opinion: Mr. Justice Blackmun
  delivered the opinion of the Court.
  This case presents the issue of the constitutionality of a federal-court-ordered reapportionment of the North Dakota Legislature, called in that State the Legislative Assembly. That State, like many others, has struggled to satisfy constitutional requirements for legislative apportionment delineated in Baker v. Carr, 369 U. S. 186 (1962); Reynolds v. Sims, 377 U. S. 533 (1964); WMCA, Inc. v. Lomenzo, 377 U. S. 633 (1964); Maryland Committee v. Tawes, 377 U. S. 656 (1964); Davis v. Mann, 377 U. S. 678 (1964); Roman v. Sincock, 377 U. S. 695 (1964); Lucas v. Colorado General Assembly, 377 U. S. 713 (1964), and other cases. This litigation is the culmination of that struggle, totally ineffectual on the legislative side, during the past decade.
  I
  The State’s Constitution and Its Statutes
  North Dakota's original Constitution, adopted at the State’s admission into the Union in 1889, is still in effect. It has been amended, of course, from time to time. Since 1918, §25 thereof has read: “The legislative power of this state shall be vested in a legislature consisting of a senate and a house of representatives.” N. D. Const. Art. II, § 25. That legislative power for 70 years has been subject to the initiative and the referendum. Ibid. The Constitution has further provided that the State’s senate “shall be composed of forty-nine members,” § 26, elected for a four-year term, § 27, with one-half thereof elected every two years, § 30, and that no one shall be a senator unless he is a qualified elector of the senatorial district, has attained the age of 25 years, and has been a resident of the State for the two years next preceding the election, § 28. Since 1960, § 29 has read:
  “Each existing senatorial district as provided by law at the effective date of this amendment shall permanently constitute a senatorial district. Each senatorial district shall be represented by one senator and no more.” Laws 1969, c. 438; Laws 1961, c. 405.
  The document also states that the house of representatives “shall be composed of not less than sixty, nor more than one hundred forty members,” § 32, elected for a two-year term, § 33, and that no one shall be a representative unless he is a qualified elector of the district, has attained the age of 21 years, and has been a resident of the State for the two years next preceding the election, § 34. Section 35 provides for at least one representative for each senatorial district and for as many representatives as there are counties in the district; states that the Legislative Assembly, after each federal decennial census, shall apportion “the balance of the members of the House of Representatives,” and, if the Legislative Assembly fails in its apportionment duty, places the task of apportioning the house in a designated group of officials of the State.
  There have been complementary statutory provisions. An apportionment effected by Laws 1931, c. 7, N. D. Cent. Code §54-03-01 (1960), was in effect for over 30 years despite the mandate of § 35 of the Constitution that apportionment be effected after each federal census.
  II
  Prior Litigation
  A. Things began to stir in North Dakota even prior to this Court’s decision in Baker v. Carr in 1962. The State’s Legislative Assembly of 1961 had failed to apportion the house following the 1960 census. After Baker had been decided at the District Court level, 179 F. Supp. 824 (MD Tenn. 1959), and between the argument and reargument of the case here, the Supreme Court of North Dakota dismissed an original action for a prerogative writ to enjoin its Chief Justice from issuing the apportionment proclamation which would have announced the conclusions of the statutorily designated “apportionment group” that were then anticipated. The petition asserted that the group's plan would apportion the house in an unconstitutional manner and not according to population. The Supreme Court ruled that the function of the group was legislative; that it had not yet completed its work; that it was performing a function the Legislative Assembly should have performed; and that, until the proclamation was issued, the group's action was not subject to challenge in the courts. State ex rel. Aamoth v. Sathre, 110 N. W. 2d 228 (1961).
  B. Citizens of North Dakota then sought declaratory and injunctive relief in federal court under the Civil Rights Acts, 42 U. S. C. §§ 1983 and 1988. By this time the State's Chief Justice had issued the proclamation. A three-judge District Court held that the presence of the proclamation eliminated the aspect of prematurity that had characterized the earlier challenge in the state court. But the “basic issues,” the court concluded with one dissent, had not been presented to the Supreme Court of North Dakota. “We believe that court should have the opportunity of passing on all questions herein.” The court, accordingly, abstained from passing upon those issues; it stayed further proceedings before it, but did not dismiss the action. Lein v. Sathre, 201 F. Supp. 535, 542 (ND 1962).
