14.3 Apportionment Methods 939 Whenever we use Adams’ method, we first round the modified quota to the nearest hundredth and then determine the modified upper quota. In Example 6, we used a modified divisor of 35,400 to obtain the desired sum of 250 seats. There are an infinite number of modified divisors (in a small range) that could be used to obtain the modified upper quotas that we obtained. In fact, any modified divisor from about 35,394 to about 35,646 would result in the modified upper quotas we obtained in Table 14.37. If you selected a modified divisor lower than about 35,394, you would obtain modified upper quotas for which the sum of the seats is too high. If you selected a modified divisor greater than about 35,646, you would obtain modified upper quotas for which the sum of the seats is too low. With Adams’ method, we will always use a modified divisor that is greater than the standard divisor used with Hamilton’s method. In some cases, the range of numbers that can be used as a modified divisor is very narrow and you may need to use a decimal number. For example, 34 may be too small for a modified divisor and 35 may be too large for a modified divisor. In that case, you will need to use a decimal number between 34 and 35 as the modified divisor. Looking at the results from Example 6, we may want to conclude that Adams’ method is the best, since the quota rule was not violated in this example. Unfortunately, that is not always the case. We have seen that Jefferson’s method can result in a state receiving more than its upper quota of seats. Adams’ method can lead to just the opposite: a state receiving fewer than its lower quota of seats. Although the Jefferson method favors large states, such as his state of Virginia, Adams’ method favors small states, such as those in his area of New England. In addition, Hamilton’s method favors large states and Webster’s method favors small states. Using d 35,400 = and rounding up to the modified quotas, we have a sum of 250 seats, as desired. Therefore, each state will be awarded the number of legislative seats listed in Table 14.37 under the category of modified upper quota. 7 Now try Exercise 17 Learning Catalytics Keyword: Angel-SOM-14.3 (See Preface for additional details.) A B C D m Tiger Republic population 10,400,000 Example 7 Comparing Apportionment Methods The Tiger Republic is a small country with a population of 10,400,000 that consists of four states A, B, C, and D. There are 260 seats in the legislature that need to be apportioned among the four states. The population of each state is shown in Table 14.38. Table 14.38 Tiger Republic Population State A B C D Total Population 3,350,000 1,850,000 2,365,000 2,835,000 10,400,000 a) Determine each state’s apportionment using Hamilton’s method. b) Determine each state’s apportionment using Jefferson’s method. c) Determine each state’s apportionment using Adams’ method. d) Determine each state’s apportionment using Webster’s method. Solution a) First we must determine the standard divisor. The standard divisor is determined by dividing the total population by the number of seats to be apportioned. The standard divisor is 10,400,000 260 40,000 =
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