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Order Code RL30711
CRS Report for Congress
Received through the CRS Web
The House Apportionment Formula
in Theory and Practice
October 10, 2000
Royce Crocker
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 . . . . . . . . . . . 6
Table 2. Calculating Priority Values for a Hypothetical Three
State House of 30 Seats Using the Method of Equal Proportions . . . . . . . . . 6
Table 3. Priority Rankings for Assigning Thirty Seats
in a Hypothetical Three-State House Delegation . . . . . . . . . . . . . . . . . . . . . . 7
Table 4. Rounding Points for Assigning Seats
Using the Equal Proportions Method of Apportionment* . . . . . . . . . . . . . . . 9
The House Apportionment Formula in
Theory and Practice1
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.2
1
This report originally was authored by David C. Huckabee, who has retired from CRS.
2
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.
(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.3 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.4
2
(...continued)
Subsequently, mathematician W.F. Willcox proposed the "major fractions" method, which
was used 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. 91-1314 (Washington: GPO, 1970), Appendix B, pp. 15-18.
3
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.
4
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.5
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.6
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 population7 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
4
(...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.
5
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.
6
Ibid., Sec. 22 (b).
7
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.8 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 573,6439 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
8
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.
9
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.10
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.11
The traditional method of constructing a priority list to apportion seats by the
equal proportions method involves first computing the reciprocals12 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.
10
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.
11
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.
12
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 Size of Size of
delegation Multiplier* delegation Multiplier* delegation Multiplier*
1 Constitution 21 0.04879500 41 0.02469324
2 0.70710678 22 0.04652421 42 0.02409813
3 0.40824829 23 0.04445542 43 0.02353104
4 0.28867513 24 0.04256283 44 0.02299002
5 0.22360680 25 0.04082483 45 0.02247333
6 0.18257419 26 0.03922323 46 0.02197935
7 0.15430335 27 0.03774257 47 0.02150662
8 0.13363062 28 0.03636965 48 0.02105380
9 0.11785113 29 0.03509312 49 0.02061965
10 0.10540926 30 0.03390318 50 0.02020305
11 0.09534626 31 0.03279129 51 0.01980295
12 0.08703883 32 0.03175003 52 0.01941839
13 0.08006408 33 0.03077287 53 0.01904848
14 0.07412493 34 0.02985407 54 0.01869241
15 0.06900656 35 0.02898855 55 0.01834940
16 0.06454972 36 0.02817181 56 0.01801875
17 0.06063391 37 0.02739983 57 0.01769981
18 0.05716620 38 0.02666904 58 0.01739196
19 0.05407381 39 0.02597622 59 0.01709464
20 0.05129892 40 0.02531848 60 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's priority value claim to a delegation size
Calculation
State Size of delegation
Multiplier (M) Population (P) Priority value (PxM)
CA 2 0.70710678 29,839,250 21,099,536.02
CA 3 0.40824829 29,839,250 12,181,822.80
CA 4 0.28867513 29,839,250 8,613,849.51
CA 5 0.22360680 29,839,250 6,672,259.14
CA 6 0.18257419 29,839,250 5,447,876.77
CA 7 0.15430335 29,839,250 4,604,296.24
CA 8 0.13363062 29,839,250 3,987,437.51
CA 9 0.11785113 29,839,250 3,516,589.34
CA 10 0.10540926 29,839,250 3,145,333.12
