Frank McNeil Individually and as Representatives of a Certified Class v. Springfield Park District and Springfield School District No. 186, Defendants

CUDAHY, Circuit Judge. On January 17, 1987, the district court held that the at-large system for electing members to Springfield’s city council violated section 2 of the Voting Rights Act of 1965, 42 U.S.C. § 1973 (1982). McNeil v. City of Springfield, 658 F.Supp. 1015 (C.D.Ill.1987). Plaintiffs in that case — five black registered voters residing in Springfield — then brought this action challenging the electoral systems for the Springfield Park District and School Board. The park district board and school board both consist of seven members who are elected at large by a plurality vote. Appendix of Appellants at 3. No black resident has ever been elected to the park board. Five blacks have been elected to the school board since 1965, filling 9.8% of the various seats available during that time. Plaintiffs claim that the multi-member voting districts dilute their voting strength, 1 impairing their ability to elect *939 candidates of their choice, and they ask the court to divide the park and school districts into seven single-member districts, one of which would have a black majority population. 2 The district court granted summary judgment for the defendants, 666 F.Supp. 1208, holding that the plaintiffs failed to satisfy the “necessary preconditions” established by the Supreme Court in Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986), which construed the 1982 amendments to section 2. 3 Gin-gles, like this case, involved a challenge to an at-large, or multi-member, district voting scheme. There the Court held that, in order to sustain a section 2 claim, a minority group must “demonstrate that it is sufficiently large and geographically compact to constitute a majority in a single-member district.” 106 S.Ct. at 2766. If it is unable to satisfy this precondition, a minority group cannot sustain its claim that the multi-member voting scheme “operates to impair minority voters’ ability to elect representatives of their choice.” Id. Applying that test in this case, the district court granted summary judgment on the ground that appellants would not comprise a voting age majority in the proposed single-member district. Appellants attack the district court’s holding on several fronts, some of which involve the merit of Gingles itself. Appellants primarily contend that summary judgment is inappropriate in section 2 voting rights cases, because the statute requires courts to take a “functional” view of the challenged process and evaluate the “totality of the circumstances.” Appellants also contend that Gingles’ population requirement should not apply here because that case involved a district with a majority vote requirement, while a candidate in the districts at issue here may prevail with a plurality of the vote. Alternatively, appellants maintain that, if Gingles’precondition warrants consideration of a motion for summary judgment, the district court erred in interpreting the precondition to require that appellants comprise a voting age majority (in contrast to a total population majority) in their proposed single-member district. Further, they argue that population growth since the 1980 census has produced a black voting age majority in the single-member district. Finally, appellants make two other arguments: first, that the court should add seats to the school and park *940 district boards to enable blacks to comprise a voting age majority in a smaller district; second, that they should be allowed to show that the multi-member scheme impairs their ability to influence elections even though they cannot show that the scheme impairs their ability to elect candidates of their choice. I. Appellants’ strongest argument is that summary judgment is inappropriate in section 2 cases, which generally call for substantial and complex factual determinations. This argument finds support in the text and legislative history of section 2 and in Supreme Court precedent. Indeed, both Congress and the Court have indicated that section 2 cases require consideration of the “totality of the circumstances.” See 42 U.S.C. § 1973(b); Gingles, 106 S.Ct. at 2764, 2781; White v. Regester, 412 U.S. 755, 769, 93 S.Ct. 2332, 2341, 37 L.Ed.2d 314 (1973). Congress, in amending section 2, expressed its preference for “a searching practical evaluation of the ‘past and present reality,’ ” and a “functional view of the political process.” S.Rep. No. 417, 97th Cong., 2d Sess., pt. 1, at 30 & n. 120 [hereinafter Report], reprinted in 1982 U.S. Code Cong. & Admin.News 177, 208 (quoting White, 412 U.S. at 769-70, 93 S.Ct. at 2341). Congress wanted “to restore the legal standard that governed voting rights discrimination cases prior to the Supreme Court’s decision” in City of Mobile v. Bolden, 446 U.S. 55, 100 S.Ct. 1490, 64 L.Ed.2d 47 (1980), which broke with precedent by requiring plaintiffs to prove discriminatory purpose to sustain their claim. Report at 16, reprinted in 1982 U.S.Code Cong. & Admin.News at 192-93. The amendment to section 2 removed the intent requirement and returned to the “results” test that had been in effect before Bolden. 