938 CHAPTER 14 Voting and Apportionment With Adams’ method, we use a modified divisor that is greater than the standard divisor and we use quotas that are rounded up, or modified upper quotas. As with Jefferson’s and Webster’s methods, the modified divisor used must result in all items being distributed, with no items left over. Let’s see what happens when we apply Adams’ method to the Republic of Hydrangea. ADAMS’ METHOD To use Adams’ method for apportionment, do the following. 1. Determine a modified divisor, d, such that when each group’s modified quota is rounded up to the nearest integer the total of the integers is the exact number of items to be apportioned. We will refer to the modified quotas that are rounded up as modified upper quotas. 2. Apportion to each group its modified upper quota. PROCEDURE Example 6 Using Adams’ Method for Apportioning Legislative Seats Once again, consider the Republic of Hydrangea. Apportion the 250 seats among the five states using Adams’ method. Use the population from Table 14.36. Table 14.36 Republic of Hydrangea Population State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000 Solution With Adams’ method, the modified quota for each group needs to be slightly smaller than the standard quota. To accomplish that, we use a modified divisor that is slightly greater than the standard divisor. When you divide a quantity by a larger number, the quotient becomes smaller. Since the standard divisor is 35,200, let’s try letting d 35,400. = Using 35,400 as the modified divisor, the modified quota for state A is 1,003,200 35,400 28.34 ≈ Table 14.37 shows the results. Table 14.37 Republic of Hydrangea Population Using a Modified Divisor, d 35,400 = State A B C D E Total Population 1,003,200 1,228,600 4,990,700 813,000 764,500 8,800,000 Standard quota 28.50 34.90 141.78 23.10 21.72 Modified quota 28.34 34.71 140.98 22.97 21.60 Modified upper quota 29 35 141 23 22 250
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