CA 11 0.09534626 29,839,250 2,845,060.86
CA 12 0.08703883 29,839,250 2,597,173.35
CA 13 0.08006408 29,839,250 2,389,052.01
CA 14 0.07412493 29,839,250 2,211,832.37
CA 15 0.06900656 29,839,250 2,059,103.87
CA 16 0.06454972 29,839,250 1,926,115.31
CA 17 0.06063391 29,839,250 1,809,270.29
CA 18 0.05716620 29,839,250 1,705,796.39
NY 2 0.70710678 18,044,505 12,759,391.85
NY 3 0.40824829 18,044,505 7,366,638.32
NY 4 0.28867513 18,044,505 5,208,999.91
NY 5 0.22360680 18,044,505 4,034,873.98
NY 6 0.18257419 18,044,505 3,294,460.81
NY 7 0.15430335 18,044,505 2,784,327.57
CRS-7
State's priority value claim to a delegation size
Calculation
State Size of delegation
Multiplier (M) Population (P) Priority value (PxM)
NY 8 0.13363062 18,044,505 2,411,298.41
NY 9 0.11785113 18,044,505 2,126,565.31
NY 10 0.10540926 18,044,505 1,902,057.84
NY 11 0.09534626 18,044,505 1,720,476.05
NY 12 0.08703883 18,044,505 1,570,572.57
FL 2 0.70710678 13,003,362 9,194,765.45
FL 3 0.40824829 13,003,362 5,308,600.31
FL 4 0.28867513 13,003,362 3,753,747.28
FL 5 0.22360680 13,003,362 2,907,640.14
FL 6 0.18257419 13,003,362 2,374,078.23
FL 7 0.15430335 13,003,362 2,006,462.32
FL 8 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
State's priority value claim to a delegation size
House Size of Calculation
size State delegation Multiplier (M) Population (P) Priority value (PxM)
4 CA 2 0.70710678 29,839,250 21,099,536.02
5 NY 2 0.70710678 18,044,505 12,759,391.85
6 CA 3 0.40824829 29,839,250 12,181,822.80
7 FL 2 0.70710678 13,003,362 9,194,765.45
8 CA 4 0.28867513 29,839,250 8,613,849.51
9 NY 3 0.40824829 18,044,505 7,366,638.32
10 CA 5 0.22360680 29,839,250 6,672,259.14
11 CA 6 0.18257419 29,839,250 5,447,876.77
12 FL 3 0.40824829 13,003,362 5,308,600.31
13 NY 4 0.28867513 18,044,505 5,208,999.91
14 CA 7 0.15430335 29,839,250 4,604,296.24
15 NY 5 0.22360680 18,044,505 4,034,873.98
16 CA 8 0.13363062 29,839,250 3,987,437.51
17 FL 4 0.28867513 13,003,362 3,753,747.28
18 CA 9 0.11785113 29,839,250 3,516,589.34
19 NY 6 0.18257419 18,044,505 3,294,460.81
20 CA 10 0.10540926 29,839,250 3,145,333.12
21 FL 5 0.22360680 13,003,362 2,907,640.14
22 CA 11 0.09534626 29,839,250 2,845,060.86
23 NY 7 0.15430335 18,044,505 2,784,327.57
24 CA 12 0.08703883 29,839,250 2,597,173.35
25 NY 8 0.13363062 18,044,505 2,411,298.41
26 CA 13 0.08006408 29,839,250 2,389,052.01
27 FL 6 0.18257419 13,003,362 2,374,078.23
28 CA 14 0.07412493 29,839,250 2,211,832.37
29 NY 9 0.11785113 18,044,505 2,126,565.31
30 CA 15 0.06900656 29,839,250 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."13 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".14
13
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.
14
"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 Round Size of Round Size of Round Size of Round
delegation up at delegation up at delegation up at delegation up at
1 16 31 46
1.41421 16.49242 31.49603 46.49731
2 17 32 47
2.44949 17.49286 32.49615 47.49737
3 18 33 48
3.46410 18.49324 33.49627 48.49742
4 19 34 49
4.47214 19.49359 34.49638 49.49747
5 20 35 50
5.47723 20.49390 35.49648 50.49752
6 21 36 51
6.48074 21.49419 36.49658 51.49757
7 22 37 52
7.48331 22.49444 37.49667 52.49762
8 23 38 53
8.48528 23.49468 38.49675 53.49766
9 24 39 54
9.48683 24.49490 39.49684 54.49771
10 25 40 55
10.48809 25.49510 40.49691 55.49775
11 26 41 56
11.48913 26.49528 41.49699 56.49779
12 27 42 57
12.49000 27.49545 42.49706 57.49783
13 28 43 58
13.49074 28.49561 43.49713 58.49786
14 29 44 59
14.49138 29.49576 44.49719 59.49790
15 30 45 60
15.49193 30.49590 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 1981.15 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
15
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.16
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
value17 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
16
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.
