The House Apportionment Formula in Theory and Practice

This report has four major purposes: to summarize the constitutional and statutory requirements governing apportionment; to explain how the current apportionment formula works in theory and in practice; to summarize recent challenges to it on grounds of unfairness; and to explain the reasoning underlying the choice of the equal

proportions method over its chief alternative, major fractions.

Order Code RL30711 CRS Report for Congress Received through the CRS Web The House Apportionment Formula in Theory and Practice October 10, 2000 David C. Huckabee Specialist in American National Government Government and Finance Division Congressional Research Service ˜ The Library of Congress The House Apportionment Formula in Theory and Practice Summary 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. Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Constitutional and Statutory Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Apportionment Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Formula In Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Challenges to the Current Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Equal Proportions or Major Fractions: an Analysis . . . . . . . . . . . . . . . . . . 10 The Case for Major Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Case for Equal Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Appendix: 1990 Priority List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 List of Tables Table 1. Multipliers for Determining Priority Values for Apportioning the House by the Equal Proportions Method . . . . . . . . . . Table 2. Calculating Priority Values for a Hypothetical Three State House of 30 Seats Using the Method of Equal Proportions . . . . . . . . Table 3. Priority Rankings for Assigning Thirty Seats in a Hypothetical Three-State House Delegation . . . . . . . . . . . . . . . . . . . . Table 4. Rounding Points for Assigning Seats Using the Equal Proportions Method of Apportionment* . . . . . . . . . . . . . . 6 6 7 9 The House Apportionment Formula in Theory and Practice Introduction One of the fundamental issues before the framers at the Constitutional Convention in 1787 was how power was to be allocated in the Congress among 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 of House seats: 65 Representatives were allocated to the states based on the framers’ estimates of how seats might be apportioned after a census. House apportionments thereafter were to be based on Article 1, section 2, as modified by 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.... From its beginning in 1789, Congress was faced with questions about how to apportion the House of Representatives–questions that the Constitution did not answer. How populous should a congressional district be on average? 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? Consequently, these two major issues dominated the apportionment debate: how populous a congressional district ought to be (later re-cast as how large the House ought to be), and how to treat fractional entitlements to Representatives.1 1 Thomas Jefferson recommended discarding the fractions. Daniel Webster and others argued that Jefferson’s method was unconstitutional because it discriminated against small states. Webster argued that an additional Representative should be awarded to a state if the fractional entitlement was 0.5 or greater–a method that decreased the size of the house by 17 Members in 1832. Congress subsequently used a “fixed ratio” method proposed by Rep. Samuel Vinton following the census of 1850 through 1900, but this method led to the paradox that Alabama lost a seat even though the size of the House was increased in 1880. Subsequently, mathematician W.F. Willcox proposed the “major fractions” method, which was used (continued...) CRS-2 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 to 435 after the 1910 Census. 2 The problem of fractional entitlement to Representatives, however, continued to be troublesome. Various methods were considered and some were tried, each raising questions of fundamental fairness. 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. The congressional debate, which sought an apportionment method that would minimize those disparities, continued until 1941, when Congress enacted the “equal proportions” method–the apportionment method still in use today. In light of the lengthy debate on apportionment, this report has four major purposes: 1. to summarize the constitutional and statutory requirements governing apportionment; 2. to explain how the current apportionment formula works in theory and in practice; 3. to summarize recent challenges to it on grounds of unfairness; and 4. to explain the reasoning underlying the choice of the equal proportions method over its chief alternative, major fractions. Constitutional and Statutory Requirements The process of apportioning seats in the House is constrained both constitutionally and statutorily. As noted previously, the Constitution defines both the maximum and minimum size of the House. There can be no fewer than one Representative per state, and no more than one for every 30,000 persons.3 1 (...continued) following the census of 1910. This method, too, had its critics; and in 1921 Harvard mathematician E.V. Huntington proposed the “equal proportions” method and developed formulas and computational tables for all of the other known, mathematically valid apportionment methods. A committee of the National Academy of Sciences conducted an analysis of each of those methods–smallest divisors, harmonic mean, equal proportions, major fractions, and greatest divisors–and recommended that Congress adopt Huntington’s equal proportions method. For a review of this history, see U.S. Congress, House, Committee on Post Office and Civil Service, Subcommittee on Census and Statistics, The Decennial Population Census and Congressional Apportionment, 91st Cong., 2nd sess. H. Rept. 911314 (Washington: GPO, 1970), Appendix B, pp. 15-18. 2 Article I, Section 2 defines both the maximum and minimum size of the House, but the actual House size is set by law. There can be no fewer than one Representative per state, and no more than one for every 30,000 persons. Thus, the House after 1990 could have been as small as 50 and as large as 8,301 Representatives. 