concurring in part and dissenting in part:
I join in the majority opinion to the extent it holds that the three-judge district court was properly convened, that plaintiffs have standing, and that plaintiffs’ claims are justiciable.1 On the merits, however, I am of the view that plaintiffs have failed to show that Congress’ present method for allocating House of Representative *1367seats to the states violates the Constitution, and hence I respectfully dissent from the order granting plaintiffs’ motion for summary judgment.
I
The State of Montana, and its governor, attorney general, secretary of state and congressional delegation (the “State”), allege that the equal proportions formula used to allocate House seats among the states violates Article I, Section 2, of the Constitution. In the history of the Republic, Congress has used four different mathematical formulae2 to apportion House of Representatives seats among the states. Bureau of the Census, U.S. Dep’t of Commerce, Counting for Representation: The Census and the Constitution 3-5 (1990). Following the 1920 census, Congress failed to reapportion House seats among the states. This failure was due in part to a lack of confidence in the population figures presented to Congress by the Census Bureau, but was also due in part to increasing doubts that the then-used “major fractions” formula accurately assigned House seats to states based on population. H.Rep. No. 1314, 91st Cong., 2d Sess. 16-17 (1970).
Hence in 1929, Congress commissioned the National Academy of Sciences (the “NAS”) to determine which mathematical formula for allocating House seats among the states would best accomplish such allocation consistent with the constraint that states cannot be assigned fractions of a representative. See Report of the Nat’l Academy of Sciences Comm, on Apportionment (1929), reprinted in H.Rep. No. 1314, 91st Cong., 2d Sess. 19-21 (1970). The NAS recommended to Congress that it abandon the major fractions formula and adopt the Hill “equal proportions” formula. Id. The committee of four prominent mathematicians convened by the NAS to respond to Congress’ inquiry studied five allocation formulae, including all of the formulae before the court in this matter. Id. The NAS study determined that the Hill formula was not only the least biased as between large states and small, but also led to the least percentage discrepancy in “sizes of congressional districts or ... numbers of Representatives per person.” Id.
In 1941, Congress passed into law a requirement that the method of equal proportions, the Hill formula, was to be used to apportion representatives among the states. See 2 U.S.C. § 2a(a). Congress has revisited the issue of allocation methodology several times since 1941. In 1948, Congress commissioned another NAS study, which concurred in the 1929 study, again finding the Hill formula superior. In 1971, a House subcommittee stated that the Hill formula served the objective of keeping “the average number of persons per congressional district ... as nearly equal as possible among the States,” and hence declined to change it. H.Rep. No. 1314, 91st Cong., 2d Sess. 5-6 (1970). In 1981, the House considered a bill that would have replaced the Hill “equal proportions” formula with the Hamilton-Vinton formula, but the bill was never passed. In the latest allocation of House seats, conducted earlier this year and based on the 1990 census figures, the Hill formula was used, as it has been since 1941.
II
The Supreme Court has never set forth the standard for evaluating claims that Congress has misapportioned House seats among the several states. However, as early as Yick Wo v. Hopkins, 118 U.S. 356, 6 S.Ct. 1064, 30 L.Ed. 220 (1886), voting had been held to be a “fundamental right.” Id. at 370, 6 S.Ct. at 1071. More recently, the Court has stated: “Our Constitution leaves no room for classification of people in a way that unnecessarily abridges” the right to vote. Wesberry v. Sanders, 376 U.S. 1, 17, 84 S.Ct. 526, 535, 11 L.Ed.2d 481 (1964). A court, therefore, should center its inquiry on the question of whether dis*1368parities in voting power are “unnecessary.” Heightened scrutiny attends allegations of deprivation of voting rights. Reynolds v. Sims, 377 U.S. 533, 562, 84 S.Ct. 1362, 1381, 12 L.Ed.2d 506 (1964).
Karcher v. Daggett, 462 U.S. 725, 103 S.Ct. 2653, 77 L.Ed.2d 133 (1983), concerned the mapping of congressional districts within one state and hence is not directly applicable here. Nonetheless, the Court there set forth a burden shifting scheme that provides a helpful analytic framework for evaluating the claims brought before us. Under this scheme, the plaintiff has the initial burden of showing that population differences exist among districts, and, more important, that such “differences were not the result of a good faith effort to achieve equality” and could have been avoided by use of a different districting plan. Karcher, 462 U.S. at 731, 103 S.Ct. at 2658. If the plaintiff meets this burden, the burden shifts to the defenders of the districting plan: “[T]he State must bear the burden of proving that each significant variance between districts was necessary to achieve some legitimate goal.” Id.