17
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).18
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).19 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.
18
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).
19
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.20
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."21
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:
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
20
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.
21
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
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.22
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.23 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
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
22
Schmeckebier, Congressional Apportionment, p. 60.
23
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
from redistricting within states -- proportional difference measures might be
accepted as most appropriate.24
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.25 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 202526 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.
24
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."
25
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.
26
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. State Seat Priority 100 CA 11 2,845,059.46
51 CA 2 21,099,535.65 101 NY 7 2,784,326.89
52 NY 2 12,759,391.63 102 NC 3 2,717,965.76
53 CA 3 12,181,821.46 103 MG 4 2,692,987.92
54 TX 2 12,063,103.59 104 PA 5 2,666,445.82
55 FL 2 9,194,765.29 105 GA 3 2,657,050.63
56 CA 4 8,613,849.35 106 TX 7 2,632,384.41
57 PA 2 8,432,043.16 107 KY 2 2,615,566.01
58 IL 2 8,108,168.46 108 AZ 2 2,600,728.09
59 OH 2 7,698,501.20 109 CA 12 2,597,172.96
60 NY 3 7,366,637.51 110 IL 5 2,564,027.67
61 TX 3 6,964,635.46 111 VA 3 2,537,902.98
62 CA 5 6,672,258.17 112 SC 2 2,478,909.15
63 MG 2 6,596,446.31 113 MA 3 2,461,349.49
64 NJ 2 5,479,111.55 114 OH 5 2,434,479.52
65 CA 6 5,447,875.79 115 NY 8 2,411,297.55
66 FL 3 5,308,599.72 116 CA 13 2,389,051.45
67 NY 4 5,208,999.81 117 FL 6 2,374,077.80
68 TX 4 4,924,741.41 118 CO 2 2,339,046.96
69 PA 3 4,868,241.93 119 CN 2 2,330,389.85
70 NC 2 4,707,655.23 120 TX 8 2,279,711.53
71 IL 3 4,681,252.81 121 IN 3 2,271,586.31
72 CA 7 4,604,295.11 122 NJ 4 2,236,837.92
73 GA 2 4,602,147.13 123 OK 2 2,232,763.16
74 OH 3 4,444,731.33 124 CA 14 2,211,830.60
75 VA 2 4,395,777.31 125 PA 6 2,177,143.82
76 MA 2 4,263,182.77 126 NY 9 2,126,564.37
77 NY 5 4,034,873.39 127 MO 3 2,097,499.46
78 CA 8 3,987,436.09 128 IL 6 2,093,519.75
79 IN 2 3,934,503.28 129 MG 5 2,085,979.21
80 TX 5 3,814,687.81 130 CA 15 2,059,102.28
81 MG 3 3,808,459.70 131 OR 2 2,017,893.92
82 FL 4 3,753,747.20 132 TX 9 2,010,516.41
