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NOTICE: This opinion is subject to formal revision before publication in the
preliminary print of the United States Reports.  Readers are requested to
notify the Reporter of Decisions, Supreme Court of the United States, Wash-
ington, D.C. 20543, of any typographical or other formal errors, in order that
corrections may be made before the preliminary print goes to press.
SUPREME COURT OF THE UNITED STATES
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No. 91-860
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UNITED STATES DEPARTMENT OF COMMERCE,
et al., APPELLANTS v. MONTANA et al.
on appeal from the united states district court for
the district of montana
[March 31, 1992]

  Justice Stevens delivered the opinion of the Court.
  Article I, 2, of the Constitution requires apportionment
of Representatives among the several States ``according to
their respective Numbers.''  An Act of Congress passed in
1941 provides that after each decennial census ``the method
known as the method of equal proportions'' shall be used to
determine the number of Representatives to which each
State is entitled.  In this case a three-judge District Court
held that statute unconstitutional because it found that the
method of equal proportions resulted in an unjustified
deviation from the ideal of equal representation.  The
Government's appeal from that holding requires us to
consider the standard that governs the apportionment of
Representatives among the several States.  In view of the
importance of the issue and its significance in this year's
congressional and Presidential elections, we noted probable
jurisdiction and ordered expedited briefing and argument.
502 U. S. ___ (1991).  We now reverse.

                            I
  The 1990 census revealed that the population of certain
States, particularly California, Florida, and Texas, had
increased more rapidly than the national average.  The
application of the method of equal proportions to the 1990
census caused 8 States to gain a total of 19 additional seats
in the House of Representatives and 13 States to lose an
equal number.  Montana was one of those States.  Its loss
of one seat cut its delegation in half and precipitated this
litigation.
  According to the 1990 census, the population of the 50
States that elect the members of the House of Representa-
tives is 249,022,783.  The average size of the 435 congres-
sional districts is 572,466.  Montana's population of 803,655
forms a single congressional district that is 231,189 persons
larger than the ideal congressional district.  If it had
retained its two districts, each would have been 170,638
persons smaller than the ideal district.  In terms of absolute
difference, each of the two districts would have been closer
to ideal size than the single congressional district.
  The State of Montana, its Governor, Attorney General,
and Secretary of State, and the State's two Senators and
Representatives (hereinafter collectively referred to as
Montana) filed suit against appropriate federal defendants
(the Government) in the United States District Court for
the District of Montana, asserting that Montana was
entitled to retain its two seats.  They alleged that the
existing apportionment method violates Article I, 2, of the
Constitution because it ``does not achieve the greatest
possible equality in the number of individuals per represen-
tative'' and also violates Article I, 2, and Article I, 7,
because reapportionment is effected ``through application of
a mathematical formula by the Department of Commerce
and the automatic transmittal of the results to the states''
rather than by legislation on which Members of Congress
vote in the normal manner.  A three-judge District Court,
convened pursuant to 28 U. S. C. 2284, granted Montana's
motion for summary judgment on the first claim.
  The majority of the three-judge District Court decided
that the principle of equal representation for equal numbers
of people that was applied to intrastate districting in
Wesberry v. Sanders, 376 U. S. 1 (1964), should also be
applied to the apportionment of seats among the States.
Under that standard the only population variances that are
acceptable are those that ``are unavoidable despite a good-
faith effort to achieve absolute equality, or for which
justification is shown,'' Kirkpatrick v. Preisler, 394 U. S.
526, 531 (1969).  The District Court held that the variance
between the population of Montana's single district and the
ideal district could not be justified under that standard.
The majority refused to accord deference to the congres-
sional decision to adopt the method of equal proportions in
1941 because that decision was made without the benefit of
this Court's later jurisprudence adopting the ``one-person,
one-vote'' rule.  Accordingly, the District Court entered a
judgment declaring the statute void and enjoining the
Government from effecting any reapportionment of the
House of Representatives pursuant to the method of equal
proportions.
