GUY, J., delivered the opinion of the court, in which CLELAND, D.J., joined. BOGGS, J. (pp. 816-17), delivered a separate concurring opinion.
RALPH B. GUY, Jr., Circuit Judge.Plaintiffs appeal the judgment entered in favor of defendants with regard to plaintiffs’ challenge, under § 2 of the Voting Rights Act and the Equal Protection Clause, to the system currently used to elect the members of the city council of Cincinnati, Ohio. Plaintiffs argue that, contrary to the district court’s findings, “white bloc voting” has been present under the challenged electoral system and that this system was enacted with racially discriminatory intent. We disagree with plaintiffs, and affirm.
I.
Between 1924 and 1957, Cincinnati utilized a system known as “proportional representation” (PR) to elect the nine members of its city council. Councilmembers were elected at large under this system. Although each voter listed his candidate preferences in rank order, the voter’s ballot was counted only towards the highest-ranked candidate whom it could help elect. The mechanics of this system were quite complex, but they essentially ensured that each voter’s ballot was credited to the voter’s highest-ranked candidate who had not yet been assured of victory or defeat based on the other ballots already counted toward the candidate’s total.
PR eroded the Republican Party’s dominance of Cincinnati government, and the party launched a sustained effort to repeal it. This effort led to voter referenda in 1936, 1939, 1947, 1954, and 1957 on the issue of whether PR should be repealed. In the debates surrounding each of these referenda, the opponents of PR argued that PR was difficult to understand and administer, caused an inordinate number of ballots to be declared invalid, yielded seemingly inequitable results, and balkanized the electorate into religious, racial, ethnic, geographic, and labor interest groups. Despite these arguments, PR narrowly avoided repeal in the referenda before 1957. In the 1957 referendum, however, the voters chose to replace PR with the current system of electing councilmembers, which is known as 9X.
Under 9X, the nine councilmembers are still elected at large, but each voter may vote for up to nine candidates. A voter cannot, however, allocate more than one vote to a particular candidate. The nine candidates who receive the most votes are elected for a two-year term of office. There are no dis*810trict or ward residency requirements for city council candidates.
Black candidates, at least initially, fared less well under 9X than they had under PR. Blacks made up about 15 percent of the electorate in Cincinnati during the mid-1950s, and were by that time routinely elected to the city council in numbers roughly equal to their proportion of the electorate. After 9X was instituted, however, no blacks were elected to the city council until 1963. Since 1963, the number of black eouncilmem-bers has ranged from zero to two, with one being the average. In the 1991 election, which was the most recent election before this lawsuit was filed, two black candidates were elected. One of these candidates, Dwight Tillery, was designated Mayor of Cincinnati because he received more votes than any other candidate, white or black. Blacks nevertheless have not been elected to the city council in numbers equal to their proportion of the electorate, because in 1990 blacks constituted 33.5 percent of the voting-age population in Cincinnati.
Plaintiffs filed this lawsuit in March 1992, alleging that 9X violates their rights under the Voting Rights Act and the Fourteenth and Fifteenth Amendments. During a ten-day bench trial, the parties presented statistical evidence that focused on the results of the six city council elections between and including the years 1981-1991. For each of these elections, the statistics isolated the nine candidates who received the most support from black voters (“blacks’ preferred candidates”).1 This evidence revealed that 40 of 54, or 74 percent, of blacks’ preferred candidates were elected; that 32 of 37, or 86 percent, of blacks’ preferred candidates who were white were elected; and that 8 of 17, or 47 percent, of blacks’ preferred candidates who were black (“blacks’ preferred black candidates”) were elected. After considering this and other evidence, the district court entered judgment in favor of defendants. This appeal followed.
II.
In considering plaintiffs’ arguments on appeal, we review de novo the court’s interpretation of the relevant law, but review the court’s factual findings for clear error only. Thornburg v. Gingles, 478 U.S. 30, 79, 106 S.Ct. 2752, 2781, 92 L.Ed.2d 25 (1986). Whether an electoral system has diluted the voting power of a minority group is a factual question, id., as is whether such a system was adopted with racially discriminatory intent. Rogers v. Lodge, 458 U.S. 613, 622-23, 102 S.Ct. 3272, 3278, 73 L.Ed.2d 1012 (1982).