83 MO 2 3,632,975.98 133 FL 7 2,006,461.82
84 CA 9 3,516,587.79 134 WS 3 2,003,170.03
85 WS 2 3,469,592.60 135 TN 3 1,999,045.09
86 TN 2 3,462,447.99 136 WA 3 1,995,493.33
87 WA 2 3,456,296.16 137 OH 6 1,987,744.13
88 PA 4 3,442,367.20 138 IO 2 1,971,006.37
89 MD 2 3,393,138.09 139 MD 3 1,959,029.01
90 IL 4 3,310,145.91 140 CA 16 1,926,114.17
91 NY 6 3,294,460.21 141 NC 4 1,921,892.20
92 NJ 3 3,163,366.23 142 NY 10 1,902,056.92
93 CA 10 3,145,331.61 143 GA 4 1,878,818.69
94 OH 4 3,142,899.95 144 PA 7 1,840,022.25
95 TX 6 3,114,679.44 145 MS 2 1,828,891.35
96 MN 2 3,102,097.90 146 CA 17 1,809,270.25
97 LA 2 2,996,871.22 147 TX 10 1,798,260.48
98 FL 5 2,907,639.71 148 VA 4 1,794,568.57
99 AL 2 2,872,697.61 149 MN 3 1,790,996.89
CRS-17
150 IL 7 1,769,347.01 204 MG 8 1,246,610.75
151 KA 2 1,757,584.58 205 NY 15 1,245,188.18
152 MA 4 1,740,437.07 206 IN 5 1,244,199.02
153 FL 8 1,737,646.72 207 FL 11 1,239,821.31
154 NJ 5 1,732,646.98 208 LA 4 1,223,467.55
155 LA 3 1,730,244.24 209 UT 2 1,221,727.76
156 NY 11 1,720,475.20 210 CA 25 1,218,182.21
157 CA 18 1,705,796.31 211 NC 6 1,215,511.15
158 MG 6 1,703,194.83 212 IL 10 1,208,693.83
159 OH 7 1,679,950.30 213 NJ 7 1,195,639.89
160 AR 2 1,670,355.18 214 GA 6 1,188,269.08
161 AL 3 1,658,552.58 215 TX 15 1,177,237.47
162 TX 11 1,626,587.79 216 AL 4 1,172,773.89
163 CA 19 1,613,521.84 217 CA 26 1,170,391.58
164 IN 4 1,606,254.23 218 OR 3 1,165,031.49
165 PA 8 1,593,505.83 219 NY 16 1,164,767.10
166 NY 12 1,570,572.33 220 MO 5 1,148,847.73
167 FL 9 1,532,460.23 221 OH 10 1,147,624.27
168 IL 8 1,532,299.29 222 IO 3 1,137,960.95
169 CA 20 1,530,721.18 223 PA 11 1,136,975.93
170 KY 3 1,510,097.60 224 VA 6 1,134,984.63
171 AZ 3 1,501,530.92 225 FL 12 1,131,797.21
172 NC 5 1,488,691.10 226 CA 27 1,126,209.87
173 TX 12 1,484,865.21 227 NB 2 1,120,493.40
174 MO 4 1,483,156.23 228 TX 16 1,101,205.03
175 CA 21 1,456,006.30 229 MA 6 1,100,748.87
176 GA 5 1,455,326.51 230 MG 9 1,099,407.25
177 OH 8 1,454,879.48 231 WS 5 1,097,181.37
178 NY 13 1,444,716.30 232 TN 5 1,094,922.05
179 MG 7 1,439,462.27 233 NY 17 1,094,108.80
180 SC 3 1,431,198.73 234 IL 11 1,093,304.69
181 WS 4 1,416,455.24 235 WA 5 1,092,976.67
182 NJ 6 1,414,700.28 236 CA 28 1,085,243.01
183 TN 4 1,413,538.47 237 NM 2 1,076,060.23
184 WA 4 1,411,027.00 238 MD 5 1,073,004.34
185 PA 9 1,405,339.93 239 KY 4 1,067,800.35
186 VA 5 1,390,066.66 240 AZ 4 1,061,742.79
187 CA 22 1,388,247.47 241 MS 3 1,055,910.81
188 MD 4 1,385,242.82 242 CA 29 1,047,152.30
189 FL 10 1,370,674.05 243 FL 13 1,041,101.93
190 TX 13 1,365,877.22 244 OH 11 1,038,065.20
191 IL 9 1,351,360.84 245 PA 12 1,037,912.62
192 CO 3 1,350,449.27 246 NJ 8 1,035,454.40
193 MA 5 1,348,136.59 247 TX 17 1,034,402.59
194 CN 3 1,345,451.08 248 NY 18 1,031,535.64