  Circuit Judge O'Scannlain dissented.  After noting that
Congress has used four different apportionment formulas
during the country's history, and that it is not possible to
create 435 districts of equal size when each district must be
located entirely within a single State, he concluded that the
goal of any apportionment formula must be a ```practical
approximation''' to a population-based allocation.  He
analyzed the two formulae proposed by Montana and
concluded that the State had failed to demonstrate that
either was better than the one that had been chosen by
Congress.

                           II
  The general admonition in Article I, 2, that Representa-
tives shall be apportioned among the several States
``according to their respective Numbers'' is constrained by
three requirements.  The number of Representatives shall
not exceed one for every 30,000 persons; each State shall
have at least one Representative; and district boundaries
may not cross state lines.  Although the text of Article I
determined the original apportionment that the Framers
had agreed upon, it did not explain how that specific
allocation had been made.
  When Congress first confronted the task of apportionment
after the census of 1790 (and after Vermont and Kentucky
had been admitted to the Union), it considered using the
constitutional minimum of 30,000 persons as the size of
each district.  Dividing that number into the total popula-
tion of 3,615,920 indicated that the House of Representa-
tives should contain 120 members.  When that number was
divided into the population of individual States, each
quotient was a whole number with a fractional remainder.
Thus, the use of the 30,000 divisor for Connecticut's
population of 236,841 indicated that it should have 7.89
Representatives, while Rhode Island, with a population of
68,446, should have 2.28 Representatives.  Because each
State must be represented by a whole number of legislators,
it was necessary either to disregard fractional remainders
entirely or to treat some or all of them as equal to a whole
Representative.
  In the first apportionment bill passed by Congress, an
additional Representative was assigned to the nine States
whose quotas had the highest fractional remainders.  Thus,
Connecticut's quota of 7.89 gave it 8 and Rhode Island's
smaller remainder was disregarded, giving it only 2.
Although that method was supported by Alexander Hamil-
ton, Thomas Jefferson persuaded President Washington to
veto the bill, in part because its allocation of eight Repre-
sentatives to Connecticut exceeded the constitutional limit
of one for every 30,000 persons.
  In response to that veto, Congress adopted a proposal
sponsored by Thomas Jefferson that disregarded fractional
remainders entirely (thus giving Connecticut only 7 Repre-
sentatives).  To overcome the basis for the veto, the size of
the House was reduced from 120 to 105 members, giving
each Representative an approximate constituency of 33,000
instead of 30,000 persons.  Although both the total number
of Representatives and the size of their districts
increased, Jefferson's method of disregarding fractional
remainders was used after each of the next four censuses.
Today mathematicians sometimes refer to that method as
the ``method of greatest divisors,'' and suggest that it tends
to favor large States over smaller States.
  In 1832, Congress considered, but did not adopt, a
proposal sponsored by John Quincy Adams that was the
exact opposite of the Jefferson method.  Instead of disre-
garding fractional remainders, Adams would have treated
every fraction as a unit.  Thus, using the former example as
a hypothetical, both Connecticut and Rhode Island would
have received one more Representative under the Adams
method than they actually received under the Jefferson
method.  The Adams method is sometimes described as the
``method of smallest divisors'' and is said to favor the
smaller States.  It has never been endorsed by Congress.
  In 1842, Congress abandoned the Jefferson method in
favor of an approach supported by Senator Daniel Webster.
The Webster method took account of fractional remainders
that were greater than one-half by allocating ``one addition-
al representative for each State having a fraction greater
than one moiety.''  Thus, if that method had been used
in 1790, Connecticut's quota of 7.89 would have entitled it
to 8 Representatives, whereas Rhode Island, with a quota
of 2.28, would have received only 2.  The Webster method
is also described as the ``method of major fractions.''
  In 1850, Congress enacted legislation sponsored by
Representative Vinton endorsing the approach that had
been sponsored by Alexander Hamilton after the first
census.  Although this method was used during the
balance of the 19th century, it occasionally seemed to
produce paradoxical results.  Congress rejected it in
1911, reverting to the Webster method.  In that year
Congress also passed legislation that ultimately fixed the
number of Representatives at 435.
