The House Apportionment Formula in Theory and Practice

Publication Date: October 2000

Publisher: Library of Congress. Congressional Research Service

Author(s):

Research Area: Politics

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Abstract:

The Constitution requires that states be represented in the House in accord with their population. It also requires that each state have at least one Representative, and that there be no more than one Representative for every 30,000 persons. Apportioning seats in the House of Representatives among the states in proportion to state population as required by the Constitution appears on the surface to be a simple task. In fact, however, the Constitution presented Congress with issues that provoked extended and recurring debate. How may Representatives should the House comprise? How populous should congressional districts be? What is to be done with the practically inevitable fractional entitlement to a House seat that results when the calculations of proportionality are made? How is fairness of apportionment to be best preserved?

Over the years since the ratification of the Constitution the number of Representatives has varied, but in 1941 Congress resolved the issue by fixing the size of the House at 435 Members. How to apportion those 435 seats, however, continued to be an issue because of disagreement over how to handle fractional entitlements to a House seat in a way that both met constitutional and statutory requirements and minimized unfairness.

The intuitive method of apportionment is to divide the United States population by 435 to obtain an average number of persons represented by a Member of the House. This is sometimes called the ideal size congressional district. Then a state's population is divided by the ideal size to determine the number of Representatives to be allocated to that state. The quotient will be a whole number plus a remainder - say 14.489326. What is Congress to do with the 0.489326 fractional entitlement? Does the state get 14 or 15 seats in the House? Does one discard the fractional entitlement? Does one round up at the arithmetic mean of the two whole numbers? At the geometric mean? At the harmonic mean? Congress has used or at least considered several methods over the years - e.g., Jefferson's discarded fractions method, Webster's major fractions method, the equal proportions method, smallest divisors method, greatest divisors, the Vinton method, and the Hamilton-Vinton method. The methodological issues have been problematic for Congress because of the unfamiliarity and difficulty of some of the mathematical concepts used in the process.

Every method Congress has used or considered has its advantages and disadvantages, and none has been exempt from criticism. Under current law, however, seats are apportioned using the equal proportions method, which is not without its critics. Some charge that the equal proportions method is biased toward small states. They urge that either the major fractions or the Hamilton-Vinton method be adopted by Congress as an alternative. A strong case can be made for either equal proportions or major fractions. Deciding between them is a policy matter based on whether minimizing the differences in district sizes in absolute terms (through major fractions) or proportional terms (through equal proportions) is most preferred by Congress.