Ill
Article I, Section 2, of the Constitution, as amended by Section 2 of the Fourteenth Amendment, requires that “Representatives shall be apportioned among the several States according to their respective numbers.” The manifest command of this text is that House seats are to be allocated to the states based on population. It is also the clear implication of this text, however, that House seats may not straddle state lines; seats must be apportioned to a particular state. Moreover, Article I, Section 2, also provides that “each State shall have at Least one Representative.” Hence, while population is an important factor in allocating House seats, other constraints affect the allocation. Because the Constitution provides for these additional constraints, Justice Harlan observed that it “is not strictly true” that “in allocating Congressmen the number assigned to each State should be determined solely by the number of the State’s inhabitants.” Wesberry, 376 U.S. at 26-27 n. 8, 84 S.Ct. at 540 n. 8 (Harlan, J., dissenting) (emphasis added).
Contemporaneous accounts of the drafting of the Constitution similarly evince the Framers’ intent that the House be apportioned according to population, subject to the constraints inherent in the Constitution’s federal structure. One of the great debates at the Constitutional Convention centered on how to allocate seats in the National Legislature. Although each state, regardless of population, had been equally represented in the Continental Congress, many now argued that “equal numbers of people ought to have an equal no. of representatives.” 1 The Records of the Federal Convention of 1787 at 179 (Far-rand ed. 1937) (statement of James Wilson of Pennsylvania). This debate culminated in the Great Compromise, which allocated seats to the states on the basis of population in one chamber, and irrespective of population in the other.
James Madison confirmed the Framers’ intent that House seats should be allocated by population. He expressed the view that “[i]t is a fundamental principle of the proposed Constitution, that ... the aggregate number of representatives allotted to the several States[] is to be determined by a federal rule, founded on the aggregate number of inhabitants.” The Federalist, No. 54 at 368 (Van Doren ed. 1945).
Hence it is clear that the general principle for allocation is that House seats are to be assigned to states based on population. Unlike in the intrastate context, however, this is not the end of the analysis in the interstate context. For the Constitution requires that the general principle of allocation by population be subject to the following constraints: there must be at least one representative per state, and congressional districts cannot cross state lines. These constraints create the so-called fractional interest problem. For instance, when Montana’s percentage of the total U.S. population is multiplied by 435, it *1369should receive 1.404 representatives.3 Since the Constitution does not permit a representative to be shared between two states, Montana cannot have four-tenths of a representative in Congress. It is impossible, therefore, to follow precisely the general principle of apportionment by population.
James Madison’s notes of the Constitutional Convention debate show that the Framers were aware that the scheme they were creating would lead to the fractional interest problem: “A State might have one Representative only, that had inhabitants enough for V-h or more, if fractions could be applied____” 2 The Records of the Federal Convention of 1787 at 358 (Farrand ed. 1937) (statement of Oliver Elsworth of Connecticut). The Framers, however, did not include in the Constitution a specific mathematical formula to address the fractional interest problem, and the allocation formula to be used became a point of contention between the First Congress and President Washington. See Joseph Story, 2 Commentaries on the Constitution § 678-79 (1833).
Justice Story addressed the fractional interest problem in his Commentaries on the Constitution. He first noted that “there can be no subdivision of [a representative]; each state must be entitled to an entire representative, and a fraction of a representative is incapable of apportionment.” Id. at § 676. Yet Justice Story rejected the notion that if the allocation of House seats could not be accomplished strictly proportionate to population, population should be entirely disregarded. Instead, he reasoned:
the truest rule seems to be, that the apportionment ought to be the nearest practical approximation to the terms of the constitution; and the rule ought to be such, that it shall always work the same way in regard to all the states, and be as little open to cavil, or controversy, or abuse, as possible.
