14.4 Flaws of the Apportionment Methods 949 entitled to, Maine’s apportionment increased from three to four seats and New York’s apportionment decreased from 38 to 37. By adding a new state and additional seats, New York was required to give a seat to Maine. This paradox became known as the new-states paradox. New-States Paradox The new-states paradox occurs when the addition of a new group, and additional items to be apportioned, reduces the previous apportionment of another group. Example 3 Demonstrating the New-States Paradox The Iowa Public Library System has received a grant to purchase 100 laptop computers to be distributed between two libraries A and B. The 100 laptops will be apportioned based on the population served by each library. The apportionment using Hamilton’s method is shown in Table 14.50. The standard divisor is 10,000 100 100 = Now try Exercise 15 Table 14.50 Iowa Public Library System Population Library A B Total Population 2145 7855 10,000 Standard quota 21.45 78.55 Lower quota 21 78 99 Hamilton’s apportionment 21 79 100 Suppose that an anonymous donor decides to donate money to purchase six more laptops provided that a third library, C, that serves a population of 625, is included in the apportionment. Show that the new-states paradox occurs when the laptops are reapportioned. Solution The total population is now 10,000 625 or 10,625 + and the total number of laptops to be apportioned is now 100 6 + or 106. Therefore, when the third library is added, the new standard divisor is 10,625 106 100.24 ≈ The new standard quotas and Hamilton’s apportionment are shown in Table 14.51. Table 14.51 Using a New Standard Divisor of 100.24 Library A B C Total Population 2145 7855 625 10,625 Standard quota 21.40 78.36 6.24 Lower quota 21 78 6 105 Hamilton’s apportionment 22 78 6 106 Before library C was added, library B would receive 79 laptops. By adding a new library and increasing the total number of laptops to be apportioned, library B ended up losing a laptop to library A. Thus, we have a case of the new-states paradox. 7 Instructor Resources for Section 14.4 in MyLab Math • Objective-Level Videos 14.4 • PowerPoint Lecture Slides 14.4 • MyLab Exercises and Assignments 14.4 • Chapter 14 Projects Andresr/Shutterstock
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