Question

An organization has four departments: A with 880 employees, B with 1,700 employees, C with 710 , and D with 1,060 employees. Suppose that it has membership on the council proportional to the number of employees in the four departments. Apportion 12 representative seats to these four departments. Assign the seats using the Hamilton apportionment method

Answer 1

To apportion 12 representatives using the Hamilton method, calculate the total number of employees, the standard divisor, and each department's quota. Allocate initial seats based on whole numbers of quotas and then distribute the remaining seats according to the largest fractional parts until all seats are apportioned.

Step-by-step explanation:

To apportion 12 representative seats using the Hamilton apportionment method, we first need to calculate the total number of employees and then determine the standard divisor. The steps are as follows:

1. Calculate the total number of employees: 880 (A) + 1,700 (B) + 710 (C) + 1,060 (D) = 4,350.
2. Determine the standard divisor: 4,350 (total employees) / 12 (seats) = 362.5.
3. Calculate the standard quota for each department by dividing the number of employees in each department by the standard divisor.

Department A's quota: 880 / 362.5 ≈ 2.43
Department B's quota: 1,700 / 362.5 ≈ 4.69
Department C's quota: 710 / 362.5 ≈ 1.96
Department D's quota: 1,060 / 362.5 ≈ 2.92

Allot each department a number of seats equal to the whole number part of its quota.

Initial allocation of seats:
Department A: 2
Department B: 4
Department C: 1
Department D: 2
Total allocated so far: 9

Distribute the remaining 3 seats (12 total - 9 allocated) to the departments with the largest fractional parts of their quotas until all 12 seats are apportioned.

Final seat allocation:
Department A: 3
Department B: 5
Department C: 2
Department D: 2