3 The actual language in of Article 1, section 2 pertaining to this minimum size reads as (continued...) CRS-3 The 1941 apportionment act, in addition to specifying the apportionment method, sets the House size at 435 and mandates administrative procedures for apportionment. The President is required to transmit to Congress “a statement showing the whole number of persons in each state” and the resulting seat allocation within one week after the opening of the first regular session of Congress following the census.4 The Census Bureau has been assigned the responsibility of computing the apportionment. As matter of practice, the Director of the Bureau reports the results of the apportionment on December 31st of the census year. Once received by Congress, the Clerk of the House 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.5 The Apportionment Formula The Formula In Theory. An intuitive way to apportion the House is through simple rounding (a method never adopted by Congress). First, the U.S. apportionment population6 is divided by the total number of seats in the House (e.g., in 1990, 249,022,783 divided by 435) to identify the “ideal” sized congressional district (572,466 in 1990). Then, each state’s population is divided by the “ideal” district population. In most cases this will result in a whole number and a fractional remainder, as noted earlier. Each state will definitely receive seats equal to the whole number, and the fractional remainders will either be rounded up or down (at the .5 “rounding point”). 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. Yet, the Constitution requires that every state must have at least one seat in the House. Thus, a method which relies entirely on rounding will not comply with the Constitution if there are states with very small populations. Second, even a method that assigns each state its constitutional minimum of one seat and otherwise relies on rounding at the .5 rounding point might require a “floating” House size because rounding at .5 could result in either fewer or more than 435 seats. Thus, this intuitive way to apportion fails because, by definition, it does not take into account the 3 (...continued) follows: “The number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at least one Representative.” This clause is sometime mis-read to be a requirement that districts can be no larger than 30,000 persons, rather than as it should be read, as a minimum-size population requirement. 4 55 Stat. 761. (1941) Sec. 22 (a). [Codified in 2 U.S.C. 2(a).] In other words, after the 2000 Census, this report is due in January 2001. 5 6 Ibid., Sec. 22 (b). The apportionment population is the population of the 50 states. It excludes the population of the District of Columbia and U.S. territories and possessions. CRS-4 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. The current apportionment method (the method of equal proportions established by the 1941 act) satisfies the constitutional and statutory requirements. Although an equal proportions apportionment is not normally computed in the theoretical way described below, the method can be understood as a modification of the rounding scheme described above. First, the “ideal” sized district is found (by dividing the apportionment population by 435) to serve as a “trial” divisor. Then each state’s apportionment population is divided by the “ideal” district size to determine its number of seats. Rather than rounding up any remainder of .5 or more, and down for less than .5, however, equal proportions rounds at the geometric mean of any two successive numbers. A geometric mean of two numbers is the square root of the product of the two numbers.7 If using the “ideal” sized district population as a divisor does not yield 435 seats, the divisor is adjusted upward or downward until rounding at the geometric mean will result in 435 seats. In 1990, the “ideal” size district of 572,466 had to be adjusted upward to between 573,555 and 573,6438 to produce a 435-Member House. Because the divisor is adjusted so that the total number of seats will equal 435, the problem of the “floating” House size is solved. The constitutional requirement of at least one seat for each state is met by assigning each state one seat automatically regardless of its population size. The Formula in Practice: Deriving the Apportionment From a Table of "Priority Values." Although the process of determining an apportionment through a series of trials using divisions near the “ideal” sized district as described above works, it is inefficient because it requires a series of calculations using different divisors until the 435 total is reached. Accordingly, the Census Bureau determines apportionment by computing a “priority” list of state claims to each seat in the House. During the early twentieth century, Walter F. Willcox, a Cornell University mathematician, discovered that if the rounding points used in an apportionment method are divided into each state's population (the mathematical equivalent of 7 The geometric mean of 1 and 2 is the square root of 2, which is 1.4142. The geometric mean of 2 and 3 is the square root of 6, which is 2.4495. Geometric means are computed for determining the rounding points for the size of any state’s delegation size. Equal proportions rounds at the geometric mean (which varies) rather than the arithmetic mean (which is always halfway between any pair of numbers). Thus, a state which would be entitled to 10.4871 seats before rounding will be rounded down to 10 because the geometric mean of 10 and 11 is 10.4881. The rationale for choosing the geometric mean rather than the arithmetic mean as the rounding point is discussed in the section analyzing the equal proportions and major fractions formulas. 