  C. The plaintiffs in the federal case promptly took to the Supreme Court of North Dakota their attack upon the plan adopted by the apportionment group. That court assumed jurisdiction. State ex rel. Lein v. Sathre, 113 N. W. 2d 679, 681 (1962). It noted that no question arising under the United States Constitution was presented, id., at 681-682, and that it was not concerned with the validity of the allotment of one representative to each senatorial district, as prescribed by the first sentence of § 35 of the Constitution, id., at 683. The court recognized that there was inherent in a constitutional direction to apportion according to population “a limited discretion to make the apportionment that will approach, as nearly as is reasonably possible, a mathematical equality.” Id., at 685. It then went on to hold that the apportionment made by the group “violates the constitutional mandate of apportionment according to the population of the several districts and is void,” id., at 687, and that the apportionment effected by the 1931 statute continued to be the law until superseded by an apportionment valid under § 35 or under a further amendment of the Constitution. Id., at 687-688.
  D. The same plaintiffs then turned again to the federal court. The three-judge court, with one judge dissenting, denied the request for injunctive relief on the ground that the only challenge before it was to the apportionment group’s plan, and that the 1931 apportionment was not challenged. Lein v. Sathre, 205 F. Supp. 536 (ND 1962). It noted that the Legislative Assembly would meet the following January, that it had “the mandatory duty” to apportion the house, and that the court would not presume that it would not perform that duty. Jurisdiction was retained, with the observation that if the Legislative Assembly failed to act, the plaintiffs, upon appropriate amendment of their complaint, might further petition the court for relief. Id., at 540.
  E. The 1963 Legislative Assembly did reapportion. Laws 1963, c. 345.
  F. Reynolds v. Sims, 377 U. S. 533, and its companion cases were decided in June 1964. A new suit then was instituted in federal court to invalidate North Dakota's entire apportionment system on federal constitutional grounds. Sections 26, 29, and 35 of the Constitution and the 1963 statute were challenged. 'I&e three-judge court held that these constitutional and statutory provisions were violative of the Equal Protection Clause. Paulson v. Meier, 232 F. Supp. 183 (ND 1964). It went oh to hold that the 1931 apportionment, being “the last valid apportionment,” as described by the North Dakota Supreme Court, and by which the 1963 legislators had been elected, was also invalid. Thus, “there is no constitutionally valid legislative apportionment law in existence in the State of North Dakota at this time.” Id., at 187. The court encountered difficulty as to an appropriate remedy. It concluded, one judge dissenting, that adequate time was not available within which to formulate a proper plan for the then forthcoming 1964 elections, id., at 188; that the 1965 Legislative Assembly would have a de jacto status; and that that Assembly should promptly devise a constitutional system. In-junctive relief was denied. Id., at 190.
  G. The 1965 Legislative Assembly produced a reapportionment act although it was not approved or disapproved by the Governor. Laws 1965, c. 338.
  H. The North Dakota Secretary of State, defendant in the federal court, then moved to dismiss the federal action on the ground that the 1965 act met constitutional requirements. The three-judge court, however, ruled otherwise. Paulson v. Meier, 246 F. Supp. 36, 43 (ND 1965). It turned to the question of remedy and concluded that the Legislative Assembly had had its opportunity and that the court now had the duty itself to take affirmative action. Id., at 43-44. It considered several plans that had been introduced in the Assembly and centered its attention on the Smith plan. Although the court found the plan “not perfect” (five multimember senatorial districts, and county lines violated in 12 instances), it concluded that the plan, if “slightly” modified, would meet constitutional standards (“impressive mathematical exactness,” namely, 25 of 39 districts within 5% of the average population, four slightly over 5%, and only two exceeding 9%). Id., at 44 — 45. The “slight” modification was made and reapportionment, really the first to be finally effected since 1931, was therefore accomplished in North Dakota by federal-court intervention.
  I. Still another original proceeding in the State's Supreme Court was instituted. This one challenged the right of senators from the multimember districts to hold office. It was claimed that this multiple membership violated § 29 of the North Dakota Constitution which provided that each senatorial district “shall be represented by one senator and no more.” The state court held that the 1965 judgment of the federal court was not res judicata as to the then plaintiffs; that the initial or “freezing” portion of §29 was clearly invalid; that the concluding portion, restricting representation of a district to one senator, would not have been desired by the people without the “balance” of the freezing portion; and that § 29 as a unit must fall as violative of equal protection. State ex rel. Stockman v. Anderson, 184 N. W. 2d 53 (1971). The result was that multi-member senatorial districts were not held illegal by the state court.
  Ill
  The Present Litigation
  The 1970 federal census was taken in due course. The 1971 Legislative Assembly failed to reapportion. The present federal action was instituted the following November. The plaintiffs alleged that substantial shifts in population had taken place, and that the court-ordered plan of 1965 no longer complied with the requirements of the Equal Protection Clause. The relief requested was that the court order apportionment upon the 1970 census figures and also provide for single-member districts; that the 1965 plan be declared invalid; and that the Secretary of State be restrained from administering the election laws under that plan.
