As a basis for understanding the reallocation of Representatives among the states based on the 2010 Census, it may prove helpful to examine the current House of Representatives apportionment formula. In addition, some members of the statistical community have, in the recent past, urged Congress to consider changing the current apportionment formula. Consequently, an examination of other methods that could be used to apportion the seats in the House of Representatives may contribute to a deeper understanding of the apportionment process. In 1991, the reapportionment of the House of Representatives was nearly overturned because the current "equal proportions" formula for the House apportionment was held to be unconstitutional by a three-judge panel of a federal district court. The court concluded that, By complacently relying, for over fifty years, on an apportionment method which does not even consider absolute population variances between districts, Congress has ignored the goal of equal representation for equal numbers of people. The court finds that unjustified and avoidable population differences between districts exist under the present apportionment, and ... [declares] section 2a of Title 2, United States Code unconstitutional and void. The three-judge panel's decision came almost on the 50 th anniversary of the current formula's enactment. The government appealed the panel's decision to the Supreme Court, where Montana argued that the equal proportions formula violated the Constitution because it "does not achieve the greatest possible equality in number of individuals per Representative." This reasoning did not prevail, because, as Justice Stevens wrote in his opinion for a unanimous court, absolute and relative differences in district sizes are identical when considering deviations in district populations within states, but they are different when comparing district populations among states. Justice Stevens noted, however, that "although common sense" supports a test requiring a "good faith effort to achieve precise mathematical equality within each State ... the constraints imposed by Article I, §2, itself make that goal illusory for the nation as a whole." He concluded "that Congress had ample power to enact the statutory procedure in 1941 and to apply the method of equal proportions after the 1990 census." The year 1991 was a banner year for court challenges to the apportionment process. At the same time the Montana case was being argued, another case was being litigated by Massachusetts. The Bay State lost a seat to Washington because of the inclusion of 978,819 federal employees stationed overseas in the state populations used to determine reapportionment. The court ruled that Massachusetts could not challenge the President's decision to include the overseas federal employees in the apportionment counts, in part because the President is not subject to the terms of the Administrative Procedure Act. In 2001, the Census Bureau's decision to again include the overseas federal employees in the population used to reapportion the House produced a new challenge to the apportionment population. Utah argued that it lost a congressional seat to North Carolina because of the Bureau's decision to include overseas federal employees in the apportionment count, but not other citizens living abroad. Utah said that Mormon missionaries were absent from the state because they were on assignment: a status similar to federal employees stationed overseas. Thus, the state argued, the Census Bureau should have included the missionaries in Utah's apportionment count. The state further argued that, unlike other U.S. citizens living overseas, missionaries could be accurately reallocated to their home states because the Mormon Church has excellent administrative records. Utah's complaint was dismissed by a three-judge federal court on April 17, 2001. The Supreme Court appears to have settled the issue about Congress's discretion to choose a method to apportion the House, and has granted broad discretion to the President in determining who should be included in the population used to allocate seats. What, if any, challenges to the apportionment formula and process the country will face after the 2010 Census and apportionment remain to be seen. Although modern Congresses have rarely considered the issue of the formula used in the calculations, this report describes apportionment options from which Congress could choose and the criteria that each method satisfies. One of the fundamental issues before the framers at the constitutional convention in 1787 was the allocation of representation in Congress between the smaller and larger states. The solution ultimately adopted, known as the Great (or Connecticut) Compromise, resolved the controversy by creating a bicameral Congress with states represented equally in the Senate, but in proportion to population in the House. The Constitution provided the first apportionment: 65 Representatives were allocated to the states based on the framers' estimates of how seats might be apportioned following a census. House apportionments thereafter were to be based on Article 1, section 2, as modified by clause 2 of the Fourteenth Amendment: Amendment XIV, section 2. Representatives shall be apportioned among the several States according to their respective numbers.... Article 1, section 2. The number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at least one Representative.... The constitutional mandate that Representatives would be apportioned according to population did not describe how Congress was to distribute fractional entitlements to Representatives. Clearly there would be fractions because districts could not cross state lines and the states' populations were unlikely to be evenly divisible. From its beginning in 1789, Congress was faced with questions about how to apportion the House of Representatives. The controversy continued until 1941, with the enactment of the Hill ("equal proportions") method. During congressional debates on apportionment, the major issues were how populous a congressional district ought to be (later recast as how large the House ought to be), and how fractional entitlements to Representatives should be treated. The matter of the permanent House size has received little attention since it was last increased to 435 after the 1910 Census. The Montana legal challenge added a new perspective to the picture—determining which method comes closest to meeting the goal of "one person, one vote." The "one person, one vote" concept was established through a series of Supreme Court decisions beginning in the 1960s. The court ruled in 1962 that state legislative districts must be approximately equal in population ( Baker v. Carr , 369 U.S. 186). This ruling was extended to the U.S. House of Representatives in 1964 ( Wesberry v. Sanders , 376 U.S. 1). Thus far, the "one person, one vote" concept has only been applied within states. States must be able to justify any deviations from absolute numerical equality for their congressional districts in order to comply with a 1983 Supreme Court decision— Karcher v. Daggett (462 U.S. 725). The population distribution among states in the 2010 Census, combined with a House size of 435, and the requirement that districts not cross state lines, means that there is a wide disparity in district sizes—from 527,624 (for Rhode Island's two congressional districts) to 994,416 (for Montana's single district) after the 2010 Census. This interstate population disparity among districts in 2010 contrasts with the intrastate variation experienced in the redistricting process. Thirty of the 43 states that had two or more districts in 2012 drew districts with a population difference between their largest and smallest districts of fewer than 10 and, of these, 26 states had a difference between their largest and smallest congressional district, with respect to population, of one or less. Only three states varied by more than 1,000 persons. Given a fixed-size House and an increasing population, there will inevitably be population deviations in district sizes among states. What should be the goal of an apportionment method? Although Daniel Webster was a proponent of a particular formula (the major fractions method), he succinctly defined the apportionment problem during debate on an apportionment bill in 1832 (4 Stat. 516). Webster said that, The Constitution, therefore, must be understood, not as enjoining an absolute relative equality, because that would be demanding an impossibility, but as requiring of Congress to make the apportionment of Representatives among the several states according to their respective numbers, as near as may be. That which cannot be done perfectly must be done in a manner as near perfection as can be. Which apportionment method is the "manner as near perfection as can be"? Although there are potentially thousands of different ways in which the House could be apportioned, six methods are most often mentioned as possibilities. These are the methods of Hamilton-Vinton, "largest fractional remainders"; of Adams, "smallest divisors"; of Dean, "harmonic mean"; of Hill, "equal proportions"; of Webster, "major fractions"; and of Jefferson, "largest divisors." Since 1941, seats in the House of Representatives have been apportioned according to the method of equal proportions (Hill)(see below, in " Rounding Methods "). However, from 1790 to the present, alternative methods for apportioning seats have been used or seriously considered. Six such methods stand out. One, the Hamilton-Vinton method, involves ranking fractional remainders. The others (the methods of Adams, Dean, Hill, Webster, and Jefferson) involve rounding fractional remainders. Why is there a controversy? Why not apportion the House the intuitive way by dividing each state's population by the national "ideal size" district (710,767 in 2010) and give each state its "quota" (rounding up at fractional remainders of .5 and above, and down for remainders less than .5)? The problem with this proposal is that the House size would not always be 435 seats. In some decades, the House might include 435 seats; in others, it might be either under or over the legal limit. In 2012, this method would have resulted in a 433-seat House (433 in 2002, 438 in 1992).