Central City School District Student Population (There Are 50 Laser Printers to Be Distributed)

Chipola College MGF 1107 15.3a Apportionment______

total population Standard divisor = number of items to be allocated

population for a particular group Standard quota = standard divisor

Central City School District Student Population (There are 50 laser printers to be distributed) School A B C D E Total Population 210 165 160 175 190 900

Compute the standard divisor:

School A B C D E Total Population 210 165 160 175 190 900 Standard quota

Compute the lower and upper quota for each school.

Hamilton’s Method 1. Calculate each group’s standard quota. 2. Round each standard quota down to the nearest integer. Initially, each group receives its lower quota. 3. Distribute any leftover items to the groups with the largest fractional parts until all items are distributed.

School A B C D E Total Population 210 165 160 175 190 900 Standard 11.67 9.17 8.89 9.72 10.56 50.01 quota Lower quota Hamilton’s apportionment Jefferson’s Method 1. Determine a modified divisor,d, such that when each group’s modified quota is rounded down to the nearest integer, the total of the integers is the exact number of items to be apportioned. 2. Apportion to each group its modified lower quota.

The Republic of Geranium needs to apportion 275 seats in the legislature.

Republic of Geranium Republic State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000

First, use Hamilton’s method to apportion the seat.

Standard divisor:

State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000 Standard Quota Lower quota Hamilton’s apportionment

Now, let’s use Jefferson method:

Suppose that we try 31,500 as our modified divisor,d.

State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000 Standard Quota Modified quota Modified lower quota

Since the sum of the modified lower quotas, 277, exceeds the number of available seats, use a higher modified divisor, like maybe 31,600.

State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000 Standard Quota Modified quota Modified lower quota