Id. Thus, in evaluating the State’s claims, this court must be mindful that representation in the House precisely proportionate to population is impossible under the constitutional plan. Because the goal of any apportionment formula is to be a “practical approximation” to a population-based allocation, merely pointing out that the equal proportions formula leads to population disparities is insufficient to condemn it. Rather, it must be shown that lesser population disparities are possible using another formula.
IV
The State alleges that the equal proportions formula used to allocate House seats among the states is unconstitutional under Article I, Section 2, of the Constitution. The initial burden is on the State to show that the population differences under the equal proportions formula are avoidable, and that they result from the lack of a good faith effort by Congress to achieve population equity among districts, subject to the constitutional provisions requiring at least one representative per state and barring congressional districts from straddling state boundaries. In my view, the State has failed to meet that burden.
Although the Supreme Court has indeed had occasion to evaluate intra state apportionment plans in cases such as Wesberry and Karcher, the standard of precise numerical equality announced in those cases is impossible to apply here. We engage in a fundamentally different inquiry. Although population equity among districts is a guiding principle, because of the constraints imposed by the Constitution it is impossible to have districts that are even approximately equal in size. Indeed, application of any of the apportionment formulae before this court results in congressional district populations varying by hundreds of thousands of people between states. In intrastate apportionment cases, we must ask the relatively straightforward question: do the districts have the same population? This court has the more complex task of evaluating the relative merits of plans *1370which, by necessity, all fall far short of population equality.4
Three different formulae for addressing the fractional interest problem are before this court. The currently used Hill “equal proportions” formula rounds upward all fractions that are greater than the geometric mean of the two whole numbers the fraction falls between. The State offers two alternative allocation formulae it contends would reduce population differences among districts. The Adams “smallest divisors” formula rounds all fractions up no matter how small. The Dean “harmonic means” formula rounds fractions upward if the fraction exceeds the harmonic mean of the two whole numbers the fraction falls between. The Adams and Dean formulae, which have in common the fact that their use would result in two House seats being allocated to Montana, are alleged by the State better to serve the constitutional requirement that House seats be allocated by population.
The Adams “smallest divisors” formula, in my view, is clearly inconsistent with the principle that House seats should be allocated to the states by population. Its most obvious defect is that it violates “quota” for four states. That is, it assigns a number of representatives to a state that is neither of the two closest whole numbers to that state’s exact, unrounded share of representation. For instance, California’s unrounded quota is 52.124; that is, if representatives could be apportioned in fractions, California would be entitled to exactly 52.124 representatives in the next Congress, based on its 1990 census population. Defs.' Ex. 1 at 12 (declaration of Ernst). While there may be room for argument whether California’s quota should be rounded down to 52 or up to 53 representatives, surely it could not be plausibly argued that the House was apportioned according to population if California were allocated only 50 House seats. Yet that is exactly the result compelled by adoption of the Adams plan. Id. And California is not an isolated case. Using the Adams formula, Illinois, New York, and Ohio would also receive an apportionment of House seats in violation of their quotas, under the 1990 census. Id. at 13.
The Hill “equal proportions” formula, by contrast, has never violated quota in the fifty years it has been in use. Id. Every state has always been assigned a number of House seats that is one of the two closest whole numbers to its exact quota. I fail to see how the Adams formula could be said to be more consistent than the Hill formula with the command of Article I, Section 2, that House seats be apportioned to the states based on population.
Nor does application of the Dean “harmonic means” formula show that the Hill “equal proportions” formula leads to unnecessary population differences. The result under the Dean formula is relatively easy to compare to that under the Hill formula because the only difference in seat allocation would be that Washington state’s ninth House seat would be reassigned and added to Montana. Pis.’ Hill Aff.Ex. G at 1. All other House seat assignments would remain the same under both formulae. This switch of one House seat would increase the population variance between the only two states affected. Under the current apportionment using the Hill formula, Montana's congressional district is 48.0% larger than Washington’s average district. Using the Dean formula, Washington’s districts would become 52.1% larger than Montana’s.
