948 CHAPTER 14 Voting and Apportionment The next and final paradox we will discuss is the new-states paradox. The New-States Paradox The new-states paradox was discovered in 1907 when Oklahoma was added as a state. When a new state is added, new seats must be added to the legislature. How do we determine the number of new seats to add? A reasonable answer would be to add the number of seats the new state would be entitled to based on its population. When reapportioning the House of Representatives with the additional five seats Oklahoma was Suppose that the population increases according to Table 14.48 and that the 100 seats are reapportioned. Show that the population paradox occurs when Hamilton’s method is used. Now try Exercise 11 Table 14.48 Alexandria Population Increase State A B C Total Population 23,926 5648 71,110 100,684 Solution To calculate the percent increase, we use the procedure discussed in Section 10.1. State A has an increase of 399 people. Therefore, state A has a percent increase of 399 23,527 0.01696 1.696% ≈ ≈ State B has an increase of 100 people. Therefore, state B has a percent increase of 100 5548 0.01802 1.802% ≈ ≈ State C has an increase of 185 people. Therefore, state C has a percent increase of 185 70,925 0.00261 0.261% ≈ ≈ All three states had an increase in their population, but state B increased at a faster rate than state A and state C. The standard divisor using the new population is 100,684 100 1006.84 = Table 14.49 shows the reapportionment, using Hamilton’s method with the standard divisor 1006.84. Table 14.49 Using a New Standard Divisor of 1006.84 State A B C Total Population 23,926 5648 71,110 100,684 Standard quota 23.76 5.61 70.63 Lower quota 23 5 70 98 Hamilton’s apportionment 24 5 71 100 State B has lost a seat to state A even though state B’s population grew at a faster rate than state A’s. As a result, we have an example of the population paradox. 7 Timely Tip In Example 2, the population paradox occurred because state B lost a seat to state A even though state B’s population grew at a faster rate than state A’s population. When checking for the population paradox, it is possible for a state to lose a seat to another state without the population paradox occurring. Remember that for the population paradox to occur, the state that loses the seat must be growing at a faster rate than the state that gains the seat.
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