940 CHAPTER 14 Voting and Apportionment Next we determine the standard quotas by dividing each state’s population by the standard divisor, 40,000. Recall that we round standard quotas to the nearest hundredth. With Hamilton’s method, we round each standard quota down to obtain the lower quota. Then we distribute any leftover seats to the states with the largest fractional parts until all seats are distributed. Table 14.39 shows the apportionment using Hamilton’s method. Table 14.39 Hamilton’s Method, Standard Divisor of 40,000 State A B C D Total Population 3,350,000 1,850,000 2,365,000 2,835,000 10,400,000 Standard quota 83.75 46.25 59.13 70.88 Lower quota 83 46 59 70 258 Hamilton’s apportionment 84 46 59 71 260 Using the lower quota, only 258 of the 260 seats were apportioned. Since states D and A, in that order, had the highest fractional parts of the standard quota (0.88 and 0.75, respectively), each of these states receives one additional seat. b) With Jefferson’s method, we use a modified divisor that is less than the standard divisor and use modified lower quotas . Table 14.40 shows the results using a modified divisor of 39,700. Table 14.40 Jefferson’s Method, Modified Divisor, d 39,700 = State A B C D Total Population 3,350,000 1,850,000 2,365,000 2,835,000 10,400,000 Modified quota 84.38 46.60 59.57 71.41 Modified lower quota 84 46 59 71 260 Using d 39,700, = we have a sum of 260 seats, as desired. Therefore, each state receives the number of seats listed under the modified lower quotas in Table 14.40. c) With Adams’ method, we use a modified divisor that is greater than the standard divisor and use modified upper quotas . Table 14.41 shows the results using a modified divisor of 40,300. Table 14.41 Adams’ Method, Modified Divisor, d 40,300 = State A B C D Total Population 3,350,000 1,850,000 2,365,000 2,835,000 10,400,000 Modified quota 83.13 45.91 58.68 70.35 Modified upper quota 84 46 59 71 260 Timely Tip Hamilton’s method is the only method that uses a standard divisor. Jefferson’s, Webster’s, and Adams’ methods use a modified divisor. Because of this, Hamilton’s method is the only method that uses a standard quota in determining apportionments. Jefferson’s, Webster’s, and Adams’ methods use a modified quota.
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