Explanation Given information: Total number of seats is 45 and the population of four states are as follows: State: A B C D Population: 235 318 564 938 . All these populations are in thousands. Total population of four states is 235 + 318 + 564 + 938 = 2 , 055 thousand. Total number of seats is 45 . Therefore, the standard divisor d = 2 , 055 45 = 45.6667 Now, divide the population of each state by the standard divisor ( d = 45.6667 ) to get the standard quota ( q ) for each state. Then, round the standard quota down to the nearest integer, but each state get at least one seat Therefore, the number of seats assigned to each state is as follows: States Population Standard Quota, q Lower Quota A 235 235 45.6667 = 5.1460 5 B 318 318 45.6667 = 6.9635 6 C 564 564 45.6667 = 12.3504 12 D 938 938 45.6667 = 20.5401 20 Total 2724 43 Here, the total number of seats is 45 and the total of the lower quota is 43 , that is two seats do not assign to any state. According to the Hamilton’s plan, give any additional seats, one at a time to the states with the largest fractional parts of their standard quotas. Since, the fraction part of state B and D is larger than any other state, one seat is assigned to each state. Therefore, the number of seats assigned for each state according to the Hamilton’s plan is as follows: States Population Lower Quota Hamilton's Plan A 235 5 5 B 318 6 7 C 564 12 12 D 938 20 21 Total 2724 43 45 Now, increase the number of seats by one, so the total number of seats becomes 46 Therefore, the new standard divisor d = 2 , 055 46 = 44

13th Edition

ISBN: 9781285697734

Author: karl J. smith

Publisher: Cengage Learning US

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Chapter 17.4, Problem 16PS

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Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment.

State: A B C DPopulation:235318564938

Total number of seats is 45.

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Chapter 17.4, Problem 15PS

Chapter 17.4, Problem 17PS

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Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment. State: A B C D Population: 235 318 564 938 Total number of seats is 45 .

Solution Summary: The author explains that the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment.

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Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment.

State: A B C DPopulation:235318564938

Total number of seats is 45.

Want to see the full answer?

Chapter 17 Solutions

Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment. State: A B C D Population: 235 318 564 938 Total number of seats is 45 .

Solution Summary: The author explains that the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment.

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Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment. State: A B C DPopulation:235318564938 Total number of seats is 45.

Want to see the full answer?

Chapter 17 Solutions

Whether the Alabama paradox occurs when the number of seats increases by one according to the Hamilton’s plan for the following apportionment.

State: A B C DPopulation:235318564938

Total number of seats is 45.