934 CHAPTER 14 Voting and Apportionment Example 4 Using Jefferson’s Method for Apportioning Legislative Seats Consider the Republic of Hydrangea from Example 3. Use Jefferson’s method to apportion the 250 legislature seats among the five states. Use the population from Table 14.31. Table 14.31 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 In Example 3, the standard divisor was calculated to be 35,200. With Jefferson’s method, the modified quota for each group needs to be slightly greater than the standard quota. To accomplish this we use a modified divisor, which is slightly less than the standard divisor. When you divide a quantity by a smaller number, the quotient becomes greater. There is no formula to determine this new modified divisor, and usually more than one divisor will work. We will use trial and error until we determine a divisor that apportions exactly 250 legislative seats using modified lower quotas. Suppose that we try 35,000 as our modified divisor, d. To determine each modified quota, we will divide each state’s population by 35,000. For example, the modified quota for state A is 1,003,200 35,000 28.66 ≈ We will round modified quotas to the nearest hundredth as we did with standard quotas. Since the modified quota for state A is 28.66, the modified lower quota for state A is 28. This result is indicated in column 1, row 4, of Table 14.32. Table 14.32 shows the results for all the states. In the table, we give the standard quotas as references, but they are not used in obtaining the apportionment using Jefferson’s method. Table 14.32 Republic of Hydrangea Population Using a Modified Divisor, d 35,000 = 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 28.66 35.10 142.59 23.23 21.84 Modified lower quota 28 35 142 23 21 249 The sum of the modified lower quotas, 249, is less than the number of available seats, 250. If the sum of the modified lower quotas is too low (as it is in this case), use a lower modified divisor. If the sum of the modified lower quotas is too high, use a higher modified divisor. Since our sum is too low, we will try a lower modified divisor. Let’s see what happens if we use 34,900 as our modified divisor. This modified divisor is a little lower than the modified divisor of 35,000 previously used. Using 34,900 as the modified divisor, the modified quota for state A is 1,003,200 34,900 28.74 ≈
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