42 U.S.C. § 1973(b); see White, 412 U.S. at 765-66, 93 S.Ct. at 2339. Prior to Bolden, plaintiffs could prevail by showing that a challenged election practice or procedure, under the totality of the circumstances, operated to minimize or cancel out the voting strength of a racial group. White, 412 U.S. at 765-66, 93 S.Ct. at 2339; Whitcomb v. Chavis, 403 U.S. 124, 149, 91 S.Ct. 1858, 1872, 29 L.Ed.2d 363 (1971); Burns v. Richardson, 384 U.S. 73, 88, 86 S.Ct. 1286, 1294, 16 L.Ed.2d 376 (1966); Fortson v. Dorsey, 379 U.S. 433, 439, 85 S.Ct. 498, 501, 13 L.Ed.2d 401 (1965). No discriminatory intent was required. Courts considered a variety of factors in appraising the impact of the challenged practice. White, 412 U.S. at 766-67, 93 S.Ct. at 2339-40; Zimmer v. McKeithen, 485 F.2d 1297, 1306-07 (5th Cir.1973) (ien banc), aff'd sub nom. East Carroll Parish School Bd. v. Marshall, 424 U.S. 636, 96 S.Ct. 1083, 47 L.Ed.2d 296 (1976) (per curiam). 4 In amending section 2, Congress instructed future courts to consider these factors in their determinations of section 2 claims. Report at 28-29, reprinted in 1982 U.S. Code Cong. & Admin.News at 206-07. These factors help define the totality of the *941 circumstances from which courts decide whether a particular scheme minimizes or cancels out minority voting strength. Id. at 29 n. 118, reprinted in 1982 U.S.Code Cong. & Admin.News at 207 n. 118. Admittedly, factors other than those listed are probative of section 2 claims, but it may be worth noting that none of the enumerated factors describes the requirement that a minority group be sufficiently large and geographically cohesive to constitute a majority in a single-member district. Neither White nor Zimmer, the principal cases expressing the standard Congress meant to codify, mentions such a requirement. 5 In the absence of Gingles, appellants might have good reason to claim that summary judgment based on minority population size and concentration is improper in section 2 cases. Despite its merits, however, appellants’ contention ultimately fails in light of Thornburg v. Gingles. Gingles involved a challenge to a multi-member district scheme for electing representatives to the North Carolina legislature. 106 S.Ct. at 2758. Registered black voters alleged that multi-member districts impaired their ability to elect representatives of their choice. Id. The district court applied the “totality of circumstances” test and, relying on the various factors considered in White and Zimmer, concluded that the multi-member districts violated section 2. Gingles v. Edmisten, 590 F.Supp. 345 (E.D.N.C.1984) (three judge panel), aff'd in part and rev’d in part sub nom. Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986). After noting that blacks were “sufficient in numbers and contiguity to constitute effective voting majorities in single-member districts,” id. at 358, the court found that North Carolina had officially discriminated against blacks with respect to their right to vote; that blacks had suffered historically from discrimination in education, housing, employment and health services; that North Carolina maintained a majority vote requirement; that white candidates had encouraged voting along color lines by appealing to racial prejudice; that *942 very few blacks had ever held public office in the state; and that voting in the challenged districts was racially polarized. Id. at 359-72. On direct appeal, the Supreme Court did not simply affirm the lower court; instead, it reworked the standard for section 2 cases. While agreeing that many or all of the White/Zimmer factors are relevant to a claim that multi-member districts violate section 2, the Court established three “necessary preconditions” that have to be met before such claims receive full consideration. Gingles, 106 S.Ct. at 2766. To pass the summary judgment threshold, a minority group “must be able to demonstrate that it is sufficiently large and geographically compact to constitute a majority in a single-member district.” Id. The group must also show that it is politically cohesive and that white bloc voting usually thwarts election of the minority’s preferred candidate. 6 Only upon satisfaction of these threshold criteria should a court conduct its totality-of-the-eircumstances analysis and consider other relevant factors set forth in White. As the Court explained, “Unless minority voters possess the potential to elect representatives in the absence of the challenged structure or practice, they cannot claim to have been injured by that structure or practice.” Id. at 2766-67 n. 17 (emphasis in original). Thus, although a section 2 claim potentially implicates many factors, the Court stated in no uncertain terms that a challenge to a multi-member district cannot be sustained unless the Gingles preconditions are met. We must therefore reject appellants’ contention that summary judgment is improper in section 2 cases. At least at first glance, a tension seems to exist between the Court’s approach toward voting rights claims and Congress’s intent in amending section 2. The Court’s preconditions are not among the White/Zimmer factors that Congress adopted to assist courts in their section 2 analyses. In fashioning a clear regime for a prima facie section 2 case, Gingles precludes some small and unconcentrated minority groups from attempting to rectify vote dilution even though they have “less opportunity than other members of the electorate to participate in the' political process and to elect representatives of their choice.” 