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

MYLAB MATH WITH PEARSON ETEXT FOR MATHEM

6th Edition

ISBN: 9780136470137

Author: Pirnot

Publisher: PEARSON

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Chapter 10.3, Problem 29E

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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.

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Chapter 10.3, Problem 28E

Chapter 10.3, Problem 30E

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MYLAB MATH WITH PEARSON ETEXT FOR MATHEM

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

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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.

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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.

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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.