  After the 1920 census Congress failed to pass a reappor-
tionment Act, but debates over the proper method of
apportionment ultimately led to a request to the National
Academy of Sciences to appoint a committee of experts to
review the subject.  That committee, composed of respected
mathematicians, recommended the adoption of the ``method
of equal proportions.''  Congress used that method in its
apportionment after the 1930 census, and formally adopted
it in the 1941 statute at issue in this case.
  The report of the National Academy of Sciences commit-
tee noted that Congress had properly rejected the Hamil-
ton/Vinton method, and concluded that the use of only five
methods could lead to a workable solution of the fractional
remainder problem.  In the opinion of the committee
members, given the fact that it is impossible for all States
to have districts of the same size, the best method was the
one that minimized the discrepancy between the size of the
districts in any pair of States.  Under their test of fairness,
a method was satisfactory if, for any pair of States, the
transfer of one Representative would not decrease the
discrepancy between those States' districts.  The choice
of a method depended on how one decided to measure the
discrepancy between district sizes.  Each of the five meth-
ods could be described as the ``best'' in the sense of minimiz-
ing the discrepancy between districts, depending on the
discrepancy measure selected.  The method of the harmonic
mean, for example, yielded the fairest apportionment if the
discrepancy was measured by the absolute difference
between the number of persons per Representative.  The
method of major fractions was the best method if the
discrepancy was measured by the absolute difference
between the number of Representatives per person (also
known as each person's ``share'' of a Representative).
The method of equal proportions produced the fairest
apportionment if the discrepancy was measured by the
``relative difference'' in either the size of the district or
the share of a Representative.
  The report concluded by endorsing the method of equal
proportions.  The committee apparently preferred this
method for two reasons.  First, the method of equal propor-
tions minimized the relative difference both between the
size of congressional districts and between the number of
Representatives per person.  Second, in comparison with
the other four methods considered, this method occupied an
intermediate position in terms of favoring small States over
large States: it favored small States more than major
fractions and greatest divisors, but not as much as smallest
divisors or the harmonic mean.
  If either the method of smallest divisors or the method of
the harmonic mean, also known as the ``Dean Method,'' had
been used after the 1990 census, Montana would have
received a second seat.  Under the method of equal propor-
tions, which was actually used, five other States had
stronger claims to an additional seat because Montana's
claim to a second seat was the 441st on the equal propor-
tions ``priority list,'' see n. 26, supra.  Montana would not
have received a second seat under either the method of
major fractions or greatest divisors.
                           III
  The Government argues that Congress' selection of any of
the alternative apportionment methods involved in this
litigation is not subject to judicial review.  Relying princi-
pally on Baker v. Carr, 369 U. S. 186 (1962), the Govern-
ment contends that the choice among these methods
presents a ``political question'' not amenable to judicial
resolution.
  In Baker v. Carr, after an extensive review of our prior
cases involving political questions, we concluded:
      ``It is apparent that several formulations which vary
    slightly according to the settings in which the questions
    arise may describe a political question, although each
    has one or more elements which identify it as essential-
    ly a function of the separation of powers.  Prominent on
    the surface of any case held to involve a political
    question is found a textually demonstrable constitution-
    al commitment of the issue to a coordinate political
    department; or a lack of judicially discoverable and
    manageable standards for resolving it; or the impossi-
    bility of deciding without an initial policy determina-
    tion of a kind clearly for nonjudicial discretion; or the
    impossibility of a court's undertaking independent
    resolution without expressing lack of the respect due
    coordinate branches of government; or an unusual need
    for unquestioning adherence to a political decision
    already made; or the potentiality of embarrassment
    from multifarious pronouncements by various depart-
    ments on one question.
      ``Unless one of these formulations is inextricable from
    the case at bar, there should be no dismissal for non-
    justiciability on the ground of a political question's
    presence.  The doctrine of which we treat is one of
    `political questions,' not one of `political cases.'  The
    courts cannot reject as `no law suit' a bona fide contro-
    versy as to whether some action denominated `political'
    exceeds constitutional authority.''  Id., at 217.
