A city with three districts has an increase in population as indicated in the table, Using Hamilton's
Method, apportion the 21 seats between the three districts both before and after the population
Increase. Look at the percent increase in population for each district to determine if the population
Paradox occurred.
A)population paradox occurred
B)population paradox did not occur

Question

A city with three districts has an increase in population as indicated in the table, Using Hamilton's
Method, apportion the 21 seats between the three districts both before and after the population
Increase. Look at the percent increase in population for each district to determine if the population
Paradox occurred. 
A)population paradox occurred 
B)population paradox did not occur

Quizplus · Accepted Answer

Before the population increase, the seat distribution using Hamilton's Method is:

District 1: 5 seats
District 2: 8 seats
District 3: 8 seats

To calculate the priority values, we use the following formula:

Priority value = (population of district) / sqrt(number of seats * (number of seats + 1))

For District 1: 5000 / sqrt(5*(5+1)) = 1000
For District 2: 8000 / sqrt(8*(8+1)) = 1299.186
For District 3: 7000 / sqrt(8*(8+1)) = 1137.668

District 2 has the highest priority value, so it receives the first seat. We continue allocating seats in this way until we have allocated all 21 seats. The seat distribution after the population increase is:

District 1: 5 seats
District 2: 9 seats
District 3: 7 seats

To calculate the priority values with the new population, we use the same formula as before:

For District 1: 6000 / sqrt(5*(5+1)) = 1200
For District 2: 10000 / sqrt(9*(9+1)) = 1908.896
For District 3: 8000 / sqrt(7*(7+1)) = 1716.741

Again, District 2 has the highest priority value and receives the first seat. We continue allocating seats in this way until we have allocated all 21 seats.

The population of each district increased by the following percentages:

District 1: (6000-5000)/5000 * 100% = 20%
District 2: (10000-8000)/8000 * 100% = 25%
District 3: (8000-7000)/7000 * 100% = 14.3%

Since the percentage increase in population is not greater than the percentage increase in seats for any district, the population paradox did not occur.

A City with Three Districts Has an Increase in Population