42 U.S.C. § 1973(b). For instance, minorities not large and concentrated enough to comprise a majority in a single-member district and therefore unable to sustain a section 2 claim under Gingles may nonetheless “possess the potential” to elect candidates of their choice in a single-member district with the help of a sizeable and long-standing white crossover vote. 7 However, given the lack of clarity with respect to the requirements for a section 2 violation, as well as the broad latitude often granted to courts having to consider the totality of the circumstances, Gingles is a reasonable exercise of the Court’s authority in statutory interpretation. The Court’s approach, by focusing up front on whether there is an effective remedy for the claimed injury, promotes' ease of application without distorting the statute or the intent underlying it. It reins in the almost unbridled discretion that section 2 gives the courts, focusing the inquiry so that plaintiffs with promising claims can develop a full record. The creation of preconditions —a choice of clear rules over muddy efforts to discern equity — shields the courts from meritless claims and ensures that clearly meritorious claims will survive summary judgment. That might not always have been true had courts been allowed to consider all of the White/Zimmer factors at the early stages of the proceedings. Thus, although in this case the Gingles *943 criteria might conceivably foreclose a meritorious claim, in general they will ensure that violations for which an effective remedy exists will be considered while appropriately closing the courthouse to marginal cases. In making that trade-off, the Gin-gles majority justifiably sacrificed some claims to protect stronger claims and promote judicial economy. 8 The Voting Rights Act is a crucially important piece of national legislation, see Derrickson v. City of Danville, 845 F.2d 715, 723-24 (7th Cir. 1988) (Cudahy, J., concurring), but it is subject to the same considerations of effective administration as other similar statutes. We therefore must reject appellants’ contention that a court, in considering section 2 claims, must explore the totality of the circumstances without first determining whether the Gingles threshold criteria are met. 9 Despite the criticisms that can be made of it, Gingles is a reasonable interpretation of a broadly drawn statute. The decision combines the desire of Congress to remove barriers to section 2 claims with the Court’s concern that without preconditions section 2 as amended might lead to a multitude of essentially irremediable claims. In any event, we must, of course, defer to the Court’s interpretation of section 2, which leads to the conclusion that summary judgment is sometimes proper in section 2 cases. 10 II. Appellants contend further that Gingles is inapposite to this case because candidates in the elections at issue in Gin-gles needed a majority of the vote to win. Gingles, 106 S.Ct. at 2761. Candidates for the Springfield park district and school board need only a plurality to win if more than two candidates run. In the context of Gingles and a majority vote requirement, the Court's requirement that a minority group constitute a majority in a single-member district makes sense. If unable to meet this precondition, minority voters do not have the potential to elect candidates of their choice. In the context of the case before us, however, the precondition is more troubling. The purpose of the precondition is to show that a minority group has the potential to elect its own candidates. The absence of a majority vote requirement means that when more than two candidates are running for the same seat, a minority group may be able to elect its candidate of choice without a majority of the vote. The obvious example, assuming racially polarized voting, is the situation of one minority candidate running against several white candidates. Because the white majority’s votes are split, the minority candidate may be elected even though his total opposition garnered more votes. In arguing that the Gingles population requirement should not apply here, appel *944 lants request that we take a “functional view” of the way politics actually works in Springfield. According to their expert, many of the elections in the area field more than two candidates. Actually, appellants simply offer proof that in “over half of the seventeen Springfield area elections ... the number of candidates was more than twice as high as the number of seats available.” Brief of Appellants at 32. This argument, however, is beset with problems. To begin with, the evidence does not focus on elections for the park district and school board; it primarily concerns other elections in the