III.
Section 2 of the Voting Rights Act 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 results 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 in 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 *811political 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.
In Gingles, the Supreme Court interpreted the above-quoted language to establish three “necessary preconditions” to a successful § 2 challenge by a minority group to an electoral district:
First, the minority group must be able to demonstrate that it is sufficiently large and geographically compact to constitute a majority in a single-member district_
Second, the minority group must be able to show that it is politically cohesive.... Third, the minority must be able to demonstrate that the white majority votes sufficiently as a bloc to enable it—in the absence of special circumstances, such as the minority candidate running unopposed— usually to defeat the minority’s preferred candidate.
Id. at 50-51, 106 S.Ct. at 2766 (citations omitted). If these three preconditions are met, a variety of other factors are then examined to determine whether, given the “totality of the circumstances,” the multimember electoral district has in fact “diluted” the minority’s electoral strength and thus denied members of the minority group a fair opportunity to elect representatives of their choice. Gingles, 478 U.S. at 48-49 & n. 15, 106 S.Ct. at 2765-66 & n. 15.
The parties do not dispute that the first and second preconditions have been met here, but the district court held that the third precondition—the existence of white bloc voting as defined by the Gingles Court—had not been proven by plaintiffs. The court noted the 74 percent success rate of blacks’ preferred candidates in the 1981-91 elections, and thus concluded that blacks’ preferred candidates were usually elected, not usually defeated. The court expressly refused, however, to consider the lower (47 percent) success rate of blacks’ preferred black candidates.
The district court’s refusal to consider a candidate’s race in its white bloc voting analysis was based on the only portion of Justice Brennan’s Gingles opinion that was not supported by (and indeed was rejected by) a majority of the Court. In that portion of his Gingles opinion, Justice Brennan asserted that “the race of the candidate per se is irrelevant” to a § 2 inquiry because, in his view, “[u]nder § 2, it is the status of the candidate as the chosen representative of a particular racial group, not the race of the candidate, that is important.” 478 U.S. at 67-68, 106 S.Ct. at 2775. Justice White, who supplied the fifth vote for the remainder of Justice Brennan’s opinion, noted that this reasoning could unduly broaden the scope of § 2:
Suppose an eight-member multimember district that is 60% white and 40% black, the blacks being geographically located so that two safe black single-member districts could be drawn. Suppose further that there are six white and two black Democrats running against six white and two black Republicans. Under Justice Brennan’s test, there would be polarized voting and a likely § 2 violation if all the Republicans, including the two blacks, are elected, and 80% of the blacks in the predominantly black areas vote Democratic. I take it that there would also be a violation in a single-member district that is 60% black, but enough of the blacks vote with the whites to elect a black candidate who is not the choice of the majority of black voters. This is interest-group politics rather than a rule hedging against racial discrimination.
Id. at 83, 106 S.Ct. at 2783 (White, J., concurring). Justice O’Connor, writing for herself and three other Justices (who did not include Justice White), agreed with Justice White’s *812conclusion on this point. Id. at 101, 106 S.Ct. at 2792 (O’Connor, J., concurring in the judgment).
Plaintiffs argue that the district court’s colorblind approach to the white bloc voting issue, and the court’s resultant focus on the overall success rate of blacks’ preferred candidates, allows the ability of black voters to elect white candidates of their choice to mask, or “submerge,” the inability of black voters to elect black candidates of their choice. Plaintiffs therefore urge us to reject the reasoning of Justice Brennan and examine whether white bloc voting denied black Cincinnatians the opportunity to elect black candidates to the city council.
