MGF 1107/ Classroom examples/ Chapter 14
1. Suppose a country consists of five states (North, South, East, West and Central) and representation in the National Assembly should be in proportion to each state’s population. The latest census figures are:
|
North |
9279 |
|
South |
7217 |
|
East |
5155 |
|
West |
3093 |
|
Central |
2062 |
|
Total |
26,806 |
If there are 26 seats in the Assembly, how should they be apportioned among the five states?
2. Suppose a later census is taken and the following population figures are revealed.
|
North |
9061 |
|
South |
7179 |
|
East |
5259 |
|
West |
3319 |
|
Central |
1182 |
|
Total |
26,000 |
How should the 26 seats be apportioned among the 5 states?
3. Suppose the National Assembly is increased in size to 27 seats. What is the new apportionment using Hamilton’s method?
4. Repeat example 2 using Jefferson’s method and 26 seats.
5. Repeat example 2 using Jefferson’s method and 40 seats.
6. Repeat problem 2 with Adams’ method and 26 seats.
7. Use Adams’ method to apportion 250 seats among the following 6 states:
State |
Population |
|
A |
1,646,000 |
|
B |
6,936,000 |
|
C |
154,000 |
|
D |
2,091,000 |
|
E |
685,000 |
|
F |
988,000 |
8. Repeat example 2 using Webster’s method and 26 seats.
9. Attempt to apportion 51 seats among the 4 states whose populations are given below using Adams’ method.
State |
Population |
|
A |
500 |
|
B |
1000 |
|
C |
1500 |
|
D |
2000 |
a) Use the modified divisor d = 100.
b) What happens if d < 100?
c) What happens if d > 100?
10. Repeat example 2 using the Hill-Huntington method and 26 seats.
11. A university consists of six academic divisions each with the following enrollment:
|
Arts & Sciences |
5877 |
|
Business |
4087 |
|
Education |
3445 |
|
Engineering |
2850 |
|
Hospitality Management |
2192 |
|
Communications |
1549 |
Apportion the 80 representatives to student government using:
a) Webster’s method
b) the Hill-Huntington method
12. A mother wishes to distribute 11 pieces of candy among her 3 children based on the number of minutes each child spends studying, as shown in the following table:
Child |
Roberto |
Gisela |
Enrique |
Minutes studied |
54 |
243 |
703 |
a) Find each child’s apportionment using Hamilton’s method.
b) Suppose that before mom has time to sit down and do the actual calculations, the children decide to do a little more studying. Here are the revised numbers:
Child |
Roberto |
Gisela |
Enrique |
Minutes studied |
56 |
255 |
789 |
Find each child’s apportionment using Hamilton’s method based on the new total time studied.
c) Explain how this is an example of the population paradox.
13.
| State | 1940 apportionment population | Hill-Huntington apportionment | Webster apportionment |
| Michigan |
5,256,106
|
17
|
18
|
| Arkansas |
1,949,387
|
7
|
6
|
a) Which state was treated better by the Hill-Huntington apportionment?
b) Which state was treated better by the Webster apportionment?
14. The 1790 census counted 15 states, none with quota less than 0.5.
| Quota | Adams apportionment | Hill-Huntington apportionment | Webster apportionment | Jefferson apportionment | |
| Large States | 64.5775 |
64
|
64
|
65
|
66
|
| Small States | 10.1361 |
11
|
11
|
10
|
9
|