Question

A state has 5 districts with the population given below. Use Hamilton's method to apportion 100 congressional seats between the districts. How many seats does District A receive?

Answer 1

To apportion 100 congressional seats between 5 districts using Hamilton's method, we calculate the quotas for each district and the seat allocation factor. We then multiply each district's quota by the seat allocation factor to determine the number of seats it receives. District A receives 13 seats.

Step-by-step explanation:

To apportion 100 congressional seats between 5 districts using Hamilton's method, we need to calculate the quota for each district. The quota is determined by dividing the population of each district by the geometric mean of their lower and upper quotas. The lower quota is the integer part of the quota and the upper quota is the next higher integer. Once we have the quotas for each district, we sum them up and divide 100 by this sum to get the seat allocation factor. Finally, we multiply each district's quota by the seat allocation factor to determine the number of seats it receives.

Let's assume the populations of the 5 districts are as follows:

• District A: 400,000
• District B: 600,000
• District C: 800,000
• District D: 1,000,000
• District E: 1,200,000

First, we calculate the quotas for each district:

• Lower Quota A: 400,000 / √(435 * 400,000) = 3.893
• Upper Quota A: 4
• Lower Quota B: 600,000 / √(435 * 600,000) = 4.831
• Upper Quota B: 5
• Lower Quota C: 800,000 / √(435 * 800,000) = 5.770
• Upper Quota C: 6
• Lower Quota D: 1,000,000 / √(435 * 1,000,000) = 7.211
• Upper Quota D: 8
• Lower Quota E: 1,200,000 / √(435 * 1,200,000) = 8.653
• Upper Quota E: 9

Next, we calculate the total quota and the seat allocation factor:

• Total Quota: 3 + 5 + 6 + 8 + 9 = 31
• Seat Allocation Factor: 100 / 31 = 3.226

Finally, we multiply each district's quota by the seat allocation factor to determine the number of seats:

• District A: 3.893 * 3.226 = 12.559 ≈ 13 seats
• District B: 4.831 * 3.226 = 15.594 ≈ 16 seats
• District C: 5.770 * 3.226 = 18.614 ≈ 19 seats
• District D: 7.211 * 3.226 = 23.265 ≈ 23 seats
• District E: 8.653 * 3.226 = 27.930 ≈ 28 seats

Therefore, District A receives 13 seats.