  On May 22, 1972, the three-judge court entered an order to the effect that the existing North Dakota apportionment failed to meet federal constitutional standards and that the court would attempt to reapportion. Jurisdictional Statement A-54. It appointed a commission to formulate and present a plan within 30 days, and it submitted guidelines to the commission. With respect to multimember districts, the order provided:
  “We have considered the matter of ‘multi-member’ districts and conclude there is insufficient time prior to the 1972 elections to fully explore and resolve the issues involved. The matter of ‘multi-member’ districts will be studied in depth by the Commission, and the results of that study be made available to us.” Id., at A-55.
  An opinion was filed on June 30. 372 F. Supp. 363 (ND). This recited that the commission had presented eight separate plans to the court; that shifts in population since 1960 had resulted in constitutionally impermissible population variations among existing districts; that a plan submitted by Commissioner Dobson substantially reduced the disproportionate representation, although it decreased the number of districts by one and increased the number of senators by two and the number of representatives by four. “[C]ertain weaknesses” in the plan were recognized, including “some variance in population . . . which, in a few instances, seems substantial,” and a continuation of multimember districts. Id., at 366. These districts included the State’s five largest cities. The court noted that the districts had been created, not by enactment of the Legislative Assembly, but by the federal court in the 1965 Paulson decision, and observed, ibid.: “In light of subsequent [United States] Supreme Court pronouncements, we believe it would be improper for this Court to permit their continuation in a court-fashioned plan.” Connor v. Johnson, 402 U. S. 690 (1971), and Connor v. Williams, 404 U. S. 549, 551 (1972), were cited. The court, however, felt
  “constrained to permit multi-member districts to continue during the 1972 elections ... to avoid extreme disruptions in the elective processes. . . . We feel that the electorate will be better served by minimizing the confusion surrounding the impending elections, than it would be by the abolition of multi-member districts at this eleventh hour.” 372 P. Supp., at 366.
  The Dobson plan was therefore approved “for the 1972 election only.” Id., at 367. An alternative, the Osten-son plan, was commended to the commission for “further study,” with a direction to modify it “so as to eliminate the existing multi-member senate districts.” Id., at 367-368. Chief District Judge Benson dissented as to the limitation of the Dobson plan to the 1972 election; for him, the Connor litigation was distinguishable on racial grounds and the desirability of multimember districts was a question for the Legislative Assembly and not for the court. Id., at 368-369. Jurisdiction was retained.
  On November 8, 1972, immediately after the election that year, the three-judge court suspended its June 30 order until further notice and directed the State’s Attorney General promptly to report any action taken by the 1973 Legislative Assembly.
  That Assembly not only passed an apportionment Act but overrode its veto by the Governor. Laws 1973, c. 411, and Note, at 1178. The Act provided for 37 legislative districts, each having one senator and two representatives, except for five multimember senatorial districts. Section 3 thereof specifically recited the population of each district and the population variance (plus 3.3% to minus 3.5%, a total of 6.8%; or plus 408 persons to minus 432 persons, a total of 840 persons) from the average of 12,355 per senator.
  The effectiveness of the legislative plan, however, promptly was suspended by a referendum petition. See Laws 1973, p. 1549. By a companion initiative petition, an amendment to the State’s Constitution was proposed ; this would have created a commission to reapportion the State and, in addition, would have mandated single-member senatorial districts. A special election on these took place December 4, 1973. Both were defeated. The Legislative Assembly’s work to reapportion was thus nullified by the people. It could be suggested, and apparently was, that the people also reacted against the elimination of the five multimember districts. In any event, the defendant thereupon moved the federal court to readopt the plan temporarily approved by its order of June 1972. The plaintiffs resisted.
  The three-judge District Court, with Circuit Judge Bright dissenting, then made “permanent” the 1972 Dob-son plan, with its five multimember districts providing 18 senators out of a statewide total of 51. 372 F. Supp. 371, 379 (ND 1974). We noted probable jurisdiction. 416 U. S. 966 (1974).
  IV
  Jurisdiction
  We are met at the threshold with a mild question of jurisdiction not pressed by the parties. We have jurisdiction under 28 U. S. C. § 1253 only if a three-judge court was required by 28 U. S. C. § 2281.