*1371The majority states that the “absolute difference from the ideal district is the proper criterion to use in determining whether Congress has met the goal of equal representation for equal numbers of people.” Ante at 1364. Yet under this criterion, the Hill “equal proportions” formula also performs better than the Dean “harmonic means” formula. Under the Hill formula, Montana has one district that is 231,189 persons larger than the ideal district size. If the Dean formula were used, Montana would have two districts, each 170,638 persons smaller than the ideal, for a total absolute variance of 341,-276 from the ideal district size. Likewise, Washington's absolute population variance would increase by shifting from the Hill formula to the Dean formula. Under the Hill formula, Washington has nine districts, each 29,361 persons too small, for a total absolute variance of 264,249, while adopting the Dean formula would create eight districts, each 38,527 persons too large, increasing the total absolute variance to 308,216. Interestingly, Montana apparently argues that it can live with a variance of 341,276 persons under the Dean formula, while it insists that its 231,189 person variance under the Hill formula is clearly unconstitutional.
The State puts great stock in the fact that under one measure, the Dean and Adams formulae do perform better than the Hill formula: both the Dean and Adams formulae produce a narrower range between the smallest district and the largest. That is, if one selects the single biggest district and the single smallest district in the country, and compare just those two, the disparity is smaller when using the Dean or Adams formulae than when using the Hill formula.
The analysis cannot be limited, however, to only two of the nation’s congressional districts to the exclusion of the other 433. Instead of examining the degree to which just two districts vary from the ideal, a rigorous analysis looks at the variance of every district in the nation. When all 435 districts are considered, the Hill method has the least absolute population variance from the ideal district size, compared to either the Dean or Adams methods. Defs.’ Ex. 1 at 13 (declaration of Ernst). Moreover, “it can be shown mathematically that the [Hill] equal proportions method minimizes this variance among all apportionment methods and all sets of populations.” Id. at 14.
In my view, the majority is mistaken in stating that “[t]he Dean method ... best accomplishes the goal of creating districts closest to the ideal district size.” Ante at 1364. The State’s expert did originally claim that “the Dean method produces the smallest variance or standard deviation.” Pis.’ Tiahrt Aff. at 5. The Census Bureau’s expert, however, has pointed out that the State erred by “fail[ing] to take into account the number of districts in each state” when computing their variance analysis.5 Defs.’ Ex. 1 at 13 (declaration of Ernst). The State has conceded this error. See Pis.’ Br. in Opp’n to Defs.’ Mot. for Summ.J. 2 n. 1 (“Plaintiffs do not dispute the factual allegations contained in the Declaration of Lawrence Ernst.”). The Census Bureau has persuasively shown that the Hill formula is superior, notwithstanding the State’s mistaken belief that the Dean formula produced the least absolute variance. See Defs.’ Ex. 1 at 13 (declaration of Ernst).
In sum, neither of the formulae proposed by the State lead to less population variance than the Hill “equal proportions” for*1372muía in use for the past fifty years. The State, in my view, has failed to demonstrate that a better formula exists than the one chosen by Congress. Surely when the Hill formula leads to the least population variance from the ideal, among the formulae put before this court, it cannot be said that Congress has failed to make a good faith effprt to achieve population equality among congressional districts. Karcher requires just such a showing by the State, and therefore I conclude that the State has failed to meet its burden of proof.
V
The State also claims that section 2a of Title 2 of the United States Code is unconstitutional under Article I, Sections 2 and 7, by not allowing legislative consideration of reapportionment. The majority did not reach this claim, but in my view it should be dismissed for failing to state a claim upon which relief can be granted.
First, there is no textual support in Article I, Sections 2 or 7, for the proposition that at each census, Congress must reexamine the mathematical formula it uses to allocate House seats.6 Article I, Section 2, mandates an “actual Enumeration" every ten years, but gives no hint that Congress must reexamine every ten years the formula it uses to address the fractional interest problem. Section 7 merely recites the process which must be followed for a bill to be enacted into law. It is not alleged that section 2a of Title 2 was enacted in violation of Article I, Section 7, and nothing in section 2a interferes with the process set forth in Section 7 for enacting law. Hence, the constitutional basis for the State’s second claim is most unclear.
Second, even if the Constitution does require Congress to reexamine the allocation methodology every ten years, nothing about section 2a of Title 2 prevents such a reexamination. As with any federal statute, Congress is always free to pass superseding legislation that expressly or impliedly repeals section 2a. Indeed, on at least three occasions since section 2a was passed in 1941, Congress has reconsidered use of the Hill “equal proportions” formula specified in section 2a. In 1948, Congress commissioned a NAS study on allocational formulae, and in 1971 and 1981, subcommittee hearings were held on whether section 2a should be amended. Moreover, to the extent the Montana congressional delegation is alleging that the action of their House and Senate colleagues has prevented consideration and passage of a replacement to the Hill formula, we lack jurisdiction because such claim presents a non-justiciable political question.
