Explanation Approach: The following are the steps to be followed in Jefferson’s Apportionment Method: Assume a modified divisor for the given apportionment. Note that the modified divisor is smaller than the standard divisor in this method. Calculate the modified quota for each state using the assumed modified divisor and round the modified quotas down. Assign the rounded value to each state. Repeat the above steps till the sum of all the assignments equals the total number of apportionments. The following are the steps to be followed in Adam’s Apportionment Method: Assume a modified divisor for the given apportionment. Note that the modified divisor is greater than the standard divisor in this method. Calculate the modified quota for each state using the assumed modified divisor and round the modified quotas up. Assign the rounded value to each state. Repeat the above steps till the sum of all the assignments equals the total number of apportionments. The standard quota or the number of representatives/seats allocated for a state is calculated by the formula Population of the state Total population × Number of representatives/seats . If the standard quota is rounded down to the nearest integer, we call it as lower quota. If the standard quota is rounded up to the nearest integer, we call it as upper quota. Quota rule states that a state/party can have only two allocations, either lower quota or upper quota. Given Information: The population of the six states are given in the following table: State Population A 700 B 1, 000 C 750 D 200 E 2, 100 F 4, 500 400 representatives are apportioned among these six states. Calculation: Jefferson’s Apportionment Method: The total population is 700 + 1 , 000 + 750 + 200 + 2 , 100 + 4 , 500 = 9 , 250 The number of representatives to be apportioned is 400. Standard divisor for the apportionment = Total population Number of representives to be apportioned = 9 , 250 400 = 23.125 Let’s calculate the standard quota for each state. State Population Standard Quota A 700 700 23.125 ≈ 30.27 B 1, 000 1 , 000 23.125 ≈ 43.24 C 750 750 23.125 ≈ 32.43 D 200 200 23.125 ≈ 8.65 E 2, 100 2 , 100 23.125 ≈ 90.81 F 4, 500 4 , 500 23.125 ≈ 194.59 Let’s begin with the modified divisor 23. (Note that the modified divisor is always smaller than the standard divisor, 23.125). The following table illustrates the modified quota for the modified divisor 23 for each state. State Population Standard Quota Modified Quota Round Modified Quota Down A 700 30.27 700 23 ≈ 30.43 30 B 1, 000 43.24 1 , 000 23 ≈ 43.48 43 C 750 32.43 750 23 ≈ 32.61 32 D 200 8.65 200 23 ≈ 8.696 8 E 2, 100 90.81 2 , 100 23 ≈ 91.30 91 F 4, 500 194.59 4 , 500 23 ≈ 195.65 195 Total 399 The total of round modified quota is 399. Since it is slightly smaller, we need to reduce the modified divisor. If the modified divisor becomes smaller, the modified quota becomes larger. Let’s try a modified divisor of 22.9 (Note that the modified divisor is always smaller than the standard divisor, 23.125). The following table illustrates the modified quota for the modified divisor 22.9 for each state. State Population Standard Quota (Natural Quota) Modified Quota Round Modified Quota Down A 700 30.27 700 22.9 ≈ 30.57 30 B 1, 000 43.24 1 , 000 22.9 ≈ 43.67 43 C 750 32.43 750 22.9 ≈ 32.75 32 D 200 8.65 200 22.9 ≈ 8.73 8 E 2, 100 90.81 2 , 100 22.9 ≈ 91.70 91 F 4, 500 194.59 4 , 500 22.9 ≈ 196.51 196 Total

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ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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Chapter 10.3, Problem 36E

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The method (Jefferson’s apportionment method or Adam’s apportionment method) that violates quota rule in apportioning 400 representatives among six states A, B, C, D, E and F.

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Chapter 10.3, Problem 35E

Chapter 10.3, Problem 37E

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The method (Jefferson’s apportionment method or Adam’s apportionment method) that violates quota rule in apportioning 400 representatives among six states A, B, C, D, E and F.

Solution Summary: The author explains Jefferson's apportionment method, which violates the quota rule, by assuming a modified divisor for each state.

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The method (Jefferson’s apportionment method or Adam’s apportionment method) that violates quota rule in apportioning 400 representatives among six states A, B, C, D, E and F.

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