  It might be suggested that the three-judge court here did not restrain the enforcement of a statute but, instead, the enforcement of the court-ordered plan of 1965 which had become unconstitutional in the circumstances of 1972, and, hence, that the provisions of § 2281 were not satisfied. The argument is less than persuasive and we conclude that it is without merit. Although the reapportionment now under attack was indeed court ordered, its enforcement is doubly based on the State’s Constitution and statutes. Its effectuation directly depends on the state election law machinery and, in addition, the plan itself is a court-imposed replacement of the North Dakota constitutional provisions and the 1931, 1963, and 1965 reapportionment statutes. It is these that are, and have been, the primary objects of attack. It would be highly anomalous if jurisdiction were not here, for then it would follow that a single judge could invalidate a reapportionment plan that had been evolved or approved, and was required so to be, by a three-judge court some time before. Subject matter of this kind is regular grist for the three-judge court, and that route typically has been employed under conditions similar to those present here. See, e. g., Skolnick v. State Electoral Board of Illinois, 336 F. Supp. 839 (ND Ill. 1971). We think this is correct procedure and we conclude that we have jurisdiction.
  V
  The Multimember Districts
  From the above review of the North Dakota constitutional and statutory provisions and of the litigation of the past 12 years, two significant facts emerge: The first is that some multimembership on the house side of the Legislative Assembly traditionally has existed. This plainly qualifies as established state policy. The second is that, in contrast, multimembership on the senate side, even as to the five districts, has never existed except as imposed (a) by the three-judge federal court by its 1965 Paulson decision; (b) by a majority of the three-judge court as a temporary expedient for the 1972 election only; (c) by the provisions of the 1973 act immediately nullified by referendum; and (d) by a different majority of the three-judge court as a “permanent” solution in the judgment under review. Thus only once has the Legislative Assembly provided for multimember senate representation and that effort was promptly aborted. Every other such provision in North Dakota’s history has been court imposed. Multimember senate representation, therefore, obviously does not qualify as established state policy.
  This Court has refrained from holding that multi-member districts in apportionment plans adopted by States for their legislatures are per se unconstitutional. White v. Regester, 412 U. S. 755, 765 (1973), and cases cited therein. On the contrary, the Court has upheld numerous state-initiated apportionment schemes utilizing multimember districts. See, e. g., Kilgarlin v. Hill, 386 U. S. 120 (1967); Burns v. Richardson, 384 U. S. 73 (1966); Fortson v. Dorsey, 379 U. S. 433 (1965). And, beginning with Reynolds v. Sims, 377 U. S., at 577, the Court has indicated that a State might devise an apportionment plan for a bicameral legislature with one body composed of at least some multimember districts, as long as substantial equality of population per representative is maintained.
  Notwithstanding this past acceptance of multimember districting plans, we recognize that there are practical weaknesses inherent in such schemes. First, as the number of legislative seats within the district increases, the difficulty for the voter in making intelligent choices among candidates also increases. See Lucas v. Colorado General Assembly, 377 U. S., at 731. Ballots tend to become unwieldy, confusing, and too lengthy to allow thoughtful consideration. Second, when candidates are elected at large, residents of particular areas within the district may feel that they have no representative specially responsible to them. Ibid. Third, it is possible that bloc voting by delegates from a multimember district may result in undue representation of residents of these districts relative to voters in single-member districts. This possibility, however, was rejected, absent concrete proof, in Whitcomb v. Chavis, 403 U. S. 124, 147 (1971). Criticism of multimember districts has been frequent and widespread. Id., at 157-160, and articles cited therein. See generally Carpeneti, Legislative Apportionment : Multimember Districts and Fair Representation, 120 U. Pa. L. Rev. 666 (1972); Banzhaf, Multi-Member Electoral Districts — Do They Violate the “One Man, One Vote” Principle, 75 Yale L. J. 1309 (1966).
  In Fortson v. Dorsey, supra, we held that the mere assertion of such possible weaknesses in a legislature's multimember districting plan was insufficient to establish a denial of equal protection. Rather, it must be shown that
  “designedly or otherwise, a multi-member constituency apportionment scheme, under the circumstances of a particular case, would operate to minimize or cancel out the voting strength of racial or political elements of the voting population.” 379 U. S., at 439.
  Further, there must be more evidence than a simple dis-proportionality between the voting potential and the legislative seats won by a racial or political group. There must be evidence that the group has been denied access to the political process equal to the access of other groups. White v. Regester, 412 U. S., at 765-766. Such evidence may be more easily developed where the multi-member districts compose a large part of the legislature, where both bodies in a bicameral legislature utilize multi-member districts, or where the members’ residences are concentrated in one part of the district. Burns v. Richardson, 384 U. S., at 88. Whether such factors are present or not, proof of lessening or cancellation of voting strength must be offered.
