946 CHAPTER 14 Voting and Apportionment In this section we will discuss three flaws of Hamilton’s method: 1. Alabama paradox 2. Population paradox 3. New-states paradox These flaws apply only to Hamilton’s method and not to Jefferson’s method, Webster’s method, or Adams’ method. The Alabama Paradox The first, and perhaps most serious, flaw of Hamilton’s method occurs when an increase in the total number of items to be apportioned results in a loss of an item for one of the groups. This flaw first occurred in the apportionment of the House of Representatives in 1880 when a discussion occurred on whether to have 299 or 300 members in the House. Using Hamilton’s method with 299 members, Alabama would receive eight seats. But if the total number of representatives were increased to 300, Alabama would receive only seven seats. As a result, this situation became known as the Alabama paradox. Alabama Paradox The Alabama paradox occurs when an increase in the total number of items to be apportioned results in a loss of an item for a group. Example 1 illustrates the Alabama paradox. Example 1 Demonstrating the Alabama Paradox Consider Stanhope, a small country with a population of 18,000 people and three states A, B, and C (Table 14.44). There are 150 seats in the legislature that must be apportioned among the three states, according to their population. Show that the Alabama paradox occurs using Hamilton's method if the number of seats is increased to 151. When appropriate, round standard divisors and standard quotas to the nearest hundredth. Table 14.44 Stanhope Population State A B C Total Population 888 8076 9036 18,000 Solution With 150 seats in the legislature, the standard divisor is 18,000 150 120 = The standard quotas for each state and the apportionment for each state are shown in Table 14.45. Table 14.45 Stanhope Population with 150 Seats in the Legislature State A B C Total Population 888 8076 9036 18,000 Standard quota 7.40 67.30 75.30 Lower quota 7 67 75 149 Hamilton’s apportionment 8 67 75 150
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