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[I]t would be better for the true physics if there were no mathematicians on earth.
In The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.
Apportioning Representatives in the United States Congress
Today and Tomorrow
After the 2000 apportionment yet another case made its way to the Supreme Court. Utah saw a sizable gain in its population during the 1990s, yet did not increase its representation in the House after the 2000 Census. Advocates for the state examined the numbers and realized that if “imputed populations” (i.e., an estimate of the number of people living in a household after repeated failed attempts to get the actual number) were thrown out of the census, Hill’s method would shift a seat from North Carolina to Utah. The state brought suit to rule the use of imputed populations illegal, but the Supreme Court ultimately rejected this challenge. See http://www.law.cornell.edu/supct/html/01-714.ZO.html.
As we look ahead to 2010, we can use the U.S. Census Bureau’s 2007 population estimates, the most recently available as of this writing, to gauge what a newly re-apportioned House of Representatives may look like after the next census is completed. See the spreadsheet 2007 estimate for details. Both Hill’s and Webster’s methods are computed, although the two apportionments agree. Currently Texas stands as the only state poised to gain two seats in the House, while Arizona, Florida, Georgia, Nevada, and Utah would each gain a single seat. These gains are offset by the losses of single seats in Iowa, Louisiana, Massachusetts, Missouri, New York, Ohio, and Pennsylvania.
What is the future of the apportionment question? It is difficult to say. On the one hand, there has been no change in the apportionment method since 1941 and, other than a temporary adjustment when Alaska and Hawaii were added to the Union, there has been no change in the size of the House since the 1920s. On the other hand, Congress has the power to change either of these at any time. With each census there may be a discrepancy between the apportionments provided by different methods, prompting the disaffected parties to seek a remedy. And from an academic point of view, research continues to investigate the inherent biases, paradoxical behaviors, and other disadvantages of the various methods. In any case, the apportionment of Congress provides a unique blend of interesting mathematics and fascinating political maneuvering. Watch for the latest installment when the next decennial census is completed.
Caulfield, Michael J., "Apportioning Representatives in the United States Congress," Loci (November 2008), DOI: 10.4169/loci003163