  This requirement that one challenging a multimember districting plan must prove that the plan minimizes or cancels out the voting power of a racial or political group has been applied in cases involving apportionment schemes adopted by state legislatures. In Connor v. Johnson, 402 U. S. 690 (1971), however, which came to us on an application for a stay, we were presented with a court-ordered reapportionment scheme having some multimember districts in both bodies of the state legislature. We stated explicitly that “when district courts are forced to fashion apportionment plans, single-member districts are preferable to large multi-member districts as a general matter.” Id., at 692. Exercising our supervisory power, we directed the District Court to devise a single-member districting plan, “absent insurmountable difficulties.” Ibid. This preference for and emphasis upon single-member districts in court-ordered plans was reaffirmed in Connor v. Williams, 404 U. S., at 551, and again in Mahan v. Howell, 410 U. S. 315, 333 (1973). In the latter case a District Court was held to have acted within its discretion in forming a multimember district as an interim remedy in order to alleviate substantial underrepresentation of military personnel in an impending election.
  The standards for evaluating the use of multimember districts thus clearly differ depending on whether a federal court or a state legislature has initiated the use. The practical simultaneity of decision in Connor v. Johnson and in Whitcomb v. Chavis, supra, so demonstrates. When the plan is court ordered, there often is no state policy of multimember districting which might deserve respect or deference. Indeed, if the court is imposing multimember districts upon a State which always has employed single-member districts, there is special reason to follow the Connor rule favoring the latter type of districting.
  Appellants do not contend that any racial or political group has been discriminated against by the multi-member districting ordered by the District Court. They only suggest that the District Court has not followed our mandate in Connor v. Johnson, and that the court has failed to articulate any reasons for this departure. We agree. Absent particularly pressing features calling for multimember districts, a United States district court should refrain from imposing them upon a State.
  The District Court cannot avoid the multimember issue by labeling it, see 372 F. Supp., at 377, a political issue to be resolved by the State. The District Court itself created multimember districting in North Dakota, and it might be said to be disingenuous to suggest that the judicial creation became a political question simply by the passage of nine 'years. The District Court’s treatment of this issue directly conflicts with its prior opinion in this case, where it allowed continuation of the multimember districts first established in the Paulson decision in 1965 only as an interim remedy. 372 F. Supp., at 367. The court there noted that in the largest multimember district, a voter would be asked to evaluate the qualifications of at least 30 candidates for the state legislature, a “most formidable” task. Id., at 366. Taking note of Connor v. Johnson, the court held in 1972 that it would be improper to permit multimember districts to remain permanently, and allowed continued use only for the impending election because of the great confusion that otherwise would result. The court appears now to have abandoned that position, with no suggestion of reasons for the abrupt change. It is especially anomalous that the court would continue with the multimem-ber districting plan, when the Special Master who initially proposed it has disavowed use of permanent multimem-ber districts. Dobson, Reapportionment Problems, 48 N. D. L. Rev. 281,289 (1972).
  In contrast, the dissent in the District Court suggests a wide range of attributes of single-member districts. 372 F. Supp., at 391. One advantage is obvious: confusion engendered by multiple offices will be removed. Other advantages perhaps are more speculative: single-member districts may prevent domination of an entire slate by a narrow majority, may ease direct communication with one’s senator, may reduce campaign costs, and may avoid bloc voting. Of course, these are general virtues of single-member districts, and there is no guarantee that any particular feature will be found in a specific plan. Neither the District Court majority nor appellee, however, has provided us with any suggestion of a legitimate state interest supporting the abandonment of the general preference for single-member districts in court-ordered plans which we recognized in Connor v. Johnson. The fact that no allegation of minority group discrimination is raised by appellants here does hot make Connor inapplicable.
  It is true that in 1973 the voters of North Dakota voted down a proposed constitutional amendment which would have re-established the State's tradition of single-member senatorial districts. At the same time the voters also rejected by referendum the Legislative Assembly’s 1973 Act which would have continued the multimember format for five districts. We are unable to infer from these simultaneous actions of the electorate any particular attitude toward multimember districts. It simply appears that North Dakota’s voters have not been satisfied with any reapportionment proposal, and that they are frustrated by the years of confusion since the obviously impermissible apportionment provisions of the State’s Constitution were invalidated.
  We are confident that the District Court, with perhaps the aid of its Special Masters, will be able to reinsti-tute the use of single-member districts while also attaining the necessary goal of substantial population equality. Special Master Ostenson had indicated that it “ 'would not be terribly difficult to adopt single-member districts.’ ” See 372 F. Supp., at 392. Unless the District Court can articulate such a “singular combination of unique factors” as was found to exist in Mahan v. Howell, 410 U. S., at 333, or unless the 1975 Legislative Assembly appropriately acts, the court should proceed expeditiously to reinstate single-member senatorial districts in North Dakota.
  VI
  The Population Variance
  The second aspect of the court-ordered reapportionment plan that is challenged by the appellants is the population divergence in the various senatorial districts. Since the population of the State under the 1970 census was 617,761, and the number of senators provided for by the court’s plan was 51, each senatorial district would contain 12,112 persons if population equality were achieved. In fant, however, one district under the plan has 13,176 persons, and thus is underrepresented by 8.71%, while another district has 10,728 persons, and is overrepresented by 11.43%. The total variance between the largest and smallest districts consequently is 20.14%, and the ratio of the population of the largest to the smallest is 1.23 to 1.