area. Also, the evidence, even if probative, does not guarantee that future park district and school board elections will feature more than two candidates for a single seat. Further, when three or more candidates run for a single seat, it is quite possible that more than one candidate will be preferred by minority voters. Modifying our earlier hypothetical slightly, the minority vote may splinter when two blacks and one white vie for the same seat. Movement away from the Gingles standard invites courts to build castles in the air, based on quite speculative foundations. In our view, the Court based its brightline requirement on a plausible scenario under which courts can estimate approximately the ability of minorities in a single-member district to elect candidates of their choice. Other scenarios are, of course, possible, but that possibility alone is not a good reason to destroy the interests in clarity and uniformity furthered by a brightline test. No one has presented a statistical probability distribution of the variations from the Gingles model in Springfield Park District or School District elections but variations favoring minorities might well be offset by variations favoring whites. To prove a section 2 violation, the potential to elect must be solid and substantial. It cannot be speculative. Blacks comprising less than a majority in a district would not necessarily have the requisite potential to elect their candidates of choice. In the elections at issue here, even if all eligible black voters supported a single candidate in the proposed single-member district, that candidate would not be assured of electoral success. A sole challenger, supported by a bloc of white voters, would win. As we have noted, there are many circumstances, including the existence of cross-over voting proclivities and various combinations of majority and minority candidates, that might strongly affect the electoral prospects of minority candidates. We believe, however, that the Supreme Court acted within the most obvious electoral context in promulgating the Gingles rule. We think the Court did not intend for the rule to be ignored or sharply modified in light of the somewhat different electoral conditions presented here. We therefore hold that the absence of a majority vote requirement here does not remove this case from the ambit of the Gingles requirements. III. Appellants next argue that they comprise a majority in a proposed single-member district. While blacks would comprise small total population majorities, with 50.4% in a single-member park district and 50.2% in a single-member school district, they would not comprise a majority of the voting age population in either single-member district. Read literally, the Gingles population requirement could be construed to require that the minority group constitute a majority only of the total population in a proposed single-member district. Substantial evidence and common sense, however, dispute this construction. In explaining its requirement, the Gingles Court consistently refers to “minority voters,” for only voters can demonstrate the potential to elect candidates of their choice. Gingles, 106 S.Ct. at 2766-67 n. 17. The Court also quotes the commentators who first proposed the requirement: [To] demonstrate [that minority voters are injured by at-large elections], the minority voters must be sufficiently concentrated and politically cohesive that a putative districting plan would result in districts in which members of a racial minority would constitute a majority of the *945 voters, whose clear electoral choices are in fact defeated by at-large voting. Id. at 2767 n. 17 (emphasis added) (quoting Blacksher & Menefee, From. Reynolds v. Sims to City of Mobile v. Bolden: Have the White Suburbs Commandeered the Fifteenth Amendment?, 34 Hastings L.J. 1, 55-56 (1982)). The threshold requirement roughly measures minority voters’ potential to elect candidates of their choice. Because only minorities of voting age can affect this potential, it is logical to assume that the Court intended the majority requirement to mean a voting age majority. Viewed another way, those ineligible to vote have not experienced a dilution of their vote. They are not parties to a section 2 claim. Moreover, courts interpreting Gingles have taken the threshold requirement to mean voting age majority. The district court in Romero v. City of Pomona, 665 F.Supp. 853, 854 (C.D.Cal.1987), stated that “[o]nly those individuals eligible can be counted in determining whether a minority group can constitute a voting majority in a single-member district.” See also Martin v. Attain, 658 F.Supp. 1183, 1204 (S.D. Miss.1987). Even before Gingles, some courts required a showing that a minority group constituted a voting age majority in a single-member district. Thus, the district court in Gingles, 590 F.Supp. 345, stated in its supplemental opinion that “the vote dilution concept ... involve[s] the impact of districting upon effective voting majorities,” and that “no aggregation of less than 50% of an area’s voting age population can possibly constitute an effective voting majority.” Id. at 381 & n. 3. The court also