8 Any number in this range divided into each state’s population and rounded at the geometric mean will produce a 435-seat House. CRS-5 multiplying the population by the reciprocal of the rounding point), the resulting numbers can be ranked in a priority list for assigning seats in the House.9 Such a priority list does not assume a fixed House size because it ranks each of the states’ claims to seats in the House so that any size House can be chosen easily without the necessity of extensive recomputations.10 The traditional method of constructing a priority list to apportion seats by the equal proportions method involves first computing the reciprocals11 of the geometric means between every pair of consecutive whole numbers (the “rounding points”) so that it is possible to multiply by decimals rather than divide by fractions (the former being a considerably easier task). For example, the reciprocal of the geometric mean between 1 and 2 (1.41452) is 1/1.414452 or .70710678. These reciprocals are computed for each “rounding point.” They are then used as multipliers to construct the “priority list.” Table 1 provides a list of multipliers used to calculate the “priority values” for each state in an equal proportions apportionment. To construct the “priority list,” each state’s apportionment population is multiplied by each of the multipliers. The resulting products are ranked in order to show each state’s claim to seats in the House. For example, assume that there are three states in the Union (California, New York, and Florida) and that the House size is set at 30 Representatives. The first seat for each state is assigned by the Constitution; so the remaining twenty-seven seats must be apportioned using the equal proportions formula. The 1990 apportionment populations for these states were 29,839,250 for California, 18,044,505 for New York, and 13,003,362 for Florida. Table 2 (p. 6) illustrates how the priority values are computed for each state. Once the priority values are computed, they are ranked with the highest value first. The resulting ranking is numbered and seats are assigned until the total is reached. By using the priority rankings instead of the rounding procedures described above, it is possible to see how an increase or decrease in the House size will affect the allocation of seats without the necessity of doing new calculations. Table 3 (p. 7) ranks the priority values of the three states in this example, showing how the 27 seats are assigned. 9 U.S. Congress, House Committee on Post Office and Civil Service, Subcommittee on the Census and Statistics, The Decennial Population Census and Congressional Apportionment, 91st Cong., 2nd sess., H. Rept. 91-1814, (Washington: GPO, 1970), p. 16. 10 The 435 limit on the size of the House is a statutory requirement. The House size was first fixed at 435 by the Apportionment Act of 1911 (37 Stat. 13). The Apportionment Act of 1929 (46 Stat. 26), as amended by the Apportionment Act of 1941 (54 Stat. 162), provided for “automatic reapportionment” rather than requiring the Congress to pass a new apportionment law each decade. By authority of section 9 of PL 85-508 (72 Stat. 345) and section 8 of PL 86-3 (73 Stat. 8), which admitted Alaska and Hawaii to statehood, the House size was temporarily increased to 437 until the reapportionment resulting from the 1960 Census when it returned to 435. 11 A reciprocal of a number is that number divided into one. CRS-6 Table 1. Multipliers for Determining Priority Values for Apportioning the House by the Equal Proportions Method Size of delegation Multiplier* Size of delegation Multiplier* Size of delegation Multiplier* 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Constitution 0.70710678 0.40824829 0.28867513 0.22360680 0.18257419 0.15430335 0.13363062 0.11785113 0.10540926 0.09534626 0.08703883 0.08006408 0.07412493 0.06900656 0.06454972 0.06063391 0.05716620 0.05407381 0.05129892 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 0.04879500 0.04652421 0.04445542 0.04256283 0.04082483 0.03922323 0.03774257 0.03636965 0.03509312 0.03390318 0.03279129 0.03175003 0.03077287 0.02985407 0.02898855 0.02817181 0.02739983 0.02666904 0.02597622 0.02531848 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 0.02469324 0.02409813 0.02353104 0.02299002 0.02247333 0.02197935 0.02150662 0.02105380 0.02061965 0.02020305 0.01980295 0.01941839 0.01904848 0.01869241 0.01834940 0.01801875 0.01769981 0.01739196 0.01709464 0.01680732 *Table by CRS, calculated by determining the reciprocals of the geometric means of successive numbers: 1/ n(n -1) , where “n” is the number of seats to be allocated to the state. Table 2. Calculating Priority Values for a Hypothetical Three State House of 30 Seats Using the Method of Equal Proportions State CA CA CA CA CA CA CA CA CA CA CA CA CA CA CA CA CA NY NY NY NY NY NY Size of delegation 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 4 5 6 7 State’s priority value claim to a delegation size Calculation Multiplier (M) Population (P) Priority value (PxM) 0.70710678 29,839,250 21,099,536.02 0.40824829 29,839,250 12,181,822.80 0.28867513 29,839,250 8,613,849.51 0.22360680 29,839,250 6,672,259.14 0.18257419 29,839,250 5,447,876.77 0.15430335 29,839,250 4,604,296.24 0.13363062 29,839,250 3,987,437.51 0.11785113 29,839,250 3,516,589.34 0.10540926 29,839,250 3,145,333.12 0.09534626 29,839,250 2,845,060.86 0.08703883 29,839,250 2,597,173.35 0.08006408 29,839,250 2,389,052.01 0.07412493 29,839,250 2,211,832.37 0.06900656 29,839,250 2,059,103.87 0.06454972 29,839,250 1,926,115.31 0.06063391 29,839,250 1,809,270.29 0.05716620 29,839,250 1,705,796.39 0.70710678 18,044,505 12,759,391.85 0.40824829 18,044,505 7,366,638.32 0.28867513 18,044,505 5,208,999.91 0.22360680 18,044,505 4,034,873.98 0.18257419 18,044,505 3,294,460.81 0.15430335 18,044,505 2,784,327.57 CRS-7 Size of delegation 8 9 10 11 12 2 3 4 5 6 7 8 State NY NY NY NY NY FL FL FL FL FL FL FL State’s priority value claim to a delegation size Calculation Multiplier (M) Population (P) Priority value (PxM) 0.13363062 18,044,505 2,411,298.41 0.11785113 18,044,505 2,126,565.31 0.10540926 18,044,505 1,902,057.84 0.09534626 18,044,505 1,720,476.05 0.08703883 18,044,505 1,570,572.57 0.70710678 13,003,362 9,194,765.45 0.40824829 13,003,362 5,308,600.31 0.28867513 13,003,362 3,753,747.28 0.22360680 13,003,362 2,907,640.14 0.18257419 13,003,362 2,374,078.23 0.15430335 13,003,362 2,006,462.32 0.13363062 13,003,362 1,737,647.34 *The “priority values” are the product of the multiplier times the state population. These values can be computed for any size state delegation, but only those values necessary for this