EXAMPLE 7 The Apportionment of 1882

In 1880, the apportionment population of the United States was 49,373,329. When the house size was set at 299, the standard divisor was . Alabama’s apportionment population was 1,262,505. Thus, Alabama’s quota was . Alabama received its upper quota, so if the house size of 299 had been chosen, Alabama would have been apportioned 8 seats. All states with quotas having fractional parts less than Alabama’s were apportioned their lower quotas. The states following Alabama when comparing fractions were Illinois and Texas, with apportionment populations of 3,077,871 and 1,591,729, respectively. Their quotas were 18.63930 and 9.63936, respectively, and they were apportioned their lower quotas.

When the house size increased to 300, the standard divisor was less, . Dividing the three states’ apportionment populations by this smaller divisor yielded the following quotas: Alabama, 7.67117; Illinois, 18.70159; and Texas, 9.67158. One additional seat was available for apportionment. With this house size, the quota for Illinois had the largest fractional part of the three, followed by Texas; Alabama was in third place. The seat that had been Alabama’s, and the 300th seat, went to Illinois and Texas; both states were apportioned their upper quotas. Alabama received its lower quota. Table 14.6 summarizes the result of these calculations.