14.4 Flaws of the Apportionment Methods 947 When the total number of items increases, each group’s standard quota increases, but not by the same amount. Therefore, it is possible that the order of assignment of the items can change. As a result, some groups can lose items they already had. When the total number of items increases, usually the larger groups benefit at the expense of the smaller groups. The next paradox we will discuss is the population paradox. Population Paradox Another paradox that can occur with Hamilton’s method is when the population of one or more states changes. It was discovered in the early 1900s that under Hamilton’s method, one state could lose a seat to another state even though its population is growing at a faster rate. At the time, Virginia lost a seat in the House of Representatives while Maine gained a seat, although Virginia’s population was growing at a much faster rate than Maine’s population. Thus, this paradox became known as the population paradox . With 151 seats in the legislature, the standard divisor is 18,000 151 119.21 ≈ The standard quotas for each state and the apportionment for each state with 151 total seats are shown in Table 14.46. Now try Exercise 7 Table 14.46 Stanhope Population with 151 Seats in the Legislature State A B C Total Population 888 8076 9036 18,000 Standard quota 7.45 67.75 75.80 Lower quota 7 67 75 149 Hamilton’s apportionment 7 68 76 151 When the number of seats increased from 150 to 151, state A’s apportionment actually decreased, from 8 to 7. This example illustrates the Alabama paradox. 7 Did You Know? Redistricting or Gerrymandering? In response to population changes, state legislatures may revise the boundaries of congressional districts. In 2006, the U.S. Supreme Court ruled that a state legislature can redraw district lines anytime. Prior to the 2006 ruling, states were only allowed to redraw district lines every 10 years. The intention of “redistricting” is to make certain that congressional seats are fairly apportioned among the residents of the state. Some legislatures, however, deliberately manipulate the boundaries of congressional districts to influence election outcomes. Legislators may design the boundries so that the district is full of their supporters. This process is called gerrymandering . Gerrymandering was first recognized in 1812 when Massachusetts’ governor Elbridge Gerry convinced the state legislature to create an oddly shaped district, that some thought resembled a salamander, so as to give his political party an advantage in elections. Thus, the term gerrymander was born. Population Paradox The population paradox occurs when group A loses items to group B even though group A’s population increased at a faster rate than group B’s. Example 2 illustrates the population paradox. Example 2 Demonstrating the Population Paradox Consider Alexandria, a small country with a population of 100,000 and three states A, B, and C. There are 100 seats in the legislature that must be apportioned among the three states. Using Hamilton’s method, the apportionment is shown in Table 14.47. Table 14.47 Alexandria Population State A B C Total Population 23,527 5548 70,925 100,000 Standard quota 23.53 5.55 70.93 Lower quota 23 5 70 98 Hamilton’s apportionment 23 6 71 100
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