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 the result obtained to each state. The surplus representatives (if any) is assigned to the states depending on the size of the state’s standard quota 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 using the Arrow, the blue Line and the City Division, 100 new cars are apportioned among these three lines. After one year, the Metrodelphia Regional Transportation authority makes a decision to reapportion the 100 cars among the three lines. The total number of passengers per day using each line is as follows: Line Passenger per Day (now) Passenger per Day (one year later) Arrow 23, 530 23, 930 Blue Line 5, 550 5, 650 City Division 70, 920 71, 100 Calculation: The total number of passengers per day (now) = 23 , 530 + 5 , 550 + 70 , 920 = 100 , 000 The number of new cars that needs to be apportioned is 100. Standard divisor for the apportionment (now) = Total number of passengers per day (now) Number of new cars = 100 , 000 100 = 1 , 000 Let’s find the standard quota for each line. Standard quota for Arrow = Number of passengers per day (now) in Arrow Standard divisor for the apportionment (now) = 23 , 530 1 , 000 = 23.53 Standard quota for Blue Line = Number of passengers per day (now) in Blue Line Standard divisor for the apportionment (now) = 5 , 550 1 , 000 = 5.55 Standard quota for City Division = Number of passengers per day (now) in City Division Standard divisor for the apportionment (now) = 70 , 920 1 , 000 = 70.92 The following table illustrates the standard quota for each line (now). Line Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota Arrow 23.53 23 0.53 Blue Line 5.55 5 0.55 City Division 70.92 70 0.92 Total 98 After allocating 23 cars to Arrow, 5 cars to Blue Line and 70 cars to City Division, we find that 2 cars are not allocated to any of the three lines. The remaining 2 cars have been allocated to the line for which the fractional part of standard quota is higher. Note that City Division and Blue Line have the highest fractional part of standard quota. Hence, City Division and Blue Line has been allocated 1 car each. The following table illustrates the number of cars to be allotted to each line. Line Standard Quota Lower Quota (Integer Part of Standard Quota) Fractional Part of Standard Quota Allocation Arrow 23.53 23 0.53 23 Blue Line 5.55 5 0.55 6 City Division 70.92 70 0.92 71 Total

6th Edition

ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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Chapter 10.3, Problem 26E

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Whether the apportionment of 100 new cars now and after 1 year among the lines, the Arrow, the Blue line and the City division illustrates population paradox when apportionment is done using Hamilton method.

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Chapter 10.3, Problem 25E

Chapter 10.3, Problem 27E

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Whether the apportionment of 100 new cars now and after 1 year among the lines, the Arrow, the Blue line and the City division illustrates population paradox when apportionment is done using Hamilton method.

Solution Summary: The author explains that the apportionment of 100 new cars now and after 1 year illustrates the population paradox. Standard divisor and standard quota play a major role.

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To Explain: Whether the apportionment of 100 new cars now and after 1 year among the lines, the Arrow, the Blue line and the City division illustrates population paradox when apportionment is done using Hamilton method.

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To Explain:

Whether the apportionment of 100 new cars now and after 1 year among the lines, the Arrow, the Blue line and the City division illustrates population paradox when apportionment is done using Hamilton method.