We agree with plaintiffs and Justices White and O’Connor that a candidate’s race can be relevant to a § 2 inquiry. The approach suggested by Justice Brennan is based on an interpretation of § 2 that is at once over- and underindusive. That interpretation is overinclusive because, as Justice White makes clear, it would cause courts to find a § 2 violation in many cases where the defeat of blacks’ preferred candidates had nothing to do with the inability of blacks to participate fully in the political process. Justice Brennan’s approach thus transforms § 2 into a categorical guarantee of a certain level of success for blacks’ preferred candidates. By its plain language, however, the Act guarantees to radal minorities an equal opportunity to elect candidates of their choice, not a floor on the success rates of those candidates. When, in the competition inherent in the democratic process, a racial group’s preferred candidates are defeated despite the ability of its members to participate fully in that process, the Voting Rights Act should not provide that group with a remedy which is unavailable to other supporters of defeated candidates.
Justice Brennan’s interpretation of § 2 is underindusive because it fails to recognize a § 2 violation in many instances where blacks truly do not enjoy an equal opportunity to “elect [their] candidate of choice on an equal basis with other voters.” Voinovich v. Quilter, — U.S. -, -, 113 S.Ct. 1149, 1155, 122 L.Ed.2d 500 (1993). When white bloc voting is “targeted” against black candidates, black voters are denied an opportunity enjoyed by white voters, namely, the opportunity to elect a candidate of their own race. If black voters nevertheless are able to elect many or most of their preferred candidates who are white, a court that refuses to consider candidate race will be unable to conclude that “the white majority votes sufficiently as a bloc to enable it ... usually to defeat the minority’s preferred candidate.” Gingles, 478 U.S. at 51, 106 S.Ct. at 2766-67 (emphasis added). Such a court thus will find no § 2 violation. But the Act’s guarantee of equal opportunity is not met when, in the words of Judge Richard Arnold, “Candidates favored by blacks can win, but only if the candidates are white.” Smith v. Clinton, 687 F.Supp. 1310, 1318 (E.D.Ark.1988) (three-judge panel). See also Jenkins v. Red Clay Consol. School Dist. Bd. of Educ., 4 F.3d 1103, 1125-26 (3d Cir.1993), cert. denied, — U.S. -, 114 S.Ct. 2779, 129 L.Ed.2d 891 (1994); Citizens for a Better Gretna v. City of Gretna, La., 834 F.2d 496, 502 (5th Cir.1987) (“That blacks also support white candidates acceptable to the majority does not negate instances in which white votes defeat a black preference [for a black candidate].”), cert. denied, 492 U.S. 905, 109 S.Ct. 3213, 106 L.Ed.2d 564 (1989); but see Carrollton Branch of NAACP v. Stallings, 829 F.2d 1547, 1559 (11th Cir.1987) (following Brennan approach), cert. denied sub nom. Duncan v. City of Carrollton, Ga., Branch of NAACP, 485 U.S. 936, 108 S.Ct. 1111, 99 L.Ed.2d 272 (1988).
We therefore accept plaintiffs’ invitation to consider whether the district court overlooked white bloc voting targeted against blacks’ preferred black candidates. As suggested earlier, the existence of racially identifiable voting patterns itself is not sufficient to demonstrate the existence of white bloc voting; rather, to find that white bloc voting is targeted against a group of candidates, “a [white] majority must usually be able to defeat” them. Gingles, 478 U.S. at 49, 106 S.Ct. at 2766 (emphasis in original). Here, the parties do not dispute that there have been racially identifiable voting patterns under 9X. In the 1981-91 city council elections, however, 47 percent of blacks’ preferred black candidates were elected. This success *813rate gives us no reason to find that blacks’ preferred black candidates have “usually” been defeated. We therefore conclude that white bloc voting has not been targeted against blacks’ preferred black candidates in the city council elections under 9X.2
The eases in which the opposite conclusion was reached are either factually distinguishable or unpersuasive. Smith and Gretna fall into the former category, as no black candidates had ever been elected under the dis-tricting schemes challenged in those cases. Smith, 687 F.Supp. at 1312; Gretna, 834 F.2d at 504. Similarly, in Jenkins, blacks’ preferred black candidates had been defeated in six of the seven elections at issue. 4 F.3d at 1113, 1130.
