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E Pluribus Confusion

There’s more than one way to turn census data into congressional seats

Barry Cipra

Math and Politics

Apportionment methods and census figures provide endless opportunity for political calculus. In 2000, for example, North Carolina’s population of 8,067,673 claimed the 435th seat, its 13th in Congress, under Hill’s method, beating out Utah’s 2,236,714 people, which would have been up for the 436th seat (the state’s fourth) had there been one. That’s because the doling-out algorithm gave North Carolina a population priority of:

—beating out Utah’s:

If Utah had only been able to round up another 856 residents, it would have slipped by North Carolina, with priority:

This is significant, and it occasioned a court case (which Utah lost). The Beehive State’s complaint revolved around who gets counted when the Census Bureau comes up with what’s called the “apportionment population,” which is what goes into the apportionment algorithm. Apportionment population has two components: the ordinary residents of the state—that is, the people actually living in the state at the time of the census—and an overseas population, consisting of military and federal civilian employees and dependents living with them, allocated to their “home” states as reported by the agencies that employ them. Utah had a mere 3,545 such people in its population count, whereas North Carolina registered 18,360. Utah’s problem: There’s no federal agency that pays the salaries of their overseas Mormon missionaries.

Under Webster, Utah would have had less of a case. As it happens, Webster and Hill result in the same apportionment for the 2000 census, and North Carolina still gets the 435th seat. But under Webster, Utah falls behind New York, Texas, Michigan and Indiana (in that order) for the 436th seat, and would have needed an additional 22,235 people to overtake North Carolina.

How things will play out after the 2010 census—in particular, whether there will be any close calls for the 435th seat—remains to be seen. The politics in Washington are so rancorous these days, it’s unlikely Congress will go anywhere near changing what’s on the books, so Hill’s method will likely continue to reign. Many apportionment theory experts consider Webster to be a superior method, but it’s clear from history that Congress is less interested in theory than in the practical results. In the meantime, apportionment is fertile ground for computational play. Call it Sim Congress.


  • Balinski, Michel, and H. Peyton Young. 1982. Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven, Conn.: Yale University Press.
  • Caulfield, Michael J. 2008. “Apportioning Representatives in the United States Congress.” Loci, November. The Mathematical Association of America’s Mathematical Digital Library, doi:10.4169/loci003163,
  • Edelman, Paul. 2006. “Getting the Math Right: Why California Has Too Many Seats in the House of Representatives.” Vanderbilt Law Review 59:297–346.
  • Szpiro, George G. 2010. Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present. Princeton, N.J.: Princeton University Press.
  • U.S. Census Bureau. 2001. Congressional Apportionment.
  • U.S. Census Bureau. 2001. Census 2000 Ranking of Priority Values. (This shows the Hill method of doling out of seats 51–435, and the next five seats beyond that, for the 2000 census).
  • Young, H. Peyton. 1994. Equity: In Theory and Practice. Princeton, N.J.: Princeton University Press.

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