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. If the population of state A increases faster than state B and if still state A loses a representative to state B, we call the situation as “population paradox”. The Hamilton’s Apportion Method can undergo population paradox. Given Information: Depending on the total number of passengers (per week) using the airports, Allen port, Bakers town and Columba City, 150 security personnel are apportioned to these three airports. After two years, the 150 personnel have been reapportioned since the number of passengers (per week) using the three airports has been increased. The total number of passengers per week using each airport is as follows: Airports Passenger per Week (now) Passenger per Week (two years later) Allen port 120, 920 121, 420 Bakers town 5, 550 5, 650 Columbia city 23, 530 23, 930 Calculation: The total number of passengers per week (now) = 120 , 920 + 5 , 550 + 23 , 530 = 150 , 000 The number of security personnel to be apportioned is 150. Standard divisor for the apportionment (now) = Total number of passengers per week (now) Number of personnel = 150 , 000 150 = 1 , 000 Let’s find the standard quota for each airport. Standard quota for Allen Port = Number of passengers per week (now) in Allen Port Standard divisor for the apportionment (now) = 120 , 920 1 , 000 = 120.92 Standard quota for Bakers Town = Number of passengers per week (now) in Bakers Town Standard divisor for the apportionment (now) = 5 , 550 1 , 000 = 5.55 Standard quota for Columbia City = Number of passengers per week (now) in Columbia City Standard divisor for the apportionment (now) = 23 , 530 1 , 000 = 23.53 The following table illustrates the standard quota for each airport (now). Airports Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota Allen Port 120.92 120 0.92 Bakers Town 5.55 5 0.55 Columbia City 23.53 23 0.53 Total 148 After allocating 120 personnel to Allen Port, 5 personnel to Bakers Town and 23 personnel to Columbia City, we find that 2 personnel are not allocated to any of the three airports. The remaining 2 personnel have been allocated to the airport for which the fractional part of standard quota is higher. Note that Allen Port and Bakers Town have the highest fractional part of standard quota. Hence, Allen Port and Bakers Town has been allocated 1 personnel each. The following table illustrates the number of personnel to be allotted to each airport. Airports Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota Allocation Allen Port 120.92 120 0.92 121 Bakers Town 5.55 5 0.55 6 Columbia City 23.53 23 0.53 23 Total

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Chapter 10.3, Problem 27E

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Whether the apportionment of 150 security personnel among three regional airports now and two years later illustrates population paradox when apportionment is done using Hamilton method.

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Chapter 10.3, Problem 26E

Chapter 10.3, Problem 28E

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Whether the apportionment of 150 security personnel among three regional airports now and two years later illustrates population paradox when apportionment is done using Hamilton method.

Solution Summary: The author explains how the apportionment of 150 security personnel between three regional airports illustrates the population paradox.

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To Explain: Whether the apportionment of 150 security personnel among three regional airports now and two years later illustrates population paradox when apportionment is done using Hamilton method.

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To Explain:

Whether the apportionment of 150 security personnel among three regional airports now and two years later illustrates population paradox when apportionment is done using Hamilton method.