  Reynolds v. Sims, supra, established that both houses of a state legislature must be apportioned so that districts are “as nearly of equal population as is practicable.” 377 U. S., at 577. While “ [mathematical exactness or precision” is not required, there must be substantial compliance with the goal of population equality. Ibid. Reynolds v. Sims, of course, involved gross population disparity among districts.
  Since Reynolds, we have had the opportunity to observe attempts in many state legislative reapportionment plans to achieve the goal of population equality. Although each case must be evaluated on its own facts, and a particular population deviation from the ideal may be permissible in some cases but not in others, Swann v. Adams, 385 U. S. 440, 445 (1967), certain guidelines have been developed for determining compliance with the basic goal of one person, one vote. In Swann we held that a variance of 25.65% in one house and 33.55% in the other was impermissible absent “a satisfactory explanation grounded on acceptable state policy.” Id., at 444. See also Kilgarlin v. Hill, 386 U. S., at 123-124. In Swann, no justification of the divergences had been attempted. Possible justifications, each requiring adequate proof, were suggested by the Court. Among these were “such state policy considerations as the integrity of political subdivisions, the maintenance of compactness and contiguity in legislative districts or the recognition of natural or historical boundary lines.” 385 U. S., at 444. See also Reynolds v. Sims, 377 U. S., at 578-581.
  On the other hand, we have acknowledged that some leeway in the equal-population requirement should be afforded States in devising their legislative reapportionment plans. As contrasted with congressional districting, where population equality appears now to be the preeminent, if not the sole, criterion on which to adjudge constitutionality, Wesberry v. Sanders, 376 U. S. 1 (1964); Kirkpatrick v. Preisler, 394 U. S. 526 (1969); Wells v. Rockefeller, 394 U. S. 542 (1969); White v. Weiser, 412 U. S. 783 (1973), when state legislative districts are at issue we have held that minor population deviations do not establish a prima facie constitutional violation. For example, in Gaffney v. Cummings, 412 U. S. 735 (1973), we permitted a deviation of 7.83% with no showing of invidious discrimination. In White v. Regester, supra, a variation of 9.9% was likewise permitted.
  The treatment of the reapportionment plan in Mahan v. Howell, supra, is illustrative of our approach in this area. There the Virginia Legislature had fashioned a plan providing a total population variance of 16.4% among house districts. This disparity was of sufficient magnitude to require an analysis of the state policies asserted in justification. We found that the deviations from the average were caused by the attempt of the legislature to fulfill the rational state policy of refraining from splitting political subdivisions between house districts, and we accepted the policy as legitimate notwithstanding the fact that subdivision splits were permitted in senatorial districts. Since the population divergences in the Virginia plan were “based on legitimate considerations incident to the effectuation of a rational state policy,” Reynolds v. Sims, 377 U. S., at 579, we held that the plan met constitutional standards.
  It is to be observed that this measure of acceptable deviation from population equality has been developed in cases that concerned apportionment plans enacted by state legislatures. In the present North Dakota case, however, the 20% variance is in the plan formulated by the federal court. We believe that a population deviation of that magnitude in a court-ordered plan is constitutionally impermissible in the absence of significant state policies or other acceptable considerations that require adoption of a plan with so great a variance. The burden is on the District Court to elucidate the reasons necessitating any departure from the goal of population equality, and to articulate clearly the relationship between the variance and the state policy furthered.
  The basis for the District Court’s allowance of the 20% variance is claimed to lie in the absence of “electorally victimized minorities,” in the fact that North Dakota is sparsely populated, in the division of the State caused by the Missouri River, and in the goal of observing geographical boundaries and existing political subdivisions. We find none of these factors persuasive here, and none of them has been explicitly shown to necessitate the substantial population deviation embraced by the plan.
  First, a variance of this degree cannot be justified simply because there is no particular racial or political group whose voting power is minimized or canceled. All citizens are affected when an apportionment plan provides disproportionate voting strength, and citizens in districts that are underrepresented lose something even if they do not belong to a specific minority group.
  Second, sparse population is not a legitimate basis for a departure from the goal of equality. A State with a sparse population may face problems different from those faced by one with a concentrated population, but that, without more, does not permit a substantial deviation from the average. Indeed, in a State with a small population, each individual vote may be more important to the result of an election than in a highly populated State. Thus, particular emphasis should be placed on establishing districts with as exact population equality as possible. The District Court’s bare statement that North Dakota’s sparse population permitted or perhaps caused the 20% deviation is inadequate justification.