195 NY 14 1,337,546.63 249 NC 7 1,027,294.36
196 CA 23 1,326,516.39 250 IN 6 1,015,884.21
197 OK 3 1,289,086.29 251 KA 3 1,014,741.83
198 OH 9 1,283,082.99 252 SC 4 1,012,010.42
199 WV 2 1,273,941.23 253 CA 30 1,011,645.28
200 CA 24 1,270,042.73 254 GA 7 1,004,270.60
201 MN 4 1,266,426.16 255 IL 12 998,046.41
202 TX 14 1,264,555.87 256 MG 10 983,339.70
203 PA 10 1,256,974.20 257 MN 5 980,969.36
CRS-18
258 CA 31 978,467.51 312 NY 23 802,176.05
259 NY 19 975,735.07 313 MN 6 800,958.10
260 TX 18 975,244.09 314 CA 38 795,784.05
261 AR 3 964,379.92 315 TX 22 793,693.91
262 FL 14 963,872.55 316 MO 7 792,780.17
263 VA 7 959,237.03 317 IL 15 791,275.62
264 CO 4 954,911.92 318 HA 2 788,617.79
265 PA 13 954,740.67 319 FL 17 788,444.61
266 CN 4 951,377.67 320 NH 2 787,656.83
267 LA 5 947,693.77 321 NC 9 784,608.87
268 OH 12 947,619.86 322 SC 5 783,899.80
269 CA 32 947,397.10 323 CA 39 775,110.76
270 MO 6 938,030.21 324 LA 6 773,788.69
271 MA 7 930,302.53 325 PA 16 769,736.26
272 NY 20 925,663.55 326 NY 24 768,025.08
273 TX 19 922,488.60 327 GA 9 767,024.19
274 CA 33 918,239.42 328 TX 23 758,400.80
275 IL 13 918,069.09 329 WS 7 757,127.00
276 NJ 9 913,184.87 330 TN 7 755,567.92
277 OK 4 911,521.74 331 CA 40 755,484.48
278 AL 5 908,426.63 332 WA 7 754,225.48
279 FL 15 897,316.53 333 OH 15 751,296.22
280 WS 6 895,844.81 334 MG 13 746,900.30
281 TN 6 894,000.08 335 MS 4 746,641.76
282 WA 6 892,411.68 336 IN 8 743,550.98
283 CA 34 890,823.07 337 FL 18 743,352.69
284 NC 8 889,662.91 338 AL 6 741,727.21
285 MG 11 889,464.22 339 MD 7 740,443.26
286 PA 14 883,917.61 340 IL 16 740,170.70
287 NY 21 880,481.68 341 CO 5 739,671.50
288 MD 6 876,104.34 342 NJ 11 738,802.90
289 TX 20 875,149.50 343 CN 5 736,933.88
290 ME 2 872,020.33 344 CA 41 736,827.74
291 OH 13 871,683.42 345 NY 25 736,663.79
292 GA 8 869,723.76 346 WV 3 735,510.24
293 CA 35 864,996.63 347 VA 9 732,629.24
294 IN 7 858,578.81 348 TX 24 726,113.47
295 NV 2 852,878.24 349 PA 17 723,041.73
296 IL 14 849,966.34 350 CA 42 719,070.17
297 CA 36 840,625.60 351 KA 4 717,530.90
298 NY 22 839,506.30 352 ID 2 715,582.15
299 FL 16 839,362.91 353 RI 2 711,338.09
300 TX 21 832,433.24 354 MA 9 710,530.16
301 VA 8 830,723.54 355 NY 26 707,763.66
302 KY 5 827,114.49 356 OK 5 706,061.61
303 OR 4 823,801.74 357 UT 3 705,364.78
304 PA 15 822,882.53 358 FL 19 703,141.28
305 AZ 5 822,422.32 359 OH 16 702,773.39
306 CA 37 817,590.39 360 CA 43 702,148.53
307 NJ 10 816,777.34 361 NC 10 701,775.48
308 MG 12 811,966.30 362 TX 25 696,463.58
309 OH 14 807,021.57 363 IL 17 695,269.70
310 MA 8 805,665.54 364 MG 14 691,494.92
311 IO 4 804,659.98 365 MO 8 686,567.69
CRS-19
366 GA 10 686,047.27 420 NY 31 591,702.60
367 CA 44 686,005.00 421 CA 51 590,905.18
368 AR 4 681,919.64 422 OH 19 588,719.10
369 PA 18 681,690.26 423 IL 20 588,228.36