example have been computed for this table. The population figures are those from the 1990 Census. Table by CRS. Table 3. Priority Rankings for Assigning Thirty Seats in a Hypothetical Three-State House Delegation House size 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 State CA NY CA FL CA NY CA CA FL NY CA NY CA FL CA NY CA FL CA NY CA NY CA FL CA NY CA State’s priority value claim to a delegation size Size of Calculation delegation Multiplier (M) Population (P) Priority value (PxM) 2 2 3 2 4 3 5 6 3 4 7 5 8 4 9 6 10 5 11 7 12 8 13 6 14 9 15 0.70710678 0.70710678 0.40824829 0.70710678 0.28867513 0.40824829 0.22360680 0.18257419 0.40824829 0.28867513 0.15430335 0.22360680 0.13363062 0.28867513 0.11785113 0.18257419 0.10540926 0.22360680 0.09534626 0.15430335 0.08703883 0.13363062 0.08006408 0.18257419 0.07412493 0.11785113 0.06900656 29,839,250 18,044,505 29,839,250 13,003,362 29,839,250 18,044,505 29,839,250 29,839,250 13,003,362 18,044,505 29,839,250 18,044,505 29,839,250 13,003,362 29,839,250 18,044,505 29,839,250 13,003,362 29,839,250 18,044,505 29,839,250 18,044,505 29,839,250 13,003,362 29,839,250 18,044,505 29,839,250 21,099,536.02 12,759,391.85 12,181,822.80 9,194,765.45 8,613,849.51 7,366,638.32 6,672,259.14 5,447,876.77 5,308,600.31 5,208,999.91 4,604,296.24 4,034,873.98 3,987,437.51 3,753,747.28 3,516,589.34 3,294,460.81 3,145,333.12 2,907,640.14 2,845,060.86 2,784,327.57 2,597,173.35 2,411,298.41 2,389,052.01 2,374,078.23 2,211,832.37 2,126,565.31 2,059,103.87 *The Constitution requires that each state have least one seat. Table by CRS. CRS-8 From the example in Table 3, we see that if the United States were made up of three states and the House size were to be set at 30 Members, California would have 15 seats, New York would have nine, and Florida would have six. Any other size House can be determined by picking points in the priority list and observing what the maximum size state delegation size would be for each state. A priority listing for all 50 states based on the 1990 Census is appended to this report. It shows priority rankings for the assignment of seats in a House ranging in size from 51 to 500 seats. Challenges to the Current Formula The equal proportions rule of rounding at the geometric mean results in differing rounding points, depending on which numbers are chosen. For example, the geometric mean between 1 and 2 is 1.4142, and the geometric mean between 49 and 50 is 49.49747. Table 4 on the following page shows the “rounding points” for assignments to the House using the equal proportions method for a state delegation size of up to 60. The rounding points are listed between each delegation size because they are the thresholds which must be passed in order for a state to be entitled to another seat. The table illustrates that, as the delegation size of a state increases, larger fractions are necessary to entitle the state to additional seats. The increasingly higher rounding points necessary to obtain additional seats has led to charges that the equal proportions formula favors small states at the expense of large states. In a 1982 book about congressional apportionment entitled Fair Representation, the authors (M.L. Balinski and H.P. Young) concluded that if “the intent is to eliminate any systematic advantage to either the small or the large, then only one method, first proposed by Daniel Webster in 1832, will do.”12 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.) Balinski and Young’s conclusion in favor of major fractions, however, contradicts a report of the National Academy of Sciences (NAS) prepared at the request of Speaker Longworth in 1929. The NAS concluded that “the method of equal proportions is preferred by the committee because it satisfies ... [certain tests], and because it occupies mathematically a neutral position with respect to emphasis on larger and smaller states”.13 12 M.L. Balinski and H.P. Young, Fair Representation, (New Haven and London: Yale University Press, 1982), p. 4. (An earlier major work in this field was written by Laurence F. Schmeckebier, Congressional Apportionment. (Washington: The Brookings Institution, 1941). Daniel Webster proposed this method to overcome the large-state bias in Jefferson’s discarded fractions method. Webster’s method was used three times, in the reapportionments following the 1840, 1910, and 1930 Censuses. 13 “Report of the National Academy of Sciences Committee on Apportionment” in The Decennial Population Census and Congressional Apportionment, Appendix C, p. 21. CRS-9 Table 4. Rounding Points for Assigning Seats Using the Equal Proportions Method of Apportionment* Size of delegation 1 Round up at Size of delegation 16 1.41421 2 Round up at 16.49242 17 2.44949 3 4.47214 5 24 10.48809 11 42.49706 57.49783 58 43.49713 29.49576 58.49786 59 44.49719 45 30.49590 56.49779 57 44 30 15.49193 41.49699 28.49561 14.49138 55.49775 56 43 29 15 40.49691 27.49545 13.49074 54.49771 55 42 28 14 54 41 26.49528 12.49000 53.49766 39.49684 40 27 13 38.49675 25.49510 11.48913 52.49762 53 39 26 12 37.49667 24.49490 25 51.49757 52 38 23.49468 9.48683 10 36.49658 22.49444 8.48528 50.49752 51 37 23 9 35.49648 21.49419 7.48331 49.49747 50 36 22 8 34.49638 20.49390 6.48074 48.49742 49 35 21 7 33.49627 19.49359 5.47723 6 47.49737 48 34 20 46.49731 32.49615 18.49324 Round up at 47 33 19 Size of delegation 46 31.49603 17.49286 3.46410 Round up at 32 18 4 Size of delegation 31 59.49790 60 45.49725 60.49793 *Any number between 574,847 and 576,049 divided into each state’s 1990 apportionment population will produce a House size of 435 if rounded at these points, which are the geometric means of each pair of successive numbers. Table by CRS. A bill that would have changed the apportionment method to another formula called the “Hamilton-Vinton” method was introduced in 1981.14 The fundamental principle of the Hamilton-Vinton method is that it ranks fractional remainders. To reapportion the House using Hamilton-Vinton, each state’s population would be divided by the “ideal” sized congressional district (in 1990, 249,022,783 divided by 435 or 572,466). Any state with fewer residents than the “ideal”sized district would receive a seat because the Constitution requires each state to have at least one House 14 H.R. 1990 was introduced by Representative Floyd Fithian and was cosponsored by 10 other Members of the Indiana delegation. Hearings were held, but no further action was taken on the measure. U.S. Congress, House Committee on Post Office and Civil Service, Subcommittee on Census and Population, Census Activities and the Decennial Census, hearing, 97th Cong., 1st sess., June 11, 1981, (Washington: GPO, 1981). CRS-10 seat. The remaining states in most cases have a claim to a whole number and a fraction of a Representative. Each such state receives the whole number of seats it is entitled to. The fractional remainders are rank-ordered from highest to lowest until 435 seats are assigned. 