  Third, the suggestion that the division of the State caused by the Missouri River and the asserted state policy of observing existing geographical and political subdivision boundaries warrant departure from population equality is also not persuasive. It is far from apparent that North Dakota policy currently requires or favors strict adherence to political lines. As the dissenting judge in this case noted, appellee’s counsel acknowledged that reapportionment proposed by the Legislative Assembly broke county lines, 372 F. Supp., at 393 n. 22, and the District Court indicated as long as a decade ago that the legislature had abandoned the strict policy. Paulson v. Meier, 246 F. Supp., at 42-43. Furthermore, a plan devised by Special Master Ostenson demonstrates that neither the Missouri River nor the policy of maintaining township lines prevents attaining a significantly lower population variance. We do not imply that the Ostenson plan should be adopted by the District Court, or that its 5.95% population variance necessarily would be permissible in a court-ordered plan. What we intend by our reference to the Ostenson plan is to show that the factors cited by the District Court cannot be viewed as controlling and persuasive when other, less statistically offensive, plans already devised are feasible. The District Court has provided no rationale for its rejection of the Ostenson plan.
  Examination of the asserted justifications of the court-ordered plan thus plainly demonstrates that it fails to meet the standards established for evaluating variances in plans formulated by state legislatures or other state bodies. The plan, hence, would fail even under the criteria enunciated in Mahan v. Howell and Swann v. Adams. A court-ordered plan, however, must be held to higher standards than a State’s own plan. With a court plan, any deviation from approximate population equality must be supported by enunciation of historically significant state policy or unique features. We h^ve felt it necessary in this case to clarify the greater responsibility of the District Court, when devising its own reapportionment plan, because of the severe problems occasioned for the citizens of North Dakota during the several years of redistricting confusion.
  VII
  We hold today that unless there are persuasive justifications, a court-ordered reapportionment plan of a state legislature must- avoid use of multimember districts, and, as well, must ordinarily achieve the goal of population equality with little more than de minimis variation. Where important and significant state considerations rationally mandate departure from these standards, it is the reapportioning court’s responsibility to articulate precisely why a plan of single-member districts with minimal population variance cannot be adopted.
  We say once again what has been said on many occasions: reapportionment is primarily the duty and responsibility of the State through its legislature or other body, rather than of a federal court. Reynolds v. Sims, 377 U. S., at 586; Maryland Committee v. Tawes, 377 U. S., at 676. It is to be hoped that the 1975 North Dakota Legislative Assembly will perform that duty and enact a constitutionally acceptable plan. If it fails in that task, the responsibility falls on the District Court and it should proceed with dispatch to resolve this seemingly interminable problem.
  The judgment of the District Court is reversed and the case is remanded for further proceedings consistent with this opinion.
  It is so ordered.
  Prior to the 1960 amendment, § 29 read:
  “The legislative assembly shall fix the number of senators, and divide the state into as many senatorial districts as there are senators, which districts,, as nearly as may be, shall be equal to each other in the number of inhabitants entitled to representation. Each district shall be entitled to one senator and no more, and shall be composed of compact and contiguous territory; and no portion of any county shall be attached to other county, or part thereof, so as to form a district. The districts as thus ascertained and determined shall continue until changed by law.”
  Section 35 reads in full as follows:
  "Each senatorial district shall be represented in the House of Representatives by at least one representative except that any senatorial district comprised of more than one county shall be represented in the House of Representatives by at least as many representatives as there are counties in such senatorial district. In addition the Legislative Assembly shall, at the first regular session after each federal decennial census, proceed to apportion the balance of the members of the House of Representatives to be elected from the several senatorial districts, within the limits prescribed by this Constitution, according to the population of the several senatorial districts. If any Legislative Assembly whose duty it is to make an apportionment shall fail to make the same as herein provided it shall be the duty of the chief justice of the supreme court, attorney general, secretary of state, and the majority and minority leaders of the House of Representatives within ninety days after the adjournment of the legislature to make such apportionment and when so made a proclamation shall be issued by the chief justice announcing such apportionment which shall have the same force and effect as though made by the Legislative Assembly.”
  Prior to the 1960 amendment, § 35 called for the Legislative Assembly (seemingly at least every 10 years) “to fix by law” the number of senators and the number of representatives “within the limits prescribed by this constitution” and to "proceed to reapportion the state into senatorial districts as prescribed by this constitution, and to fix the number of members of the house of representatives to be elected from the several senatorial districts,” with the proviso that at any regular session "the legislative assembly may . . . redistrict the state into senatorial districts, and apportion the senators and representatives respectively.”
  This feature was later described as “a radical departure from state precedent.” Chapman v. Meier, 372 F. Supp. 371, 382 (ND 1974) (dissenting opinion).