370 NY 27 681,045.92 424 IN 10 586,520.84
371 MN 7 676,933.10 425 MN 8 586,241.20
372 KY 6 675,336.13 426 PA 21 581,866.26
373 NJ 12 674,431.92 427 NC 12 579,472.22
374 AZ 6 671,504.99 428 CA 52 579,430.15
375 CA 45 670,587.24 429 TX 30 578,381.53
376 TX 26 669,140.55 430 MS 5 578,346.15
377 FL 20 667,058.37 431 WS 9 578,265.19
378 OH 17 660,141.03 432 FL 23 578,069.92
379 NY 28 656,272.29 433 TN 9 577,074.42
380 CA 46 655,847.22 434 OK 6 576,496.87
381 IN 9 655,750.27 435 WA 9 576,049.11
382 WS 8 655,691.14 Last seat assigned by law
383 IL 18 655,506.55 436 MA 11 574,847.17
384 VA 10 655,283.49 437 NJ 14 574,366.50
385 TN 8 654,340.94 438 NY 32 572,913.58
386 LA 7 653,970.76 439 KY 7 570,763.16
387 WA 8 653,178.36 440 CA 53 568,392.42
388 NB 3 646,917.11 441 MT 2 568,269.89
389 PA 19 644,814.46 442 AZ 7 567,525.26
390 TX 27 643,880.82 443 GA 12 566,485.07
391 MG 15 643,746.75 444 LA 8 566,355.23
392 CA 47 641,741.37 445 MG 17 565,640.60
393 MD 8 641,242.61 446 MD 9 565,522.77
394 SC 6 640,051.48 447 IL 21 559,516.78
395 OR 5 638,114.00 448 TX 31 559,413.02
396 MA 10 635,517.47 449 OH 20 558,507.97
397 NC 11 634,779.80 450 CA 54 557,767.31
398 FL 21 634,499.09 451 KA 5 555,796.97
399 NY 29 633,237.93 452 NY 33 555,281.24
400 CA 48 628,229.44 453 PA 22 554,787.68
401 AL 7 626,873.87 454 FL 24 553,459.80
402 IO 5 623,286.86 455 CA 55 547,532.16
403 OH 18 622,386.91 456 AL 8 542,888.63
404 NM 3 621,263.60 457 TX 32 541,649.33
405 GA 11 620,553.10 458 MO 10 541,571.83
406 TX 28 620,459.09 459 VA 12 541,082.71
407 NJ 13 620,387.08 460 SC 7 540,942.20
408 IL 19 620,047.14 461 NY 34 538,701.92
409 CA 49 615,274.87 462 CA 56 537,665.94
410 NY 30 611,765.99 463 NJ 15 534,706.13
411 PA 20 611,724.70 464 IL 22 533,478.29
412 MO 9 605,495.74 465 MG 18 533,291.06
413 FL 22 604,971.11 466 NC 13 533,036.87
414 CO 6 603,939.23 467 OH 21 531,247.06
415 CA 50 602,843.86 468 FL 25 530,860.00
416 MG 16 602,170.06 469 IN 11 530,528.06
417 CN 6 601,703.97 470 PA 23 530,117.99
418 TX 29 598,681.74 471 AR 5 528,212.62
419 VA 11 592,726.21 472 CA 57 528,148.99
CRS-20
473 TX 33 524,979.20
474 MA 12 524,761.45
475 NY 35 523,084.05
476 GA 13 521,090.43
477 OR 6 521,017.88
478 WV 4 520,084.33
479 CA 58 518,963.07
480 WS 10 517,216.08
481 MN 9 517,016.09
482 TN 10 516,151.03
483 WA 10 515,233.97
484 CO 7 510,421.77
485 CA 59 510,091.18
486 FL 26 510,033.77
487 IL 23 509,756.16
488 TX 34 509,304.61
489 IO 6 508,911.57
490 CN 7 508,532.64
491 NY 36 508,346.32
492 PA 24 507,549.32
493 OH 22 506,524.17
494 MD 10 505,818.92
495 MG 19 504,442.86
496 ME 3 503,461.12
497 CA 60 501,517.64
498 NJ 16 500,171.88
499 LA 9 499,478.32
500 UT 4 498,768.26
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For other versions of this document, see http://wikileaks.org/wiki/CRS-RL30711