 19

Given the cities and the populations below, use the Hill-Huntington method of apportionment to distribute 25 seats on a regional board.

Question 20

The Hamilton method of apportionment always satisfies what is called the "quota condition." What does this mean?

Question 21

Use the Hamilton's method to determine how many cars should go to each precinct.

Question 22

A town board has 10 members, divided among three regions of the town using the Hamilton method of apportionment. The regions and their populations are shown below. Find the difference in district population for the North and South regions.

Question 23

A country has three states with the populations shown below. The House of Representatives for the country is to have 15 members. Find the district population for each state if the country uses the Jefferson method of apportionment.

Question 24

The manager of a busy restaurant is working on a schedule for the restaurant's 25 food servers. There are three shifts, as identified below: Use the Hill-Huntington method to determine how many food servers should be scheduled for each shift.

Question 25

A town board has 10 members, divided among three regions of the town using the Hamilton method of apportionment. The regions and their populations are given below. Find the difference in representative share for the North and South regions.

Question 26

The manager of a busy restaurant is working on a schedule for the restaurant's 25 food servers. There are three shifts, as identified below: Use the Hamilton method to determine how many food servers should be scheduled for each shift.

Question 27

A small country has four states and a House of Representatives with 20 seats. Given the states, populations, and apportionment below, find the percentage difference in district population between states A and C.

Question 28

What is the geometric mean of 7 and 8? Use four decimal places.

Question 29

List three paradoxes of the Hamilton method.

Question 30

What is the Hill-Huntington rounding point of 6.475? Use four decimal places.

Question 31

Among all divisor methods, which method shows no bias with regard to state population?

Question 32

The manager of a busy restaurant is working on a schedule for the restaurant's 25 food servers. There are three shifts, as identified below: Use the Jefferson method to determine how many food servers should be scheduled for each shift.

Question 33

Use the Jefferson's method to determine how many cars should go to each precinct.

Question 34

The manager of a busy restaurant is working on a schedule for the restaurant's 25 food servers. There are three shifts, as identified below: Use the Webster method to determine how many food servers should be scheduled for each shift.

Question 35

Use the Hill-Huntington method to determine how many cars should go to each precinct.

Question 36

A city is divided into four regions for distributing the 20 representatives on a public utility board. The regions and their populations are shown below. The board uses the Hamilton method of apportionment to distribute seats. Find the representative share for each region based on this apportionment.

Question 37

Use the following information to answer Questions 32-35.
Thirty patrol cars are to be apportioned to three precincts according to the monthly crime totals, which are as follows:
Precinct Crimes reported last month
I 94
II 130
III 108
Use the Webster's method to determine how many cars should go to each precinct.

Question 38

A small country has four states and a House of Representatives with 20 seats. Given the states, populations, and apportionment below, find the percentage difference in representative share between states A and C.

Question 39

What is the Hill-Huntington rounding of 6.475?

Question 40

A country has three states with the populations shown below. The House of Representatives for the country is to have 15 members. Find the representative share for each state if the country uses the Jefferson method of apportionment.

Question 41

The d'Hondt method always leads to the same apportionment as Jefferson's method.

Question 42

The Jefferson method of apportionment can display the population paradox.

Question 43

For a given set of populations and house sizes, different methods of apportionment may lead to different apportionments.

Question 44

The Hamilton method of apportionment can display the population paradox.

Question 45

Use the following information to answer the Questions:
Three states have the following populations: $\begin{array}{ll}\underline {\text {State}}&\underline {\text {Population}}\\\mathrm{A} & 10,040 \\\mathrm{~B} & 8000 \\\mathrm{C} & 2050\end{array}$ A house of representatives with 17 members is to be apportioned among these states.

-What is the tentative apportionment for state A using Hamilton's method?

A) 8
B) 8.5
C) 9
D) 9.5

Question 46

An apportionment method exists that satisfies the quota condition and is free from both the population paradox and the Alabama paradox.

Question 47

We are scheduling seven course sections for a total of 217 students. Enrollments are 109 in calculus I, 79 in calculus II, 29 in advanced calculus. Find the apportionment for advanced calculus using the Hamilton method.

A) 0
B) 1
C) 2
D) 3

Question 48

The Jefferson method of apportionment can display the Alabama paradox.

Question 49

Use the following information to answer the Questions:
Three states have the following populations: $\begin{array}{ll}\underline {\text {State}}&\underline {\text {Population}}\\\mathrm{A} & 10,040 \\\mathrm{~B} & 8000 \\\mathrm{C} & 2050\end{array}$ A house of representatives with 17 members is to be apportioned among these states.

-What is the tentative apportionment for state C using Webster's method?

A) 0
B) 1
C) 2
D) 3

Question 50

For a given set of populations and house sizes, different methods of apportionment may lead to the same apportionment.

Question 51

The Webster method of apportionment can display the population paradox.

Question 52

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Find the apportionment for the Applewood district.

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

Question 53

We are scheduling seven course sections for a total of 217 students. Enrollments are 109 in calculus I, 79 in calculus II, and 29 in advanced calculus. Find the quota of sections for calculus II.

A) 2
B) 2.55
C) 3.64
D) 3

Question 54

Which of the following is a true statement?

A) Jefferson's method of apportionment is not biased with respect to a state's population.
B) Jefferson's method of apportionment is biased toward states with smaller populations.
C) Jefferson's method of apportionment is biased toward states with larger populations.

Question 55

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. Find the quota for the Applewood district.