The facts set forth in Collins v. City of Norfolk, Va, 883 F.2d 1232 (4th Cir.1989), cert. denied, 498 U.S. 938, 111 S.Ct. 340, 112 L.Ed.2d 305 (1990), though, are similar to those present here. In Collins, 54 percent of blacks’ preferred black candidates had been elected in the ten city council elections studied. Despite this success, black voters had never been able to elect more than one of their preferred candidates (of any race) during any single election. Over a vehement dissent, a majority of the panel found a § 2 violation because the record indicated that “the white majority normally voted sufficiently as a bloc” to frustrate black voters’ efforts “to elect a second black councilman.” IcL at 1240 (emphasis added).
The reasoning of the Collins majority appears flawed, however, because it has no stopping point short of guaranteed proportional representation for racial minorities. The Collins approach ignores the extent to which a racial group’s preferred candidates are successful, and considers only the elections in which those candidates lose. Since this approach normally would yield a finding of white bloc voting, it likewise would lead courts to find a § 2 violation in virtually every ease brought under that section. The handful of exceptional cases would be those in which defendants demonstrate that plaintiffs have enjoyed “persistent proportional representation,” Gingles, 478 U.S. at 77, 106 S.Ct. at 2780, which, the Supreme Court has instructed, is presumptively inconsistent with the existence of a § 2 violation. Id.; see also id. at 102, 106 S.Ct. at 2793 (O’Connor, J., concurring in the judgment). Thus, the Collins approach effectively would delete from § 2 the language that was so critical to its approval by Congress: “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(b) (emphasis in original). We therefore decline to follow Collins.
Plaintiffs next argue that “special circumstances” have concealed the existence of white bloc voting in the Cincinnati city council elections. In Gingles, the Court stated that “the success of a minority candidate in a particular election does not necessarily prove that the district did not experience [racially] polarized voting in that election; special circumstances, such as the absence of an opponent, incumbency, or the utilization of bullet voting, may explain minority electoral success in a polarized contest.” 478 U.S. at 57, 106 S.Ct. at 2770 (emphasis added) (footnote omitted). Plaintiffs assert that the special circumstance of incumbency explains away the success enjoyed by black candidates for city council because five of the eight blacks elected to the city council under 9X were first appointed to that body.
The Supreme Court has not yet had occasion to describe the conditions under which incumbency may be a “special circumstance.” But unlike other “special circumstances,” incumbency plays a significant role in the vast majority of American elections. To qualify as a “special” circumstance, then, incumbency must play an unusually important role in the election at issue; a contrary rule would confuse the ordinary with the special, and thus “make practically every *814American election a ‘special circumstance.’” Collins, 883 F.2d at 1250 (Chapman, J., dissenting).
If, as plaintiffs suggest, black candidates have needed the benefits of incumbency to overcome an otherwise insurmountable degree of white voter opposition to their candidacies, one would expect black challengers to have been almost uniformly unsuccessful. But under 9X, over one-third — or 3 of 8 — of the successful black candidates for city council were first elected as challengers. (App. at 161.) This fact indicates that, in elections involving black candidates, incumbency has played not a “special” role, but only its usual role in American polities. We therefore agree with the district court’s implicit finding that special circumstances do not account for the success enjoyed by black candidates for city council.3
Since plaintiffs failed to prove the “necessary precondition” of white bloc voting, we need not consider the various other factors that can be probative of a § 2 violation.4 Even if we were to do so, however, the result we reach would be no different. After considering all of the evidence presented by the parties at trial, the district court expressly found that discrimination by the City “has not touched the right of African American citizens to register, to vote, or otherwise to participate in the electoral process”; that the city council nomination processes of the major parties are “open to and participated in by African Americans”; and that “[t]he City’s approach to dealing with issues of concern to the African American community displays a consistent pattern of responsiveness to those concerns.” (App. at 482, 474, and 480.) The record amply supports these findings. Moreover, given the difficulties experienced in the administration of PR, we cannot say that the policy underlying 9X is “tenuous.” It is true that the 9X district is large, that black Cincinnatians generally are poorer and less-educated than white Cincin-natians, and that, in recent elections, candidates campaigning in the mostly white west side of the City have said that they “know what the West Side needs” or support ‘West Side values.” (App. at 3130, 2194). On the whole, however, we cannot conclude that the district court — which is “composed of [a] local judge[ ] who [is] well acquainted with the political realities” of the City, Gingles, 478 U.S. at 80, 106 S.Ct. at 2781—clearly erred in concluding that the use of 9X has not caused black voters in Cincinnati “to have less opportunity than white voters to elect representatives of their choice.” Id.5
IV.