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 peculiarities.15 Equal Proportions or Major Fractions: an Analysis Each of the major competing methods–equal proportions (currently used) and major fractions–can be supported mathematically. Choosing between them is a policy decision, rather than a matter of conclusively proving that one approach is mathematically better than the other. A major fractions apportionment results in a House in which each citizen’s share of his or her Representative is as equal as possible on an absolute basis. In the equal proportions apportionment now used, each citizen’s share of his or her Representative is as equal as possible on a proportional basis. The state of Indiana in 1980 would have been assigned 11 seats under the major fractions method, and New Mexico would have received 2 seats. Under this allocation, there would have been 2.004 Representatives per million for Indiana residents and 1.538 Representative per million in New Mexico. The absolute value16 of the difference between these two numbers is 0.466. Under the equal proportions assignment in 1980, Indiana actually received 10 seats and New Mexico 3. With 10 seats, Indiana got 1.821 Representatives for each million persons, and New Mexico with 3 seats received 2.308 Representatives per million. The absolute value of the difference is 0.487. Because major fractions minimizes the absolute population differences, under it Indiana would have received 11 seats and New Mexico 2, because the absolute value of subtracting the population shares with an 11 and 2 assignment (0.466) is smaller than a 10 and 3 assignment (0.487). An equal proportions apportionment, however, results in a House where the average sizes of all the states’ congressional districts are as equal as possible if their differences in size are expressed proportionally–that is, as percentages. The proportional difference between 2.004 and 1.538 (major fractions) is 30%. The proportional difference between 2.308 and 1.821 (equal proportions) is 27%. Based 15 The Hamilton-Vinton method (used after the 1850-1900 censuses) is subject to the “Alabama paradox” and various other population paradoxes. The Alabama paradox was so named in 1880 when it was discovered that Alabama would have lost a seat in the House if the size of the House had been increased from 299 to 300. Another paradox, known as the population paradox, has been variously described, but in its modern form (with a fixed size House) it works in this way: two states may gain population from one census to the next. State “A,” which is gaining population at a rate faster than state “B,” may lose a seat to state “B.” There are other paradoxes of this type. Hamilton-Vinton is subject to them, whereas equal proportions and major fractions are not. 16 The absolute value of a number is its magnitude without regard to its sign. For example, the absolute value of -8 is 8. The absolute value of the expression (4-2) is 2. The absolute value of the expression (2-4) is also 2. CRS-11 on this comparison, the method of equal proportions gives New Mexico 3 seats and Indiana 10 because the proportional difference is smaller (27%) than if New Mexico gets 2 seats and Indiana 10 (30%). From a policy standpoint, one can make a case for either method by arguing that one measure of fairness is preferable to the other. The Case for Major Fractions. It can be argued that the major fractions minimization of absolute size differences among districts most closely reflects the “one person, one vote” principle established by the Supreme Court in its series of redistricting cases (Baker v. Carr, 369 U.S. 186 (1964) through Karcher v. Daggett, 462 U.S.725 (1983).17 Although the “one person, one vote” rules have not been applied by the courts to apportioning seats among states, major fractions can reduce the range between the smallest and largest district sizes more than equal proportions–one of the measures which the courts have applied to within-state redistricting cases. Although this range would have not changed in 1990, if major fractions had been used in 1980, the smallest average district size in the country would have been 399,592 (one of Nevada’s two districts). With equal proportions it was 393,345 (one of Montana’s two districts). In both cases the largest district was 690,178 (South Dakota’s single seat).18 Thus, in 1980, shifting from equal proportions to major fractions as a method would have improved the 296,833 difference between the largest and smallest districts by 6,247 persons. It can be argued, because the equal proportions rounding points ascend as the number of seats increases, rather than staying at .5, that small states may be favored in seat assignments at the expense of large states. It is possible to demonstrate this using simulation techniques. The House has only been reapportioned 20 times since 1790. The equal proportions method has been used in five apportionments, and major fractions in three. Eight apportionments do not provide enough historical information to enable policy makers to generalize about the impact of using differing methods. Computers, however, can enable reality to be simulated by using random numbers to test many different hypothetical situations. These techniques (such as the “Monte Carlo” simulation method) are a useful way of observing the behavior of systems when experience does not provide enough information to generalize about them. 17 Major fractions best conforms to the spirit of these decisions if the population discrepancy is measured on an absolute basis, as the courts have done in the recent past. The Court has never applied its “one person, one vote” rule to apportioning seats–states (as opposed to redistricting within states). Thus, no established rule of law is being violated. Arguably, no apportionment method can meet the “one person, one vote” standard required for districts within states unless the size of the House is increased significantly (thereby making districts smaller). 