  The Government insists that each of the factors identified
in Baker supports the conclusion that the question present-
ed here is committed to the ``political branches'' to the
exclusion of the Judiciary.  Significantly, however, the Gov-
ernment does not suggest that all congressional decisions
relating to apportionment are beyond judicial review.  The
Government does not, for instance, dispute that a court
could set aside an apportionment plan that violated the
constitutional requirement that ``[t]he number of Represen-
tatives shall not exceed one for every thirty Thousand.''
Further, with respect to the provision that Representatives
``shall be apportioned among the several States . . . accord-
ing to their respective Numbers,'' the Government ac-
knowledges that Congress has a judicially enforceable
obligation to select an apportionment plan that is related to
population.  The gravamen of the Government's argu-
ment is that the District Court erred in concluding that the
Constitution imposes the more rigorous requirement of
greatest possible equality in the size of congressional
districts, as measured by absolute deviation from ideal
district size.  The Government then does not dispute
Montana's contention that the Constitution places substan-
tive limitations on Congress' apportionment power and that
violations of those limitations would present a justiciable
controversy.  Where the parties differ is in their under-
standing of the content of these limitations.  In short, the
Government takes issue not with the existence of a judicial-
ly enforceable right, but with the definition of such a right.
  When a court concludes that an issue presents a non-
justiciable political question, it declines to address the
merits of that issue.  See Gilligan v. Morgan, 413 U. S. 1,
10-12 (1972); Baker v. Carr, 369 U. S., at 197; see also
Colegrove v. Green, 328 U. S. 549, 552-556 (1946) (plurality
opinion).  In invoking the political question doctrine, a court
acknowledges the possibility that a constitutional provision
may not be judicially enforceable.  Such a decision is of
course very different from determining that specific congres-
sional action does not violate the Constitution.  That
determination is a decision on the merits that reflects the
exercise of judicial review, rather than the abstention from
judicial review that would be appropriate in the case of a
true political question.
  The case before us today is ``political'' in the same sense
that Baker v. Carr was a ``political case.''  369 U. S., at 217.
It raises an issue of great importance to the political
branches.  The issue has motivated partisan and section-
al debate during important portions of our history.  Never-
theless, the reasons that supported the justiciability of
challenges to state legislative districts, as in Baker v. Carr,
as well as state districting decisions relating to the election
of Members of Congress, see, e.g., Wesberry v. Sanders, 376
U. S. 1 (1964); Karcher v. Daggett, 462 U. S. 725 (1983),
apply with equal force to the issues presented by this
litigation.  The controversy between Montana and the
Government turns on the proper interpretation of the
relevant constitutional provisions.  As our previous rejection
of the political question doctrine in this context should
make clear, the interpretation of the apportionment
provisions of the Constitution is well within the competence
of the Judiciary.  See Davis v. Bandemer, 478 U. S. 109,
123 (1986); Baker v. Carr, 369 U. S., at 234-237; cf.
Gilligan v. Morgan, 413 U. S., at 11.  The political question
doctrine presents no bar to our reaching the merits of this
dispute and deciding whether the District Court correctly
construed the constitutional provisions at issue.
  Our previous apportionment cases concerned States'
decisions creating legislative districts; today we review the
actions of Congress.  Respect for a coordinate branch of
Government raises special concerns not present in our prior
cases, but those concerns relate to the merits of the contro-
versy rather than to our power to resolve it.  As the issue
is properly raised in a case otherwise unquestionably within
our jurisdiction, we must determine whether Congress
exercised its apportionment authority within the limits
dictated by the Constitution.  See INS v. Chadha, 462 U. S.
919, 940-941 (1983); Powell v. McCormack, 395 U. S. 486,
521 (1969).  Without the need for another exploration of the
Baker factors, it suffices to say that, as in Baker itself and
the apportionment cases that followed, the political question
doctrine does not place this kind of constitutional interpre-
tation outside the proper domain of the Judiciary.

