House of Representatives Reapportionment by Hill's Method

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This Demonstration illustrates Hill's method for reapportionment, which is the method currently used in the United States House of Representatives.


A standard divisor is found by dividing the total population by the number of seats. Dividing each state's population by that divisor results in the quota—the ideal number of representatives, which is almost never an integer. Finally, that number is compared to the geometric mean of the two integers closest to it; if it is larger, the state is given an extra seat, and if it is smaller, it is rounded down and given that integer number of seats.

In the pie chart, the inner ring shows each state's population, the second ring shows its quota, and the outer ring shows the final apportionment; note how Hill's method tends to favor smaller states.


Contributed by: Michelle Zhao (February 2016)
Open content licensed under CC BY-NC-SA




[1] M. J. Caulfield, "What If? How Apportionment Methods Choose Our Presidents," Mathematics Teacher, 106(3), 2012 pp. 178–183.

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