18 Nevada had two seats with a population of 799,184. Montana was assigned two seats with a population of 786,690. South Dakota's single seat was required by the Constitution (with a population of 690,178). The vast majority of the districts based on the 1980 census (323 of them) fell within the range of 501,000 to 530,000). CRS-12 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. A 1984 exercise prepared for the Congressional Research Service (CRS) involving 1,000 simulated apportionments examined the results when two of these variables were changed–the method and the state populations. In order to further approximate reality, the state populations used in the apportionments were based on the Census Bureau's 1990 population projections available at that time. Each method was tested by computing 1,000 apportionments and tabulating the results by state. There was no discernible pattern by size of state in the results of the major fractions apportionment. The equal proportions exercise, however, showed that the smaller states were persistently advantaged.19 Another way of evaluating the impact of a possible change in apportionment methods is to determine the odds of an outcome being different than the one produced by the current method–equal proportions. If equal proportions favors small states at the expense of large states, would switching to major fractions, a method that appears not to be influenced by the size of a state, increase the odds of the large states gaining additional representation? Based on the simulation model prepared for CRS, this appears to be true. The odds of any of the 23 largest states gaining an additional seat in any given apportionment range from a maximum of 13.4% of the time (California) to a low of .2% of the time (Alabama). The odds of any of the 21 multi-districted smaller states losing a seat range from a high of 17% (Montana, which then had two seats) to a low of 0% (Colorado), if major fractions were used instead of equal proportions. In the aggregate, switching from equal proportions to major fractions “could be expected to shift zero seats about 37% of the time, to shift 1 seat about 49% of the time, 2 seats 12% of the time, and 3 seats 2% of the time (and 4 or more seats almost never), and, these shifts will always be from smaller states to larger states.”20 The Case for Equal Proportions. Support for the equal proportions formula primarily rests on the belief that minimizing the proportional differences among districts is more important than minimizing the absolute differences. Laurence Schmeckebier, a proponent of the equal proportions method, wrote in Congressional Apportionment in 1941, that: 19 Comparing equal proportions and major fractions using the state populations from the 19 actual censuses taken since 1790, reveals that the small states would have been favored 3.4% of the time if equal proportions had been used for all the apportionments. Major fractions would have also favored small states, in these cases, but only .03 % of the time. See Fair Representation, p. 78. 20 H.P. Young and M.L. Balinski, Evaluation of Apportionment Methods, Prepared under a contract for the Congressional Research Service of the Library of Congress. (Contract No. CRS84-15), Sept. 30, 1984, p. 13. CRS-13 Mathematicians generally agree that the significant feature of a difference is its relation to the smaller number and not its absolute quantity. Thus the increase of 50 horsepower in the output of two engines would not be of any significance if one engine already yielded 10,000 horsepower, but it would double the efficiency of a plant of only 50 horsepower. It has been shown ... that the relative difference between two apportionments is always least if the method of equal proportions is used. Moreover, the method of equal proportions is the only one that uses relative differences, the methods of harmonic mean and major fraction being based on absolute differences. In addition, the method of equal proportions gives the smallest relative difference for both average population per district and individual share in a representative. No other method takes account of both these factors. Therefore the method of equal proportions gives the most equitable distribution of Representatives among the states.21 An example using Massachusetts and Oklahoma 1990 populations, illustrates the argument for proportional differences. The first step in making comparisons between the states is to standardize the figures in some fashion. One way of doing this is to express each state’s representation in the House as a number of Representatives per million residents.22 The equal proportions formula assigned 10 seats to Massachusetts and 6 to Oklahoma in 1990. When 11 seats are assigned to Massachusetts, and five are given to Oklahoma (using major fractions), Massachusetts has 1.824 Representatives per million persons and Oklahoma has 1.583 Representatives per million. The absolute difference between these numbers is .241 and the proportional difference between the two states’ Representatives per million is 15.22%. When 10 seats are assigned to Massachusetts and 6 are assigned to Oklahoma (using equal proportions), Massachusetts has 1.659 Representatives per million and Oklahoma has 1.9 Representative per million. The absolute difference between these numbers is .243 and the proportional difference is 14.53%. Major fractions minimizes absolute differences, so in 1990, if this if this method had been required by law, Massachusetts and Oklahoma would have received 11 and five seats respectively because the absolute difference (0.241 Representatives per million) is smaller at 11 and five than it would be at 10 and 6 (0.243). Equal proportions minimizes differences on a proportional basis, so it assigned 10 seats to Massachusetts and six to Oklahoma because the