  Cf. Minnesota State Senate v. Beens, 406 U. S. 187 (1972).
  The Governor’s principal objection, as announced in his veto message, was the failure of the Legislative Assembly to eliminate the multimember senatorial districts. Return to and Compliance with Order, filed March 30, 1973.
  28 U. S. C. § 1253:
  “Except as otherwise provided by law, any party may appeal to the Supreme Court from an order granting or denying) after notice and hearing, an interlocutory or permanent injunction in any civil action, suit or proceeding required by any Act of Congress to be heard and determined by a district court of three judges.”
  28 U. S. C. §2281:
  “An interlocutory or permanent injunction restraining the enforcement, operation or execution of any State statute by restraining the action of any officer of such State in the enforcement or execution of such statute . . . shall not be granted by any district court or judge thereof upon the ground of the unconstitutionality of such statute unless the application thereof is heard and determined by a district court of three judges under section 2284 of this title.”
  Indeed, at oral argument, the appellants did not oppose the allocation of two house members to each senatorial district. Tr. of Oral Arg. 16-17.
  Cf., however, Fort-son v. Dorsey, 379 U. S. 433, 438 (1965), for the suggestion that the at-large representative serves all residents in the subdistricts. Furthermore, while we mentioned these potential weaknesses of multimember districts in Lucas v. Colorado General Assembly, 377 U. S., at 731 n. 21, we noted that we
  “do not intimate that apportionment schemes which provide for the at-large election of a number of legislators from a county, or any political subdivision, are constitutionally defective. Rather, we merely point out that there are certain aspects . . . that might well make the adoption of such a scheme undesirable to many voters residing in multimember counties.”
  In Whitcomb v. Chavis, 403 U. S., at 158-159, we acknowledged that
  “[c]ritieism [of multimember districts] is rooted in their winner-take-all aspects, their tendency to submerge minorities and to over-represent the winning party as compared with the party’s statewide electoral position, a general preference for legislatures reflecting community interests as closely as possible and disenchantment with political parties and elections as devices to settle policy differences between contending interests.”
  Such criticism did not amount to a showing that the use of multi-member districts was “inherently invidious” or violative of the Fourteenth Amendment. Id., at 160.
  These factors have been criticized as not being particularly helpful. See Carpeneti, Legislative Apportionment: Multimember Districts and Fair Representation, 120 U. Pa, L. Rev. 666, 69-5H395 (1972).
  In Mahan v. Howell, 410 U. S., at 333, we stated that the District Court
  “was confronted with plausible evidence of substantial malapportionment with respect to military personnel, the mandate of this Court that voting discrimination against military personnel is constitutionally impermissible, Davis v. Mann, [377 U. S. 678,] 691-692 [(1964)], and the fear that too much delay would have seriously disrupted the fall 1971 elections. Facing as it did this singular combination of unique factors, we cannot say that the District Court abused its discretion in fashioning the interim remedy of combining the three districts into one multimember district.”
  North Dakota, too, has its military personnel apportionment problem with respect to the bases near Grand Forks and Minot. The appellants recognize the existence of that problem and acknowledge that, conceivably, it could result in some type of multimember districting. Tr. of Oral Arg. 10.
  The only minority group of significant size in North Dakota is Indians, and the court-ordered reapportionment plan affects them no differently from any other group.
  For an example of a conceivable rationale supporting multi-member districts, see Carpeneti, supra, n. 11, at 695-696, where it is suggested that multimember districts may insure that certain interests such as city- or region-wide views are represented.
  See also the views of the late Special Master Smith, 372 F. Supp., at 392.
  As early as Reynolds v. Sims, 377 U. S. 533 (1964), the Court indicated that suggestions that population deviation was necessary “to insure effective representation for sparsely settled areas and to prevent legislative districts from becoming so large [geographically] that the availability of access of citizens to their representatives is impaired” were unconvincing. Id., at 580.
  See Appendix B to memorandum opinion and order of June 30, 1972, by Judges Bright and Van Sickle (the Ostenson plan), App. 12-22. The Ostenson plan would allow a total population deviation of only 5.95%.
  Another plan appearing to be more acceptable with respect to population variance than that adopted by the District Court is the one suggested by the State’s Special Committee on Reapportionment, referred to in Judge Bright’s dissenting opinion, 372 F. Supp., at 394 n. 23.
  This is not to say, however, that court-ordered reapportionment of a state legislature must attain the mathematical preciseness required for congressional redistricting under Wesberry v. Sanders, 376 U. S. 1 (1964); Kirkpatrick v. Preisler, 394 U. S. 526 (1969); Wells V. Rockefeller, 394 U. S. 542 (1969); and White v. Weiser, 412 U. S. 783 (1973).
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