Explanation Approach: Standard divisor and standard quota play a major role in doing an apportionment. Standard quota is also called the natural quota for the state. If the natural quota is rounded down to the nearest integer, we call it as lower quota. If the natural quota is rounded up to the nearest integer, we call it as upper quota. Consider two states, A and B. The following are the steps to be followed in Hamilton’s Apportionment Method: Calculate the standard divisor for the given apportionment. Calculate the standard quota for each state and assign it to each state. The surplus representatives (if any) is assigned to the states depending on the size of the state’s standard quotas found in step 2. The “new states paradox” takes place if a state is added additionally and its share of seats is included to the legislature which in turn causes some modification in the seat allocation previously given to another state. The Hamilton’s Apportion Method can undergo new states paradox. Given Information: A legislature has 2 states, A and B. These two states have formed a 100-member commission in order to explore the ways to improve business climate by working together. State C has been added additionally to the legislature. As per the approval of states A and B, state C will add its members to the commission according to the current standard divisor. The population of the three states is given in the following table: State Population (thousands) A 2, 000 B 7, 770 C 600 Calculation: Consider the legislature with state A and B. State Population (thousands) A 2, 000 B 7, 770 The total population (in thousands) is 2 , 000 + 7 , 770 = 9 , 770 The number of members in the commission is 100. Standard divisor for the apportionment = Total population Number of members in the commission = 9 , 770 100 = 97.70 Let’s find the standard quota for each state. Standard quota for state A = Population in state A Standard divisor for the apportionment = 2 , 000 97.70 ≈ 20.471 Standard quota for state B = Population in state B Standard divisor for the apportionment = 7 , 770 97.70 ≈ 79.53 The following table illustrates the standard quota for each state. State Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota A 20.471 20 0.471 B 79.53 79 0.53 Total 99 After allocating 20 members to state A and 79 members to state B, we find that 1 member is not allocated to any of the two states. The remaining 1 member have been allocated to the state for which the fractional part of standard quota is higher. Note that state B have the highest fractional part of standard quota. Hence, the remaining one member has been allocated to state B. The following table illustrates the number of members to be allotted to each state. State Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota Allocation A 20.471 20 0.471 20 B 79.53 79 0.53 80 Total 99

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 10.3, Problem 29E

To determine

To Explain:

Whether the apportionment of 100-member commission among states A and B and the apportionment of commission members after including state C illustrates new states paradox when apportionment is done using Hamilton method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.3, Problem 28E

Chapter 10.3, Problem 30E

Students have asked these similar questions

CHAPTER 2 Apportionment: Shan 11. Hawaii's House of Representatives has 51 members. Suppose they are appor- tioned among the five counties in Hawaii based on the 2010 census data shown in the table. Perform the apportionment using (a) Jefferson's method, (c) Hamilton's method, (e) Which method(s) seems to help the large Honolulu County the most? (f) Which method(s) seems to help the small Kalawao County the most? (b) Webster's method, (d) Lowndes' method. Kalawao Kauai Maui Hawaii 185,079 Source: U.S. Census Bureau. Honolulu 953,207 County Population 67,091 154,834 90 mang ite three

Two states A and B have formed a 100- member commission to explore ways in which they can work jointly to improve the business climate in their states. The members will be apportioned to the commission according to the population of the two states (using Hamilton's Method). After seeing the success of the commission, a third state asks to join and appoint members to the commission. States A and B agree and will allow state C to add as many members to the commission as they would deserve now using the current standard divisor. The populations of the three states are given below. Does this example illustrate the new states paradox? Explain. State Population A 2,000 B 7,770 C 600

9. A grant and a newly passed levy will allow a county to buy 13 new fire trucks for its fire precincts. The new trucks are going to be allotted to the precincts based on the number of times each precinct had to respond to calls in the last six months. Use the Hamilton Apportionment Plan and the table below to determine the number of fire trucks each precinct will receive. District Number of Calls D-1 45 D-2-1 73 D-2-2 100 D-3 67 D-4-1 179 D-4-2 95

Chapter 10 Solutions

Mathematics All Around (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.

Whether the apportionment of 100-member commission among states A and B and the apportionment of commission members after including state C illustrates new states paradox when apportionment is done using Hamilton method.

Solution Summary: The author illustrates the new states paradox when apportionment is done using the Hamilton's Apportion Method.

Concept explainers

Videos

To Explain: Whether the apportionment of 100-member commission among states A and B and the apportionment of commission members after including state C illustrates new states paradox when apportionment is done using Hamilton method.

Want to see the full answer?

Chapter 10 Solutions

To Explain:

Whether the apportionment of 100-member commission among states A and B and the apportionment of commission members after including state C illustrates new states paradox when apportionment is done using Hamilton method.