Determine when the Hamilton method gives an Alabama paradox and who lost the representative.

Increase the committee size by one seat at a time, starting from an 8-member committee.

Given: City A, City B, and City C are cooperating to build a community center catering to the three cities. Seats on the 8-member committee are assigned according to the populations of the cities. The population of City A is 6204, City B is 4884, and City C is 2112.

(Hint: First apportion for 8 members then apportion for 9 members. If the Alabama paradox occurred, then determine who lost the representative. If the paradox did not occur, then apportion for 10 members. Compare the 9-member committee to the 10-member committee. If the Alabama paradox occurred, then determine who lost the representative. If the paradox did not occur, the apportion for 11 members and continue the process until the paradox occurs.)

Possible Anwsers:
Assignment of 11th seat; City C


Assignment of 10th seat; City C


Assignment of 12th seat; City C


Assignment of 10th seat; City A

Would the answer be, Assignment of 10th seat; City C?

Thanks!

To determine when the Hamilton method gives an Alabama paradox and who lost the representative, we can follow the given instructions and start by increasing the committee size by one seat at a time.

First, let's apportion for an 8-member committee:

1. Calculate the total population: 6204 (City A) + 4884 (City B) + 2112 (City C) = 13,200.
2. Divide each city's population by the total population and multiply by the committee size to get the initial allocations:

City A: (6204 / 13,200) * 8 = 3.8 (round down to 3)
City B: (4884 / 13,200) * 8 = 2.9 (round down to 2)
City C: (2112 / 13,200) * 8 = 1.3 (round down to 1)

So, City A gets 3 seats, City B gets 2 seats, and City C gets 1 seat.

Next, let's apportion for a 9-member committee:

1. Calculate the total population: 6204 (City A) + 4884 (City B) + 2112 (City C) = 13,200.
2. Divide each city's population by the total population and multiply by the committee size to get the allocations:

City A: (6204 / 13,200) * 9 = 4.25 (round down to 4)
City B: (4884 / 13,200) * 9 = 3.33 (round down to 3)
City C: (2112 / 13,200) * 9 = 1.44 (round down to 1)

Now, let's compare the allocations of the 9 and 10-member committees:

For the 9-member committee, City A has 4 seats, City B has 3 seats, and City C has 1 seat.
For the 10-member committee, we need to find the allocations.

1. Calculate the total population: 6204 (City A) + 4884 (City B) + 2112 (City C) = 13,200.
2. Divide each city's population by the total population and multiply by the committee size to get the allocations:

City A: (6204 / 13,200) * 10 = 4.70 (round down to 4)
City B: (4884 / 13,200) * 10 = 3.70 (round down to 3)
City C: (2112 / 13,200) * 10 = 1.60 (round down to 1)

From the above calculations, we can see that the allocations remain the same between the 9 and 10-member committees. Therefore, the Alabama paradox does not occur at this stage, and City C does not lose the representative.

To confirm, let's apportion for an 11-member committee:

1. Calculate the total population: 6204 (City A) + 4884 (City B) + 2112 (City C) = 13,200.
2. Divide each city's population by the total population and multiply by the committee size to get the allocations:

City A: (6204 / 13,200) * 11 = 5.28 (round down to 5)
City B: (4884 / 13,200) * 11 = 3.96 (round down to 3)
City C: (2112 / 13,200) * 11 = 1.76 (round down to 1)

From the above calculations, we can see that the allocations have changed, and the Alabama paradox has occurred. In this case, City C loses the representative. Therefore, the correct answer is the "Assignment of 11th seat; City C".

So, to answer your question, the answer is not "Assignment of 10th seat; City C". Instead, it is "Assignment of 11th seat; City C".