                           IV
  In Wesberry v. Sanders, 376 U. S. 1 (1964), the Court
considered the claim of voters in Fulton County, Georgia,
that the disparity between the size of their congressional
district (823,680) and the average size of the ten districts in
Georgia (394,312) deprived them of the right ``to have their
votes for Congressmen given the same weight as the votes
of other Georgians.''  Id., at 3.  This Court upheld the claim,
concluding that Article I, 2, had established a ``high
standard of justice and common sense'' for the apportion-
ment of congressional districts:  ``equal representation for
equal numbers of people.''  Id., at 18.  The constitutional
command that Representatives be chosen ``by the People of
the several States'' meant that ``as nearly as is practicable
one man's vote in a congressional election is to be worth as
much as another's.''  Id., at 7-8.  Writing for the Court,
Justice Black explained:
         ``It would defeat the principle solemnly embodied in
    the Great Compromise-equal representation in the
    House for equal numbers of people-for us to hold that,
    within the States, legislatures may draw the lines of
    congressional districts in such a way as to give some
    voters a greater voice in choosing a Congressman than
    others.  The House of Representatives, the Convention
    agreed, was to represent the people as individuals, and
    on a basis of complete equality for each voter.''  Id., at
    14.
In subsequent cases, the Court interpreted that standard as
imposing a burden on the States to ``make a good-faith
effort to achieve precise mathematical equality.''  Kirkpat-
rick v. Preisler, 394 U. S. 526, 530-531 (1969); see also
Karcher v. Daggett, 462 U. S., at 730.
  Our cases applying the Wesberry standard have all
involved disparities in the size of voting districts within the
same State.  In this case, however, Montana contends, and
a majority of the District Court agreed, that the Wesberry
standard also applies to apportionment decisions made by
Congress and that it was violated because of an unjustified
variance between the population of Montana's single district
and the ideal district size.
  Montana's evidence demonstrated that if Congress had
used the method of the harmonic mean (sometimes referred
to as the ``Dean method'') instead of the method of equal
proportions (sometimes called the ``Hill method'') to appor-
tion the districts, 48 of the States would have received the
same number of Representatives, while Washington would
have received one less-eight instead of nine-and Montana
would have received one more.  Under an apportionment
undertaken according to the Hill method, the absolute
difference between the population of Montana's single
district (803,655) and the ideal (572,466) is 231,189; the
difference between the average Washington district
(543,105) and the ideal is 29,361.  Hence, the sum of the
differences between the average and the ideal district size
in the two States is 260,550.  Under the Dean method,
Montana would have two districts with an average popula-
tion of 401,838, representing a deviation from the ideal of
170,638; Washington would then have eight districts
averaging 610,993, which is a deviation of 38,527 from the
ideal district size.  The sum of the deviations from the ideal
in the two States would thus be 209,165 under the Dean
method (harmonic mean), while it is 260,550 under the Hill
method (equal proportions).  More generally, Montana
emphasizes that the Dean method is the best method for
minimizing the absolute deviations from ideal district size.
  There is some force to the argument that the same
historical insights that informed our construction of Article
1, 2 in the context of intrastate districting should apply
here as well.  As we interpreted the constitutional command
that Representatives be chosen ``by the People of the several
States'' to require the States to pursue equality in represen-
tation, we might well find that the requirement that
Representatives be apportioned among the several States
``according to their respective Numbers'' would also embody
the same principle of equality.  Yet it is by no means clear
that the facts here establish a violation of the Wesberry
standard.  In cases involving variances within a State,
changes in the absolute differences from the ideal produce
parallel changes in the relative differences.  Within a State,
there is no theoretical incompatibility entailed in minimiz-
ing both the absolute and the relative differences.  In this
case, in contrast, the reduction in the absolute difference
between the size of Montana's district and the size of the
ideal district has the effect of increasing the variance in the
relative difference between the ideal and the size of the
districts in both Montana and Washington.  Moreover,
whereas reductions in the variances among districts within
a given State bring all of the affected districts closer to the
ideal, in this case a change that would bring Montana
closer to the ideal pushes the Washington districts away
from that ideal.