proportional difference between a 10 and 6 allocation (14.53%) is smaller than would occur with an 11 and 5 assignment (15.22%). The proportional difference versus absolute difference argument could also be cast in terms of the goal of “one person, one vote.” The courts’ use of absolute difference measures in state redistricting cases may not necessarily be appropriate when applied to the apportionment of seats among states. The courts already recognize that different rules govern redistricting in state legislatures than in 21 22 Schmeckebier, Congressional Apportionment, p. 60. Representatives per million is computed by dividing the number of Representatives assigned to the state by the state’s population (which gives the number of Representatives per person) and then multiplying the resulting dividend by 1,000,000. CRS-14 congressional districting. If the “one person, one vote” standard were ever to be applied to apportionment of seats among states–a process that differs significantly from redistricting within states–proportional difference measures might be accepted as most appropriate.23 If the choice between methods were judged to be a tossup with regard to which mathematical process is fairest, are there other representational goals that equal proportions meets which are perhaps appropriate to consider? One such goal might be the desirability of avoiding geographically large districts, if possible. After the 1990 apportionment, five of the seven states which had only one Representative (Alaska, Delaware, Montana, North Dakota, South Dakota, Vermont, and Wyoming) have relatively large land areas.24 The five Representatives of the larger states served 1.27% of the U.S. population, but also represented 27% of the U.S. land area. Arguably, an apportionment method that would potentially reduce the number of very large districts would serve to increase representation in those states. Very large districts limit the opportunities of constituents to see their Representatives, may require more district based offices, and may require toll calls for telephone contact with the Representatives’ district offices. Switching from equal proportions to major fractions may increase the number of states represented by only one Member of Congress. Although it is impossible to predict with any certainty, using Census Bureau projections for 202525 as an illustration, a major fractions apportionment would result in eight states represented by only one Member, while an equal proportions apportionment would result in six single-district states. 23 Montana argued in Federal court in 1991 and 1992 that the equal proportions formula violated the Constitution because it “does not achieve the greatest possible equality in number of individuals per Representative” Department of Commerce v. Montana 503 U.S. 442 (1992). Writing for a unanimous court, Justice Stevens however, noted that 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, “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.” 24 The total area of the U.S. is 3,618,770 square miles. The area and (rank) among all states in area for the seven single district states in this scenario are as follows: Alaska–591,004 (1), Delaware–2,045 (49), Montana–147,046 (4), North Dakota–70,762 (17), South Dakota–77,116 (16), Vermont–9,614 (43), Wyoming–97,809 (9). Source: U.S. Department of Commerce, Bureau of the Census, Statistical Abstract of the United States 1987, (Washington: GPO, 1987), Table 316: Area of States, p. 181. 25 U.S. Census Bureau, Projections of the Total Population of States: 1995-2025, Series A, http://www.census.gov/population/projections/stpjpop.txt, visited Aug. 11, 2000. CRS-15 The appendix which follows is the priority listing used in reapportionment following the 1990 Census. This listing shows where each state ranked in the priority of seat assignments. The priority values listed beyond seat number 435 show which states would have gained additional representations if the House size had been increased. CRS-16 Appendix: 1990 Priority List Seq. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 State Seat Priority CA 2 21,099,535.65 NY 2 12,759,391.63 CA 3 12,181,821.46 TX 2 12,063,103.59 FL 2 9,194,765.29 CA 4 8,613,849.35 PA 2 8,432,043.16 IL 2 8,108,168.46 OH 2 7,698,501.20 NY 3 7,366,637.51 TX 3 6,964,635.46 CA 5 6,672,258.17 MG 2 6,596,446.31 NJ 2 5,479,111.55 CA 6 5,447,875.79 FL 3 5,308,599.72 NY 4 5,208,999.81 TX 4 4,924,741.41 PA 3 4,868,241.93 NC 2 4,707,655.23 IL 3 4,681,252.81 CA 7 4,604,295.11 GA 2 4,602,147.13 OH 3 4,444,731.33 VA 2 4,395,777.31 MA 2 4,263,182.77 NY 5 4,034,873.39 CA 8 3,987,436.09 IN 2 3,934,503.28 TX 5 3,814,687.81 MG 3 3,808,459.70 FL 4 3,753,747.20 MO 2 3,632,975.98 CA 9 3,516,587.79 WS 2 3,469,592.60 TN 2 3,462,447.99 WA 2 3,456,296.16 PA 4 3,442,367.20 MD 2 3,393,138.09 IL 4 3,310,145.91 NY 6 3,294,460.21 NJ 3 3,163,366.23 CA 10 3,145,331.61 OH 4 3,142,899.95 TX 6 3,114,679.44 MN 2 3,102,097.90 LA 2 2,996,871.22 FL 5 2,907,639.71 AL 2 2,872,697.61 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 CA NY NC MG PA GA TX KY AZ CA IL VA SC MA OH NY CA FL CO CN TX IN NJ OK CA PA NY MO IL MG CA OR TX FL WS TN WA OH IO MD CA NC NY GA PA MS CA TX VA MN 11 7 3 4 5 3 7 2 2 12 5 3 2 3 5 8 13 6 2 2 8 3 4 2 14 6 9 3 6 5 15 2 9 7 3 3 3 6 2 3 16 4 10 4 7 2 17 10 4 3 2,845,059.46 2,784,326.89 2,717,965.76 2,692,987.92 2,666,445.82 2,657,050.63 2,632,384.41 2,615,566.01 2,600,728.09 2,597,172.96 2,564,027.67 2,537,902.98 2,478,909.15 2,461,349.49 2,434,479.52 2,411,297.55 2,389,051.45 2,374,077.80 2,339,046.96 2,330,389.85 2,279,711.53 2,271,586.31 2,236,837.92 2,232,763.16 2,211,830.60 2,177,143.82 2,126,564.37 2,097,499.46 2,093,519.75 2,085,979.21 2,059,102.28 2,017,893.92 2,010,516.41 2,006,461.82 2,003,170.03 1,999,045.09 1,995,493.33 1,987,744.13 1,971,006.37 1,959,029.01 1,926,114.17 1,921,892.20 1,902,056.92 1,878,818.69 1,840,022.25 1,828,891.35 1,809,270.25 1,798,260.48 1,794,568.57 1,790,996.89 CRS-17 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 IL KA MA FL NJ LA NY CA MG OH AR AL TX CA IN PA NY FL IL CA KY AZ NC TX MO CA GA OH NY MG SC WS NJ TN WA PA VA CA MD FL TX IL CO MA CN NY CA OK OH WV CA MN TX PA 7 2 4 8 5 3 11 18 6 7 2 3 11 19 4 8 12 9 8 20 3 3 5 12 4 21 5 8 13 7 3 4 6 4 4 9 5 