EXAMPLE 12 Apportioning TAs with the Jefferson Method
in Example 8 (page 582), a mathematics department was to apportion its TAs among five courses. The populations were the numbers of students enrolled in each course, the states were the courses, and the house size was the number of TAs that were available. Here are the enrollment data: College Algebra, 188; Calculus l, 142; Calculus ll, 138; Calculus ill, 64; and Contemporary Mathematics, 218. For a house size of 30, the standard divisor was 25. in Table 14.13, we will follow the procedure used in the previous two examples. The apportionment quotients are not shown, just the tentative apportionments that were obtained by rounding them.
| Divisors | ||||
|---|---|---|---|---|
| Subject | Population | 23 | 24 | 23.5 |
| College Algebra | 188 | 8 | 7 | 8 |
| Calculus I | 142 | 6 | 5 | 6 |
| Calculus II | 138 | 6 | 5 | 5 |
| Calculus III | 64 | 2 | 2 | 2 |
| Contemporary Math | 218 | 9 | 9 | 9 |
| Totals | 750 | 31 | 28 | 30 |
589
The first trial divisor was 23, less than the standard divisor. The number of sections apportioned was 31, which is what we will need when the additional TA arrives. Attempting to apportion 30 sections, we increase the divisor to 24, but that reduces the seats apportioned to 28. The divisor that we need is therefore between 23 and 24, so we will try 23.5, which indeed produces an apportionment of exactly 30 sections.