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

Mathematics All Around, Books a la carte edition (6th Edition)

6th Edition

ISBN: 9780134462448

Author: Pirnot, Tom

Publisher: PEARSON

See similar textbooks

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Videos

Question

Chapter 10.3, Problem 36E

To determine

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.3, Problem 35E

Chapter 10.3, Problem 37E

Students have asked these similar questions

6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4

The general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5

show work in paper

Chapter 10 Solutions

Mathematics All Around, Books a la carte edition (6th Edition)

Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Sharpening your Skills In Exercises 1-6, use the...Ch. 10.1 - Prob. 6E Ch. 10.1 - Sharpening Your Skills If the American Nurses...Ch. 10.1 - Prob. 8E Ch. 10.1 - Sharpening your Skills Which state is more poorly...Ch. 10.1 - Prob. 10E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 10 Solutions