doubted “whether the concept of racial vote dilution can ... be applied ... to ... aggregations of black voters [smaller] than those sufficient to make up effective single-member district voting majorities.” Id. at 380-81. Similarly, another district court held that Boston’s districting plan did not impermissibly dilute hispanic ' voting strength because plaintiffs were unable to show that a district containing an hispanic voting majority could be created. Latino Political Action Comm. v. City of Boston, 609 F.Supp. 739 (D.C.Mass.1985), aff'd, 784 F.2d 409 (1st Cir.1986). Finally, in Ketchum v. Byrne, 740 F.2d 1398, 1412-13 (7th Cir.1984), we noted that voting age population at the very least (and as augmented to reflect other factors) is an appropriate measure • of potential voting strength. Plaintiffs here simply failed to meet their burden of showing such strength. IV. Appellants next maintain that their proposed single-member district contains a black voting age majority because of population growth since the 1980 census, which indicated a minority voting age population of roughly 43%. Appellants rely on their expert’s demographic analysis estimating a minority population of 56% in the proposed district as of 1987. They support the use of these estimates through reference to dicta in Gaffney v. Cummings, 412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973). The Gaffney Court stated the following: [I]t must be recognized that total population, even if absolutely accurate as to each district when counted, is nevertheless not a talismanic measure of the weight of a person’s vote under a later-adopted reapportionment plan. The United States census is more of an event than a process. It measures population at only a single instant in time. District populations are constantly changing, often at different rates in either direction, up or down. Substantial differentials in population growth rates are striking and well-known phenomena. Id. at 746, 93 S.Ct. at 2328. Here the plaintiffs put their finger on a problem that applies not only to voting rights litigation but also to the fairness of presidential elections by the electoral college, districting of the House of Representatives and other political apportionment situations. With a mobile population, the demographic facts may always be a bit stale. Nonetheless, we think there are two problems with the plaintiffs’ argument. First, they never raised it in the court below. Although the plaintiffs filed an af *946 fidavit containing projections of population figures based upon past trends,'they never argued the point raised here in responding to the summary judgment motion. “It is a wellsettled rule that a party opposing summary judgment must inform the trial judge of the reasons, legal or factual, why summary judgment should not be entered. If it does not do so, and loses the motion, it cannot raise such issues on appeal.” Liberales v. County of Cook, 709 F.2d 1122, 1126 (7th Cir.1983). Therefore, we must consider this issue to have been waived. Were we not to find waiver, plaintiffs would still face a tough battle. Whatever the practical merits, they base their argument on a slender legal reed: the Gaffney language quoted above. But that language really does not help them. It simply suggests that census data may not accurately reflect present population; it does not require courts to use a different talisman. The census is presumed accurate until proven otherwise. Latino Political Action Comm., 568 F.Supp. at 1018. Proof of changed figures must be clear and convincing to override the presumption. Dixon v. Hassler, 412 F.Supp. 1036, 1040 (W.D.Tenn.) (three judge panel), aff'd sub nom. Republican Party v. Dixon, 429 U.S. 934, 97 S.Ct. 346, 50 L.Ed.2d 303 (1976). Plaintiffs fail to provide any concrete evidence to rebut the presumption. In the present state of the demographic art, estimates based on past trends are generally not sufficient to override “hard” decennial census data. As the Supreme Court pointed out in Gaffney, 412 U.S. at 746, 93 S.Ct. at 2328, populations change constantly and kinks in the data are common. Perhaps in the future, there will be some shift in the decennial approach to the facts of population. But the meager evidence before us cannot override the presumption of census accuracy. In any event, if the plaintiffs’ view of the population trends is correct, they will have a good claim based on the 1990 census. V. Appellants further argue that we should order the creation of additional seats to the park and school boards to enable black voters to satisfy the threshold requirement. Thus, instead of the seven seats mandated by state law, we would fashion eight or nine districts, one of which would be predominantly black. Although courts have broad remedial powers, plaintiffs must first show injustice. Here the purpose of the Gingles preconditions is to determine, as a preliminary matter, whether a multi-member district illegally dilutes minority voting strength. Since we have found that it does not, we cannot fashion a remedy. Adding seats to the boards would create a voting rights violation where none presently exists by enabling