A) 4.57
B) 4
C) 5
D) 8.28

Question 56

Use the following information to answer the Questions:
Three states have the following populations: $\begin{array}{ll}\underline {\text {State}}&\underline {\text {Population}}\\\mathrm{A} & 10,040 \\\mathrm{~B} & 8000 \\\mathrm{C} & 2050\end{array}$ A house of representatives with 17 members is to be apportioned among these states.

-What is the tentative apportionment for state A using the Hill-Huntington method?

A) 8
B) 8.5
C) 9
D) 9.5

Question 57

Use the following information to answer the Questions:
Three states have the following populations: $\begin{array}{ll}\underline {\text {State}}&\underline {\text {Population}}\\\mathrm{A} & 10,040 \\\mathrm{~B} & 8000 \\\mathrm{C} & 2050\end{array}$ A house of representatives with 17 members is to be apportioned among these states.

-What is the standard divisor?

A) 1100.50
B) 1180.50
C) 1181.76
D) 1200

Question 58

Which method of apportionment always satisfies the quota condition?

A) Hamilton
B) Hill-Huntington
C) Jefferson
D) Webster

Question 59

A small county has populations in three districts as shown below. They are to apportion 10 seats on the county council. Find the quota for Riverdale.

A) 4.13
B) 2
C) 4
D) 2.42

Question 60

Use the following information to answer the Questions:
Three states have the following populations: $\begin{array}{ll}\underline {\text {State}}&\underline {\text {Population}}\\\mathrm{A} & 10,040 \\\mathrm{~B} & 8000 \\\mathrm{C} & 2050\end{array}$ A house of representatives with 17 members is to be apportioned among these states.

-What is the quota for state B?

A) 6
B) 6.8
C) 7
D) 7.4

Question 61

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. If the county uses the d'Hondt method, what is the initial priority number for Central?

A) 476
B) 522
C) 5220
D) 5221

Question 62

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. What would be the standard divisor?

A) 1533
B) 1656
C) 1740
D) 1810

Question 63

A state has four districts with the populations shown below. The House of Representatives has 20 seats that are to be apportioned using the d'Hondt method. After District B has received 3 seats, what is its new priority number?

A) 14,000
B) 28,000
C) 56,000
D) None of the above.

Question 64

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the d'Hondt method. After District A receives its second seat, what is its priority number?

A) 14,000
B) 14,333.3
C) 15,300
D) None of the above.

Question 65

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Webster method. Find the apportionment for each district.

A) 5, 4, 2
B) 5, 3, 3
C) 4, 4, 3
D) 6, 3, 2

Question 66

Find the geometric mean of 5 and 6.

A) 5.5
B) 5.48
C) 4.69
D) 3.32

Question 67

A small county has populations in three districts as shown below. They are to apportion 15 seats on the county council using the Webster method. Find the apportionment for each district.

A) 7, 5, 3
B) 6, 6, 3
C) 6, 5, 4
D) 7, 4, 4

Question 68

Find the geometric mean of 3 and 7.

A) 4.38
B) 5.00
C) 4.58
D) 3.16

Question 69

A state has four districts with the populations shown below. The House of Representatives has 20 seats that are to be apportioned using the Jefferson method. Find the apportionment for each district.

A) 6, 5, 6, 3
B) 7, 4, 5, 4
C) 6, 4, 6, 4
D) 7, 4, 6, 3

Question 70

A country has four states with the populations shown below. The House of Representatives is to have 15 members. Use the Hill-Huntington method of apportionment to find the number of seats for each state.

A) 5, 4, 4, 2
B) 6, 4, 3, 2
C) 5, 4, 3, 3
D) 6, 3, 3, 3

Question 71

Use the following information to answer the Questions:
A senate of 20 faculty members represents three departments: math, statistics, and applied math. The seats are to be apportioned according to the numbers of students in each department, which are as follows: $\begin{array}{lccc} \text { Math} &97\\ \text { Statistics} && 83\\ \text { Applied math} &134\\\end{array}$


-What apportionment is produced by Jefferson's method?

A) 5, 5, 10
B) 6, 5, 9
C) 7, 4, 9
D) 6, 4, 10

Question 72

A country has four states with the populations shown below. The House of Representatives is to have 15 members. Use the Webster method of apportionment to find the number of seats for each state.

A) 6, 4, 3, 2
B) 5, 4, 4, 2
C) 6, 3, 3, 3
D) 5, 4, 3, 3

Question 73

A country has four states with the populations shown below. The House of Representatives is to have 15 members, apportioned by the Hill-Huntington method. Find the tentative apportionment for district C.

A) 3
B) 3.4
C) 3.46
D) 4

Question 74

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district.

A) 5, 3, 3
B) 5, 4, 2
C) 6, 3, 2
D) 4, 4, 3

Question 75

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Find the apportionment for the Boxwood district.

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

Question 76

A county has four districts with the populations shown below. They are to use the Hill -Huntington method of apportionment to distribute 20 seats on a county council. Find the tentative apportionment for district B.

A) 3
B) 4
C) 5
D) 6

Question 77

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Webster method. Find the tentative apportionment for district A.

A) 4
B) 4.5
C) 4.73
D) 5

Question 78

Find the geometric mean of 8 and 9.

A) 5.83
B) 8.5
C) 8.74
D) 8.49

Question 79

Given three states with the populations shown below, and a national senate with 10 seats, use the Hill-Huntington method of apportionment to distribute the seats to the states.

A) 4, 3, 3
B) 4, 4, 2
C) 5, 4, 1
D) 5, 3, 2

Question 80

A small county has populations in three districts as shown below. They are to apportion 15 seats on the county council using the Hill-Huntington method. Find the apportionment for each district.

A) 7, 5, 3
B) 6, 6, 3
C) 6, 5, 4
D) 7, 4, 4