22 4 10 13 9 3 5 3 14 23 3 9 2 24 4 14 10 1,769,347.01 1,757,584.58 1,740,437.07 1,737,646.72 1,732,646.98 1,730,244.24 1,720,475.20 1,705,796.31 1,703,194.83 1,679,950.30 1,670,355.18 1,658,552.58 1,626,587.79 1,613,521.84 1,606,254.23 1,593,505.83 1,570,572.33 1,532,460.23 1,532,299.29 1,530,721.18 1,510,097.60 1,501,530.92 1,488,691.10 1,484,865.21 1,483,156.23 1,456,006.30 1,455,326.51 1,454,879.48 1,444,716.30 1,439,462.27 1,431,198.73 1,416,455.24 1,414,700.28 1,413,538.47 1,411,027.00 1,405,339.93 1,390,066.66 1,388,247.47 1,385,242.82 1,370,674.05 1,365,877.22 1,351,360.84 1,350,449.27 1,348,136.59 1,345,451.08 1,337,546.63 1,326,516.39 1,289,086.29 1,283,082.99 1,273,941.23 1,270,042.73 1,266,426.16 1,264,555.87 1,256,974.20 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 MG NY IN FL LA UT CA NC IL NJ GA TX AL CA OR NY MO OH IO PA VA FL CA NB TX MA MG WS TN NY IL WA CA NM MD KY AZ MS CA FL OH PA NJ TX NY NC IN KA SC CA GA IL MG MN 8 15 5 11 4 2 25 6 10 7 6 15 4 26 3 16 5 10 3 11 6 12 27 2 16 6 9 5 5 17 11 5 28 2 5 4 4 3 29 13 11 12 8 17 18 7 6 3 4 30 7 12 10 5 1,246,610.75 1,245,188.18 1,244,199.02 1,239,821.31 1,223,467.55 1,221,727.76 1,218,182.21 1,215,511.15 1,208,693.83 1,195,639.89 1,188,269.08 1,177,237.47 1,172,773.89 1,170,391.58 1,165,031.49 1,164,767.10 1,148,847.73 1,147,624.27 1,137,960.95 1,136,975.93 1,134,984.63 1,131,797.21 1,126,209.87 1,120,493.40 1,101,205.03 1,100,748.87 1,099,407.25 1,097,181.37 1,094,922.05 1,094,108.80 1,093,304.69 1,092,976.67 1,085,243.01 1,076,060.23 1,073,004.34 1,067,800.35 1,061,742.79 1,055,910.81 1,047,152.30 1,041,101.93 1,038,065.20 1,037,912.62 1,035,454.40 1,034,402.59 1,031,535.64 1,027,294.36 1,015,884.21 1,014,741.83 1,012,010.42 1,011,645.28 1,004,270.60 998,046.41 983,339.70 980,969.36 CRS-18 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 CA NY TX AR FL VA CO PA CN LA OH CA MO MA NY TX CA IL NJ OK AL FL WS TN WA CA NC MG PA NY MD TX ME OH GA CA IN NV IL CA NY FL TX VA KY OR PA AZ CA NJ MG OH MA IO 31 19 18 3 14 7 4 13 4 5 12 32 6 7 20 19 33 13 9 4 5 15 6 6 6 34 8 11 14 21 6 20 2 13 8 35 7 2 14 36 22 16 21 8 5 4 15 5 37 10 12 14 8 4 978,467.51 975,735.07 975,244.09 964,379.92 963,872.55 959,237.03 954,911.92 954,740.67 951,377.67 947,693.77 947,619.86 947,397.10 938,030.21 930,302.53 925,663.55 922,488.60 918,239.42 918,069.09 913,184.87 911,521.74 908,426.63 897,316.53 895,844.81 894,000.08 892,411.68 890,823.07 889,662.91 889,464.22 883,917.61 880,481.68 876,104.34 875,149.50 872,020.33 871,683.42 869,723.76 864,996.63 858,578.81 852,878.24 849,966.34 840,625.60 839,506.30 839,362.91 832,433.24 830,723.54 827,114.49 823,801.74 822,882.53 822,422.32 817,590.39 816,777.34 811,966.30 807,021.57 805,665.54 804,659.98 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 NY MN CA TX MO IL HA FL NH NC SC CA LA PA NY GA TX WS TN CA WA OH MG MS IN FL AL MD IL CO NJ CN CA NY WV VA TX PA CA KA ID RI MA NY OK UT FL OH CA NC TX IL MG MO 23 6 38 22 7 15 2 17 2 9 5 39 6 16 24 9 23 7 7 40 7 15 13 4 8 18 6 7 16 5 11 5 41 25 3 9 24 17 42 4 2 2 9 26 5 3 19 16 43 10 25 17 14 8 802,176.05 800,958.10 795,784.05 793,693.91 792,780.17 791,275.62 788,617.79 788,444.61 787,656.83 784,608.87 783,899.80 775,110.76 773,788.69 769,736.26 768,025.08 767,024.19 758,400.80 757,127.00 755,567.92 755,484.48 754,225.48 751,296.22 746,900.30 746,641.76 743,550.98 743,352.69 741,727.21 740,443.26 740,170.70 739,671.50 738,802.90 736,933.88 736,827.74 736,663.79 735,510.24 732,629.24 726,113.47 723,041.73 719,070.17 717,530.90 715,582.15 711,338.09 710,530.16 707,763.66 706,061.61 705,364.78 703,141.28 702,773.39 702,148.53 701,775.48 696,463.58 695,269.70 691,494.92 686,567.69 CRS-19 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 GA CA AR PA NY MN KY NJ AZ CA TX FL OH NY CA IN WS IL VA TN LA WA NB PA TX MG CA MD SC OR MA NC FL NY CA AL IO OH NM GA TX NJ IL CA NY PA MO FL CO CA MG CN TX VA 10 44 4 18 27 7 6 12 6 45 26 20 17 28 46 9 8 18 10 8 7 8 3 19 27 15 47 8 6 5 10 11 21 29 48 7 5 18 3 11 28 13 19 49 30 20 9 22 6 50 16 6 29 11 686,047.27 686,005.00 681,919.64 681,690.26 681,045.92 676,933.10 675,336.13 674,431.92 671,504.99 670,587.24 669,140.55 667,058.37 660,141.03 656,272.29 655,847.22 655,750.27 655,691.14 655,506.55 655,283.49 654,340.94 653,970.76 653,178.36 646,917.11 644,814.46 643,880.82 643,746.75 641,741.37 641,242.61 640,051.48 638,114.00 635,517.47 634,779.80 634,499.09 633,237.93 628,229.44 626,873.87 623,286.86 622,386.91 621,263.60 620,553.10 620,459.09 620,387.08 620,047.14 615,274.87 611,765.99 611,724.70 605,495.74 604,971.11 603,939.23 602,843.86 602,170.06 601,703.97 598,681.74 592,726.21 420 NY 31 591,702.60 421 CA 51 590,905.18 422 OH 19 588,719.10 423 IL 20 588,228.36 424 IN 10 586,520.84 425 MN 8 586,241.20 426 PA 21 581,866.26 427 NC 12 579,472.22 428 CA 52 579,430.15 429 TX 30 578,381.53 430 MS 5 578,346.15 431 WS 9 578,265.19 432 FL 23 578,069.92 433 TN 9 577,074.42 434 OK 6 576,496.87 435 WA 9 576,049.11 Last seat assigned by law 436 MA 11 574,847.17 437 NJ 14 574,366.50 438 NY 32 572,913.58 439 KY 7 570,763.16 440 CA 53 568,392.42 441 MT 2 568,269.89 442 AZ 7 567,525.26 443 GA 12 566,485.07 444 LA 8 566,355.23 445 MG 17 565,640.60 446 MD 9 565,522.77 447 IL 21 559,516.78 448 TX 31 559,413.02 449 OH 20 558,507.97 450 CA 54 557,767.31 451 KA 5 555,796.97 452 NY 33 555,281.24 453 PA 22 554,787.68 454 FL 24 553,459.80 455 CA 55 547,532.16 456 AL 8 542,888.63 457 TX 32 541,649.33 458 MO 10 541,571.83 459 VA 12 541,082.71 460 SC 7 540,942.20 461 NY 34 538,701.92 462 CA 56 537,665.94 463 NJ 15 534,706.13 464 IL 22 533,478.29 465 MG 18 533,291.06 466 NC 13 533,036.87 467 OH 21 531,247.06 468 FL 25 530,860.00 469 IN 11 530,528.06 470 PA 23 530,117.99 471 AR 5 528,212.62 472 CA 57 528,148.99 CRS-20 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 TX MA NY GA OR WV CA WS MN TN WA CO CA FL IL TX IO CN NY PA OH MD MG ME CA NJ LA UT 33 12 35 13 6 4 58 10 9 10 10 7 59 26 23 34 6 7 36 24 22 10 19 3 60 16 9 4 524,979.20 524,761.45 523,084.05 521,090.43 521,017.88 520,084.33 518,963.07 517,216.08 517,016.09 516,151.03 515,233.97 510,421.77 510,091.18 510,033.77 509,756.16 509,304.61 508,911.57 508,532.64 508,346.32 507,549.32 506,524.17 505,818.92 504,442.86 503,461.12 501,517.64 500,171.88 499,478.32 498,768.26