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?

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.

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!).

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?)

5. The population paradox occurs when

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 ________.

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

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

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

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.

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?

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

13. The Jefferson method frequently

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

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

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

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

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.

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

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 .

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

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

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

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.

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?

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.

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 _________.

27. The Hill-Huntington method minimizes percentage differences in

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

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

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.