EXAMPLE 22 The 435th Seat

The Webster and Hill-Huntington methods give almost the same apportionments, based on the 2010 census. The only difference is that the Webster method apportions the last seat to North Carolina, while the Hill-Huntington method gives it to Rhode Island.

The standard divisor is the apportionment population of the United States, 309,183,463, divided by the number of seats, 435. Thus, . The quotas, obtained by dividing the states’ populations by s, are for North Carolina and for Rhode Island. With the Webster method, both quotas would be rounded down and only 434 seats would be apportioned. If we reduce the divisor to 708,000, North Carolina’s quotient becomes 13.51, which will be rounded up, and Rhode Island’s quotient is 1.49, which will be rounded down. North Carolina will get 14 seats, and Rhode Island will get 1.

With the Hill-Huntington method, the rounding point for numbers between 13 and 14 is , which is greater than North Carolina’s quota. The rounding point for numbers between 1 and 2 is , which is less than Rhode Island’s quota. Therefore, North Carolina’s quota is rounded down to get its apportionment, 13, and Rhode Island’s quota is rounded up to get its apportionment, 2, with the Hill-Huntington method.