vmt-award-2024_48-1-_red

As n becomes large, the harmonic and geometric means approach the arithmetic mean from below. For the large states, there is little difference be tween the three methods: Dean, Huntington - Hill, and Webster. However, for smaller states, lower rounding points become more noticeable so that the Huntington - Hill Method shows a slight bias in favor of smaller states compared to Webster, but not as strong of a bias as Dean ’ s Method shows. 1. Start with the divisor D = P/N . Compute each state ’ s quota 2. If ______________ , then round down so that . Otherwise round up so that _______ . is less than N , decrease the divisor D until the number of seats awarded increases to the desired N . If the sum of the is greater than N , increase D until the num ber of seats awarded decreases to the desired N . In 1920, this new method was advanced by the Census Bureau and competed with Webster ’ s Method in Congress. However, this competition was overshadowed by something else—changing demographics. Rapid industrialization before and during World War I led to a dramatic internal mi gration. Prior to 1910, internal migration was mainly east - to - west. Between 1910 and 1920, this shifted from rural - to - urban. Rural areas lost five million people while urban areas gained fourteen million. For the first time in our history, a majority of the population lived in urban areas. Congress debated the new apportionment method that overrepresented the rural population, which would soon lose influence. The House subcommittee proposed the Webster ’ s method and increasing N by 48 to 483 so that no state would lose a seat. However, smaller states balked at how many of these new seats would go to states with large urban areas. Plus, there was concern that this number of representatives would not actually fit into the House chamber. The small er states favored the Huntington - Hill Method, be cause of its small - state bias, but the larger states favored the Webster Method. This deadlock con 3. If the sum of the Huntington - Hill Method

tinued for nine years.

In June 1929, with the 1930 Census looming, a grand bargain was finally reached with the Reap portionment Act of 1929. It did not actually ap prove an apportionment but, instead focused on establishing a process. The 1920 Census would not be used for apportionment, and they would just wait for the 1930 Census. The House number of representatives would become fixed at the current size. It could increase temporarily when new states were added, but that would only last until the next Census cycle to returned the size to N = 435. The president would transmit to Congress apportion ments methods of Webster and Huntington - Hill. If Congress took no action to change the method, the most recently used method would be used. In 1930, the two methods gave the same apportion ment, and so without specifying the method, Con gress chose Webster ’ s by default since it had been used in 1910. However, after the 1940 Census, the two methods did not agree. Webster gave Michigan 18 and Ar kansas 6, whereas Huntington - Hill gave Michigan 17 and Arkansas 7. With Arkansas more likely to send another Democrat to Washington, the Demo cratically controlled Congress decided to switch to the Huntington - Hill method, and it has been used for each reapportionment since. After the 1990 Census, Montana lost a seat and sued in federal court saying that the Huntington - Hill method did not provide equal representation. A panel of three district court judges agreed, but in US Department of Commerce v. Montana , the Supreme Court re versed that decision and said that the Huntington Hill method was constitutional. Though delayed, the 2020 Census results were eventually released in April 2021, and the results based on the Huntington - Hill method, to round with respect to the geometric mean, the algorithm uses the if() function. Its first argument is a logical test. The second argument is returned if the test is true, and the third argument is returned if the test if false. We use this logical statement in the exam ples that follow.

Virginia Mathematics Teacher vol. 48, no. 1

18