appellants to meet the necessary precondition of their section 2 claim. This is a sort of bootstrapping we cannot accept. Appellants cite only one case that even remotely supports this argument. The Eleventh Circuit in Carrollton Branch of NAACP v. Stallings, 829 F.2d 1547 (11th Cir.1987), cert. denied sub nom. Duncan v. Carrollton, — U.S. -, 108 S.Ct. 1111, 99 L.Ed.2d 272 (1988), affirmed the power of the district court to increase the number of government officials in order to give minority voters an opportunity to elect candidates of their choice. But the facts of Carrollton clearly distinguish that case from this one. In Carrollton, the membership of the county commission was reduced in number from five to three and later to one as the black voting age population rose to 15.3%. There was evidence that the single-member county commission had been adopted in 1947 solely in order to diffuse black voting strength. Id. at 1551. In our view, these unique circumstances of Car-rollton distinguish it from the present case. Where courts have changed the size of an elected body, they have done so with extreme caution. See Sixty-Seventh Minnesota State Senate v. Beens, 406 U.S. 187, 199, 92 S.Ct. 1477, 1485, 32 L.Ed.2d (1972) (reversing court-mandated alteration of State Senate; change might be permissible where “necessary to meet constitutional requirements”) (emphasis added). Such action upsets principles of federalism *947 and may disrupt the operation of the affected body. See id. at 200, 92 S.Ct. at 1486 (“Size is for the State to deter-mine_”). It is not reasonable to add seats to the park and school boards essentially to create a section 2 violation. VI. Appellants finally argue that, although the application of Gingles may warrant summary judgment on the claim that the multi-member districts impair their ability to elect their preferred candidates, they can prevail on a claim that the system impairs their ability to influence elections. Appellants rely on a distinction made briefly by the Gingles majority. See 106 S.Ct. at 2764 n. 12. The Gingles Court indeed divided section 2' claims into two categories. In the first, plaintiffs with a sufficiently large and compact population to constitute a majority in a single-member district would be able to allege that the multi-member district impairs their ability to elect candidates of their choice. The Court added that it was not considering whether section 2 may permit claims brought by a minority group, not sufficiently large and compact to constitute a majority in a single-member district, that the multi-member district impairs its ability to influence elections. Id. This distinction seems inconsistent with the statute’s language. Section 2 states that a voting rights violation is established “if it is shown that the political processes ... are not equally open to participation by members ... [of a minority group] in that its members have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice.” 42 U.S.C. § 1973(b). The essential inquiry is thus whether the political processes are equally open to participation by minority voters. It calls for only one claim. We cannot accept the appellants’ contention that they can avoid the Gingles criteria by arguing that the multi-member districts impair their ability to influence elections. Given the Court’s decision to draw a bright line for summary judgment purposes, it seems counterproductive to permit plaintiffs who cannot satisfy the threshold Gingles tests to make alternative claims that would obliterate the bright line. If allowed, the “ability to influence” claim would severely undermine whatever good purpose is served by the threshold factors. See Gingles, 106 S.Ct. at 2787 n. 1 (O’Con-nor, J., concurring in the judgment) (criticizing the distinction). Courts might be flooded by the most marginal section 2 claims if plaintiffs had to show only that an electoral practice or procedure weakened their ability to influence elections. While Congress intended to make it easier for minorities to show that their vote has been diluted, it presumably did not intend to require courts to entertain claims by a tiny segment of a multi-mem-ber district’s population that the group’s inescapably minimal influence has been impaired by the electoral arrangements. In view of the Court’s apparent objective of sharpening section1 2’s focus, we cannot consider claims that multi-member districts merely impair plaintiffs’ ability to influence elections. Plaintiffs’ ability to win elections must also be impaired. VII. We are trying to carry out the Supreme Court’s mandate in Thornburg v. Gingles. Essentially the Court attempted to define a point at which an arguable voting rights deprivation becomes so marginal as to be unworthy of analysis under a “totality of the circumstances” approach. The appellants have attempted to point out imperfections in the Supreme Court’s test as applied to the particular facts of this case. Con-cededly there are imperfections at the margins. But taken in context they are not so significant as to justify departure from the Court’s threshold rule. The test cuts rough justice, a fact that becomes apparent in