Question

A small college has 10 professors in the Mathematics Department. The department teaches pure math, applied math, and

statistics. Professors are apportioned using Hamilton's apportionment method, according to the number of majors in each
field. There are 4 pure math majors, 12 applied math majors, and 12 statistics majors.
If the department receives a grant to hire 1 more professor, will the Alabama paradox occur? Why or why not?

Answer 1

Yes, because while the total number of professors increases, the number of pure math professors decreases.

Explanation:

Using Hamilton's method:

pure math 4/28 = 0.142857

applied math 12/28 = 0.42857

statistics = 12/28 = 0.42857

10 × 0.142857 = 1.42857

10 × 0.42857 = 4.2857

10 × 0.42857 = 4.2857

numbers of professors:

pure math 1

applied math 4

statistics 4

total 9

Add 1 to pure math

Final original numbers of professors using Hamilton's method

pure math 2

applied math 4

statistics 4

total 10

Add 1 professor to department.

11 × 0.142857 = 1.5714

11 × 0.42857 = 4.71428

11 × 0.42857 = 4.71428

numbers of professors:

pure math 1

applied math 4

statistics 4

total 9

Add 1 to applied math and 1 to statistics

Final new numbers of professors using Hamilton's method

pure math 1

applied math 5

statistics 5

total 11

Despite the addition of 1 professor to the department, the field of pure mathematics went from 2 professors to 1 professor. This is an example of the Alabama paradox.

Answer: Yes, because while the total number of professors increases, the number of pure math professors decreases.