  What is the better measure of inequality-absolute
difference in district size, absolute difference in share of a
Representative, relative difference in district size or share?
Neither mathematical analysis nor constitutional interpre-
tation provides a conclusive answer.  In none of these
alternative measures of inequality do we find a substantive
principle of commanding constitutional significance.  The
polestar of equal representation does not provide sufficient
guidance to allow us to discern a single constitutionally
permissible course.
  A State's compliance with Wesberry's ``high standard of
justice and common sense'' begins with a good-faith effort
to produce complete equality for each voter.  As our cases
involving variances of only a fraction of one percent demon-
strate, that goal is realistic and appropriate for State
districting decisions.  See Karcher v. Daggett, 462 U. S., at
730-743.  In this case, however, whether Montana has one
district or two, its variance from the ideal will exceed 40
percent.
  The constitutional guarantee of a minimum of one Repre-
sentative for each State inexorably compels a significant
departure from the ideal.  In Alaska, Vermont, and Wyo-
ming, where the statewide districts are less populous than
the ideal district, every vote is more valuable than the
national average.  Moreover, the need to allocate a fixed
number of indivisible Representatives among 50 States of
varying populations makes it virtually impossible to have
the same size district in any pair of States, let alone in all
50.  Accordingly, although ``common sense'' supports a test
requiring ``a good-faith effort to achieve precise mathemati-
cal equality'' within each State, Kirkpatrick v. Preisler, 394
U. S., at 530-531, the constraints imposed by Article I, 2,
itself make that goal illusory for the Nation as a whole.
  This commonsense understanding of a characteristic of
our Federal Government must have been obvious to the
masters of compromise who framed our Constitution.  The
spirit of compromise that provided two Senators for every
State and Representatives of the People ``according to their
respective Numbers'' in the House must also have motivat-
ed the original allocation of Representatives specified in
Article I, 2, itself.  Today, as then, some compromise
between the interests of larger and smaller States must be
made to achieve a fair apportionment for the entire country.
  The constitutional framework that generated the need for
compromise in the apportionment process must also
delegate to Congress a measure of discretion that is broader
than that accorded to the States in the much easier task of
determining district sizes within State borders.  Article I,
8, cl. 18, expressly authorizes Congress to enact legislation
that ``shall be necessary and proper'' to carry out its
delegated responsibilities.  Its apparently good-faith choice
of a method of apportionment of Representatives among the
several States ``according to their respective Numbers''
commands far more deference than a state districting
decision that is capable of being reviewed under a relatively
rigid mathematical standard.
  The District Court suggested that the automatic charac-
ter of the application of the method of equal proportions,
was inconsistent with Congress' responsibility to make a
fresh legislative decision after each census.  We find no
merit in this suggestion.  Indeed, if a set formula is other-
wise constitutional, it seems to us that the use of a proce-
dure that is administered efficiently and that avoids
partisan controversy supports the legitimacy of congressio-
nal action, rather than undermining it.  To the extent that
the potentially divisive and complex issues associated with
apportionment can be narrowed by the adoption of both
procedural and substantive rules that are consistently
applied year after year, the public is well served, provided,
of course, that any such rule remains open to challenge or
change at any time.  We see no constitutional obstacle
preventing Congress from adopting such a sensible proce-
dure.
  The decision to adopt the method of equal proportions
was made by Congress after decades of experience, experi-
mentation, and debate about the substance of the constitu-
tional requirement.  Independent scholars supported both
the basic decision to adopt a regular procedure to be
followed after each census, and the particular decision to
use the method of equal proportions.  For a half century
the results of that method have been accepted by the States
and the Nation.  That history supports our conclusion that
Congress had ample power to enact the statutory procedure
in 1941 and to apply the method of equal proportions after
the 1990 census.
  The judgment of the District Court is reversed.

                                      It is so ordered.