the contrast between plaintiffs’ claim that the requirement is too strict and Justice O’Connor’s claim that it is too lax. See supra p. 942 n. 7. We are, of course, bound by the Supreme Court’s determination. Further, we think the rule works no injustice in the present circumstances. *948 This is precisely the kind of case where the Court thought invocation of the Voting Rights Act would be inappropriate. Appellants cannot show that the at-large election system at issue here impairs their ability to elect candidates of their choice. We therefore affirm the district court. AFFIRMED. Footnotes [1] "Vote dilution” refers to "the impermissible discriminatory effect that a multi-member or other districting plan has when it operates 'to cancel out or minimize the voting strength of racial groups.' ” Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 2786, 92 L.Ed.2d 25 (1986) (O’Connor, J., concurring in the judgment) (quoting White v. Regester, 412 U.S. 755, 765, 93 S.Ct. 2332, 2339, 37 L.Ed.2d 314 (1973)). The most commonly litigated situation leading to vote dilution is at-large districting. If voting is racially polarized, a white majority is able to consistently elect its candidates of choice, submerging the preferences of minority *939 voters. When the district is divided into smaller single-member districts, one or more with a majority of minority group voters, the electoral results may more fully reflect societal diversity. Section 2 was intended to force modification of electoral systems evidencing historical patterns of unacceptable vote dilution. [2] The boundaries of the school district differ slightly from the park district. According to the 1980 census, the population of the park district was 119,334, of which 11,198 (or 9.4%) were black. The population of the school district was 122,997, of which 11,217 (or 9.1%) were black. The population of appellants' proposed single-member park district would be 50.4% black, but the voting age population would be only 43.7% black, according to 1980 census figures. Similarly, while the total population of the proposed single-member school district would be 50.2% black, the voting age population would be 43.2% black. [3] Section 2 of the Voting Rights Act, as amended, provides: (a) No voting qualification or prerequisite to voting or standard, practice, or procedure shall be imposed or applied by any State or political subdivision in a manner which re-suits in a denial or abridgement of the right of any citizen of the United States to vote on account of race or color, or in contravention of the guarantees set forth in section 1973b(f)(2) of this title, as provided by subsection (b) of this section. (b) A violation of subsection (a) of this section is established if, based on the totality of circumstances, it is shown that the political processes leading to nomination or election in the State or political subdivision are not equally open to participation by members of a class of citizens protected by subsection (a) of this section in that its members have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice. The extent to which members of a protected class have been elected to office in the State or political subdivision is one circumstance which may be considered: Provided, That nothing in this section establishes a right to have members of a protected class elected in numbers equal to their proportion in the population. 42 U.S.C. § 1973 (1982). [4] Those factors include: 1. The extent of any history of official discrimination touching the right of minorities to register, vote, or participate in the political process; 2. The extent to which voting in the elections is racially polarized; 3. The extent to which the state or political subdivision has used unusually large election districts, majority vote requirements, or other voting practices or procedures that may enhance the opportunity for discrimination against the minority group; 4. Whether members of the minority group have been denied access to the candidate slating process; 5. The extent to which members of the minority group in the state or political subdivision bear the effects of discrimination in such areas as education, employment and health, which hinder their ability to participate effectively in the political process; 6. Whether political campaigns have been characterized by overt or subtle racial appeals; 7. The extent-to which minorities have been elected to public office in the jurisdiction; 8. Whether there is a significant lack of responsiveness on the part of elected officials to the particularized needs of minorities; 9. Whether the policy underlying the state or political subdivision’s voting practice or procedure is tenuous. Report at 28-29, reprinted in 1982 U.S.Code Cong. & Admin.News at 206-07. [5] White involved a constitutional challenge to a multi-member district voting scheme. Plaintiff alleged that multi-member districts in Dallas and Bexar Counties, Texas, violated the fourteenth amendment’s equal protection clause. In affirming the district court’s judgment that the multi-member Dallas district was not equally open to participation by minority voters, the Court cited the