Despite the State’s characterization of section 2a as an “automatic” allocation scheme that is somehow beyond congressional control, nothing but a lack of political will prevents Congress from repealing or amending section 2a now or in the future to change the allocation formula. That Congress has chosen for the time being not to amend section 2a of the statute does not violate either Sections 2 or 7 of Article I. I would dismiss the State’s second claim.
VI
The Framers could have created a system where congressional districts disregarded state boundaries, in the same way intrastate districts are now drawn across county lines or city limits. This would have largely eliminated the fractional interest problem, since without the constraint of staying within state boundaries, the nation could be divided up into 435 districts each of equal population. But although they recognized the fractional interest problem, the Framers persisted in creating a scheme whereby House seats are assigned to states, not directly to groups of 572,466 people (the current ideal district size), because of the sovereign role the states play in our federal system. Under our scheme of federalism the population within congressional districts must inevitably vary from state to state, and as Justice Story *1373instructs us, the best we can seek is “the nearest practical approximation” to the ideal of apportionment exactly proportionate to population. Either of the alternative formulae put forward by the State creates a greater absolute population variance from the ideal district size than the Hill “equal proportions” formula. The State, in my view, has failed to show that the formula mandated by Congress is not “the nearest practical approximation,” and hence I would grant defendants’ motion for summary judgment.
. To the extent, however, that plaintiffs' second claim alleges that the internal organization or processes of Congress have denied the Montana congressional delegation the opportunity to vote on apportionment issues, it is a non-justiciable political question. See United States v. Munoz-Flores, 495 U.S. 385, 110 S.Ct. 1964, 1970, 109 L.Ed.2d 384 (1990) (political question "doctrine is designed to restrain the judiciary from inappropriate interference in the business of the other branches of government”); see also Armstrong v. United States, 759 F.2d 1378, 1380 (9th Cir.1985) (matter is justiciable because it "does not require delving into the internal records or workings of Congress”).
. These are: Jefferson "greatest divisors” (1792-1830); Webster "major fractions” (1840, 1910, and 1930); Hamilton-Vinton "simple rounding" (1850-1900); and Hill “equal proportions" (1941-present).
. This number, the exact, unrounded proportion of representation a state would be entitled to if fractions of representatives could be apportioned, is referred to by statisticians as the state’s "quota.”
. Variance analysis is a less than straightforward inquiry. In testimony before the House Subcommittee on Census and Population in 1980, a former Census Bureau statistician observed that there are at least three ways in which the constitutional command of representation based on population could be translated into a statistical test for allocation formulae: (1) variability from the ideal number of persons per district, (2) variability from the ideal share each person should have of his representative’s vote, or (3) variability of nearness to quota. H.Rep. No. 18, 97th Cong., 1st Sess. 58 (1981). Moreover, variability could be measured both as the absolute variance, or as the variance of the mean squared, which is more typically used by statisticians. Id. When the statistician evaluated several allocation formulae, no one formula proved best under all of these measures. Id.
. The reason a variance analysis must account for the number of districts per state is not that there could be variance among the districts within a given state. Indeed, Dr. Ernst’s calculations assume that districts within a given state will be evenly sized, as required under Karcher. Rather, the necessity of accounting for the number of districts per state is illustrated by the following hypothetical: State A has one district which is 100,000 persons larger than the ideal district. State B has fifty districts, each 10,000 persons larger than the ideal. Under the State's incorrect variance analysis using the average variance for each state, State A’s average variance of 100,000 persons is greater than State B’s average variance of 10,000 persons. When the number of districts in each state is accounted for, however, State B’s variance of 500,000 persons (50 x 10,000) is much larger than State A’s variance of 100,000 persons (1 x 100,000).
. Seldom in constitutional jurisprudence does a court encounter a claim, as here, where there is an utter void of case law. We must perforce make direct recourse to the naked text of the Constitution, a daunting prospect indeed.