How many Representatives should the House comprise? Moreover, no matter how one specified the ideal population of a congressional district or the number of Representatives in the House, a state's ideal apportionment would, as a practical matter, always be either a fraction, or a whole number and a fraction—say, 14.489326. Thus, another question was whether that state would be apportioned 14 or 15 representatives? The questions of how populous a congressional district should be and how many Representatives should constitute the House have received little attention since the number of Representatives was last increased from 386 to 435 after the 1910 Census. The problem of fractional entitlement to Representatives, however, continued to be troublesome. The issue of fairness could not be perfectly resolved: inevitable fractional entitlements and the requirement that each state have at least one representative lead to inevitable disparities among the states' average congressional district populations. In light of the lengthy debate on apportionment, this report has four major purposes:
1. summarize the constitutional and statutory requirements governing apportionment; 2. explain how the current apportionment formula works in theory and in practice; 3. summarize challenges to it on grounds of inequity; and 4. explain the reasoning underlying the choice of the equal proportions method over its chief alternative, the method of major fractions. There can be no fewer than one Representative per state, and no more than one for every 30,000 persons. Once received by Congress, the Clerk of the House of Representatives is charged with the duty of sending to the governor of each state a "certificate of the number of Representatives to which such state is entitled" within 15 days of receiving notice from the President. First, the U.S. apportionment population is divided by the total number of seats in the House (e.g., 309,183,463 divided by 435, in 2010) to identify the "ideal" sized congressional district (708,377 in 2010). In most cases this will result in a whole number and a fractional remainder, as noted earlier. There are two fundamental problems with using simple rounding for apportionment, given a House of fixed size. First, it is possible that some state populations might be so small that they would be "entitled" to less than half a seat. Thus, this intuitive way to apportion fails because, by definition, it does not take into account the constitutional requirement that every state have at least one seat in the House and the statutory requirement that the House size be fixed at 435. Then each state's apportionment population is divided by the "ideal" district size to determine its number of seats. Next, the seventh seat's allocation is determined. The fact that higher rounding points are necessary for states to obtain additional seats has led to charges that the equal proportions formula favors small states at the expense of large states. This method, called the Webster method in Fair Representation , is also referred to as the major fractions method (major fractions uses the concept of the adjustable divisor as does equal proportions, but rounds at the arithmetic mean [.5] rather than the geometric mean.) For the purpose of this analysis, we will concentrate on the differences between the equal proportions and major fractions methods because the Hamilton-Vinton method is subject to several mathematical anomalies. Apportioning the House can be viewed as a system with four main variables: (1) the size of the House, (2) the population of the states, (3) the number of states, and (4) the method of apportionment. 2010 Priority List for Apportioning Seats to the House of Representatives
On December 21, 2010, the number of seats allocated to each state for the House of Representatives was announced. This allocation likely will determine representation to the House for the next five Congresses.
The Constitution requires that states be represented in the House of Representatives 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. For the 2010 apportionment, this could have meant a House of Representatives as small as 50 or as large as 10,306 Representatives.
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 many 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? Apportioning the House can be viewed as a system with four main variables: (1) the size of the House, (2) the population of the states, (3) the number of states, and (4) the method of apportionment.
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 inequity.
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.
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 Congress to adopt either the major fractions or the Hamilton-Vinton method as more equitable alternatives. A strong mathematical 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.