following factors considered by the district court: the history of official racial discrimination in Texas, touching the right of blacks to register, vote and otherwise participate; the presence of a majority vote requirement for nomination; the facts that only two blacks from Dallas County had ever served in the state House of Representatives since Reconstruction, and that these two men were the only blacks ever slated to run for legislative office from Dallas County; the lack of responsiveness of elected officials to the needs of minorities in Dallas County; and the use of racial campaign tactics to defeat candidates supported by minority voters. White, 412 U.S. at 766-67, 93 S.Ct. at 2339-40. The Court did not discuss the size of the black voting community in Dallas County. The White Court also upheld the district court’s determination that the voting rights of hispanics in Bexar County had been violated. Despite comprising 29% of the county’s total population of 800,000, hispanics had only been able to elect five of their own to the state House of Representatives since 1880, and just two from the largely hispanic "Barrio." Id. at 768, 93 S.Ct. at 2340. Given that the county sent twelve people to the state House of Representatives, hispanics easily could have had much greater representation in the state legislature if the county had been divided into single-member districts. Nevertheless, the Court chose not to emphasize the potential hispanic voting strength, instead opting to focus on the collateral, economic and language barriers to hispanic participation in the political process. Id. at 769, 93 S.Ct. at 2341. The Court noted that the Barrio was an area of poor housing, low income and high unemployment, and that cultural in-compatability along with the poll tax and severely restrictive voter registration procedures effectively denied hispanics access to the political processes. Id. In Zimmer, the Fifth Circuit held that an at-large voting scheme for parish school board and police jury elections impermissibly diluted minority voting- strength. 485 F.2d at 1300. Although blacks comprised a majority (58.7%) of total population in the parish, the court emphasized that "access to the political process and not population was the barometer of dilution of minority voting strength.” Id. at 1303. In reaching its decision, the court considered the White "panoply -of factors." Id. at 1305. The Court noted that blacks were forced to attend racially segregated schools, subjected to a literacy test to qualify to vote, and not permitted to register to vote until 1962; the Court also considered the majority vote requirement in the parish, which tended to submerge a racial minority. Id. at 1306. [6] The latter two requirements are not at issue here. [7] Somewhat ironically, a different concern led Justice O’Connor, joined by three others, to write separately. Justice O’Connor believed that the Gingles criteria might make it too easy for plaintiffs to prevail in section 2 cases, by encouraging a failure to give adequate weight to other factors. 106 S.Ct. at 2788-89 (O’Connor, J., -concurring in the judgment). She warned that the Gingles regime would lead courts usually to require proportional representation, in contravention of clear congressional intent. Id.; see also 42 U.S.C. § 1973(b) (proviso stating the statute should not be construed to require proportional representation). [8] We also note that, while White and Zimmer did not require that plaintiffs show they can constitute a majority in a single-member district, plaintiffs in both cases were apparently sufficiently populous and geographically compact to satisfy this requirement. In White, his-panics in Bexar County, composing 29% of the county’s total population, could easily have constituted a majority in a single-member district, which, because the county had twelve representatives, would have contained roughly 8.5% of the county’s total population. See White, 412 U.S. at 768, 93 S.Ct. at 2340; see also supra p. 941 n. 5. Likewise, plaintiffs in Zimmer would no doubt have comprised a majority in a single-member district since they already had a majority in the multi-district parish. 485 F.2d at 1301. These numbers make understandable the court’s broad dicta that the size of the minority population was not "the barometer of vote dilution.” Id. at 1303. Minority voting strength was clearly present; therefore other factors became important. [9] Because of this holding, we do not consider plaintiffs’ claim that white cross-over votes would enable black candidates to prevail in the proposed districts. Cross-over voting is to be considered only after the Gingles prerequisites are met. The existence of a cross-over, of course, weakens pro tanto the assumption of racial bloc voting. [10] Several other circuits have reached the same conclusion. See Carrollton Branch of NAACP v. Stallings, 829 F.2d 1547, 1550 (11th Cir.1987), cert. denied sub nom. Duncan v. Carrollton, — U.S. -, 108 S.Ct. 1111, 99 L.Ed.2d 272 (1988); Collins v. City of Norfolk, 816 F.2d 932, 936 (4th Cir.1987); Buckanaga v. Sisseton Indep. School Dist., No. 54-5, 804 F.2d 469, 472 (8th Cir. 1986).