932 CHAPTER 14 Voting and Apportionment Let’s look at another example using Hamilton’s method. Example 3 Using Hamilton’s Method for Apportioning Legislative Seats Now try Exercise 31 A B D E C m Republic of Hydrangea population 8,800,000 The Republic of Hydrangea needs to apportion 250 seats in the legislature. Suppose that the population of Hydrangea is 8,800,000 and that there are five states in Hydrangea, A, B, C, D, and E. The 250 seats are to be divided among the five states according to their respective populations, given in Table 14.29. Table 14.29 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 Use Hamilton’s method to apportion the seats. Solution The standard divisor is determined by dividing the total population by the number of seats in the legislature. Standard divisor 8,800,000 250 35,200 = = The standard quotas are determined by dividing the population of each state by the standard divisor. Recall that we will round the standard quotas to the nearest hundredth. The results are shown in the second row in Table 14.30. Table 14.30 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 Standard quota 28.50 34.90 141.78 23.10 21.72 Lower quota 28 34 141 23 21 247 Hamilton’s apportionment 28 35 142 23 22 250 The sum of the lower quotas is 247, leaving three additional seats to be distributed. Since states B, C, and E, in this order, have the three highest fractional parts in the standard quota (0.90, 0.78, and 0.72, respectively), they each receive the additional seats using Hamilton’s method. 7 As we can see from both examples, an advantage of Hamilton’s method is that every apportionment is either the lower quota or the upper quota. If an apportionment method assigns either the lower or upper quota to every group under consideration, it is said to satisfy the quota rule. The Quota Rule An apportionment for every group under consideration should always be either the upper quota or the lower quota.
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