Skills Check

Skills Check

Question 14.1

1. Amy, Bill, and Connie have bought lottery tickets that won 13 identical rubies. The number of tickets each bought was: Amy, 13; Bill, 5; and Connie, 19. They wish to divide the rubies fairly. What was Connie’s quota?

  1. Less than 7 rubies
  2. Between 7 and 8 rubies
  3. More than 8 rubies

1.

a

Question 14.2

2. Two calculus teachers can teach a total of 8 classes. Enrollments are as follows: Calculus I, 200; Calculus II, 100; Calculus III, 80. In this apportionment problem, the population is ________________, the standard divisor is _____________________, and the quotas are ___________________________ for Calculus I, for Calculus II, and _____________ for Calculus III.

2.

380; 47.5; 4.2; 2.1; 1.7

Question 14.3

3.A, B, and C are arguing about fractions of a cent. On a project, they worked exactly 33, 34, and 35 minutes, respectively, and were paid $100. Use the Hamilton method to see who gets his upper quota (in cents!).

  1. A
  2. B
  3. C

3.

c

Question 14.4

4. Round each number in the sum 14.48 + 12.40 + 17.49 + 16.33 + 19.30 = 80 to a whole number.

(What is it about these numbers that makes this complicated?)

4.

15 + 12 + 18 + 16 + 19 = 80

Question 14.5

5. The population paradox occurs when

  1. a state’s apportionment decreases because the house size increased.
  2. a state’s apportionment decreases and its apportionment increases, while another state’s apportionment decreases even though its population has increased.
  3. the Jefferson method is used.

5.

b

Question 14.6

6. The Alabama paradox occurred when it was noticed that Alabama would lose a seat, in apportionment by the Hamilton method, if the house size was changed from 299 to ________.

6.

300

Question 14.7

7. If the Jefferson method is used to do the rounding in Skills Check Question 4, it will be necessary to find a divisor that is

  1. less than 1.
  2. at least 1, but less than 2.
  3. at least 2.

7.

a

Question 14.8

8. Using the Webster method, round the numbers in Skills Check 4.

8.

612

Question 14.9

9. When rounding the numbers in the sum by the Jefferson method, which number gets its upper quota?

  1. 20.45
  2. 30.30
  3. 49.25

9.

c

Question 14.10

10. Seats in a parliament are apportioned by the Hare (Hamilton) method. Jane had planned to vote for party but changed her mind and voted for party . If her vote switch caused party to lose a seat, this would be an instance of the ___________ paradox.

10.

population

Question 14.11

11. The parliament in Skills Check Question 10 will be apportioned by the d’Hondt (Jefferson) method. Now is it possible for Jane’s vote switch to cause party to lose a seat?

  1. Yes, because the Jefferson method does not satisfy the quota condition.
  2. No, because the Jefferson method is not susceptible to the Alabama paradox.
  3. No, because the Jefferson method is not susceptible to the population paradox.

11.

c

Question 14.12

12. Use the Jefferson method to apportion the sum as a sum of whole numbers.

12.

Question 14.13

13. The Jefferson method frequently

  1. gives the smallest state less than its lower quota.
  2. gives the largest state more than its upper quota.
  3. gives a state a lesser apportionment if the house size increases.

13.

b

Question 14.14

14. Use the Webster method to apportion the sum as a sum of whole numbers.

14.

Question 14.15

15. We want to apportion the sum as a sum of whole numbers. Which method will violate the quota condition?

  1. Hamilton
  2. Jefferson
  3. Webster

15.

b

Question 14.16

16. The sum has to be rounded as a sum of whole numbers. If the __________ method is used, there will be a tie.

16.

Hamilton

Question 14.17

17. When rounding the numbers in the sum by the Webster method, which number gets rounded up?

  1. 20.45
  2. 30.30
  3. 49.25

17.

a

Question 14.18

18. States and have populations of 1 million and 2 million, respectively. If they are apportioned 2 and 3 seats, respectively, then the absolute difference in representative share is __________ per million.

18.

0.5 seats

Question 14.19

19. If the apportionment in Skills Check 18 gave state 1 seat and gave state 4 seats, then

  1. the absolute difference in representative share would increase.
  2. the absolute difference in representative share would decrease.
  3. the absolute difference in representative share would be unchanged.

19.

a

Question 14.20

20. If the criterion is absolute difference in district population, the equitable apportionment of 5 seats to states and in Skills Check 18 is _____________ for and _________________ for .

20.

2; 3

Question 14.21

21. If the initial calculations leading to the Hill-Huntington apportionment result in a sum that is too large, what happens next?

  1. Apportionment quotients must be calculated, using a divisor slightly larger than the standard divisor.
  2. Apportionment quotients must be calculated, using a divisor slightly less than the standard divisor.
  3. The largest apportionment is reduced.
  4. A different method must be used.

21.

a

Question 14.22

22. The __________ method has been used since 1941 to apportion seats in the U.S. House of Representatives.

22.

Hill–Huntington

Question 14.23

23. Which divisor method never apportions to a state fewer seats than its lower quota?

  1. Hill-Huntington
  2. Webster
  3. Jefferson

23.

c

Question 14.24

24. A school principal is apportioning sections of the school’s mathematics classes. She wants to set a minimum section size and to adjust it so that a total of 32 sections are open. She should use the ________ method.

24.

Jefferson

Question 14.25

25. The U.S. Constitution says that each state must get at least one representative in the House. Which apportionment method or methods automatically satisfy this requirement?

  1. Hamilton
  2. Jefferson
  3. Webster
  4. Hill-Huntington

24.

Jefferson

613

Question 14.26

26. Five parties, , , , , and , participate in a parliamentary election. The parliament has 10 seats. The number of votes received (in thousands) were , 120; , 78; , 50; , 35; and , 20. Here is a d’Hondt table.

A B C D E
120 78 50 35 20
60 39 25 17.5 10
40 26 16.67 11.67 6.67
30 19.5 12.5 8.75 5

When the seats are apportioned, the seventh seat goes to party ___________, the eighth seat goes to party ___________, the ninth goes to party ___________, and the tenth goes to party _________.

25.

d

Question 14.27

27. The Hill-Huntington method minimizes percentage differences in

  1. district population.
  2. representative share.
  3. Both (a) and (b) are correct.

27.

c

Question 14.28

28. The divisor method that shows the least bias in favor of either large states or small states is the ________________ method.

28.

Webster

Question 14.29

29. A parliament has 466 seats and there are 13 parties with lists on the ballot. It is proposed that there should be a minimum number of votes to qualify for a seat, and that number should be chosen so that exactly 466 seats are filled. We should point out that this idea is not new; it is the method of

  1. Hare.
  2. d’Hondt.
  3. Sainte-Laguë.

29.

b

Question 14.30

30. In the election described in Skills Check 29, party received exactly 12 million of the votes, and each of the other 12 parties received exactly 1 million votes. Although Party received exactly half of the votes, the number of seats that it will receive is ______________ more than half of the seats, and therefore it can form a government without a coalition partner. This will violate the _________ condition.

30.

5; quota