Plaintiffs also argue that 9X was enacted with a racially discriminatory purpose, in violation of the Equal Protection Clause.6 At trial, plaintiffs presented evidence that racial tensions had been on the rise prior to the 1957 referendum; that then-Mayor Charles *815Taft (a PR supporter) blamed the defeat of PR on “the nastiest kind of anti-negro whispering campaign by the hard-core Republican precinct people” (app. at 458-59); that the public debate concerning the referendum addressed the extent to which “religious, ethnic, racial, and political minorities” were represented on the city council under the PR system (app. at 457); that the only incumbent defeated in the 1957 city council elections (which were the first held under 9X) was Theodore Berry, a leading black politician; that no black was elected to the city council until six years after 9X was adopted; and that a number of scholars concluded that race was the decisive factor in the repeal of PR.
The district court rejected, however, plaintiffs’ equal protection argument. Although the court stated that “the motive of voters in casting their particular votes [in the 1957 referendum] is irrelevant to the inquiry before this Court[]” (app. at 490), the court found that “[i]t is unlikely that race was a motivating factor in any campaign to repeal PR[ ]” (app. at 458), and that it was “highly unlikely that the citizens of Cincinnati defeated PR because they were threatened by the fact that Theodore Berry could have been Mayor.” (App. at 460.) The court further noted that the officials of “the City did not invidiously inject race as an issue in the 1957 campaign to repeal PR.” (App. at 459.) The district court thus concluded that “[t]he repeal of PR can be attributed to objective factors such as low voter turnout at a special election; the deficiencies of PR; and partisan political interests.” (App. at 459.)
Plaintiffs now contend that the district court erred in refusing to examine in isolation the motives of the electorate in repealing PR. This error of law, plaintiffs assert, caused the district court to reach an erroneous conclusion on the ultimate question of discriminatory purpose.
It is well settled that electoral systems “violate the Fourteenth Amendment if ‘conceived or operated as purposeful devices to further racial discrimination’ by minimizing, cancelling out or diluting the voting strength of racial elements of the voting population.” Rogers v. Lodge, 458 U.S. 613, 617, 102 S.Ct. 3272, 3275, 73 L.Ed.2d 1012 (1982) (quoting Whitcomb v. Chavis, 403 U.S. 124, 149, 91 S.Ct. 1858, 1872, 29 L.Ed.2d 363 (1971)). That such a system is adopted by means of the referendum process does not “immunize” it from constitutional scrutiny, since “[t]he sovereignty of the people is itself subject to those constitutional limitations which have been duly adopted and remain unrepealed.” Hunter v. Erickson, 393 U.S. 385, 392, 89 S.Ct. 557, 561, 21 L.Ed.2d 616 (1969).
In Arthur v. City of Toledo, Ohio, 782 F.2d 565 (6th Cir.1986), however, we closely examined the Supreme Court cases involving equal protection challenges to referendum election results, and concluded that “neither the Supreme Court nor this Court has ever inquired into the motivation of voters in an equal protection clause challenge to a referendum election involving a facially neutral referendum unless racial discrimination was the only possible motivation behind the referendum results.” Id. at 573 (footnote omitted). Writing for a unanimous panel, Judge Kennedy articulated “[s]everal important policy considerations [that] limit a court’s examination of the factors motivating the electorate in a referendum election.” Id. These considerations included the difficulty of “ascertaining what motivated the electorate” and our belief that “the ‘bigoted comments of a few citizens, even those with power, should not invalidate action which in fact has a legitimate basis.’ ” Id. at 574-75. We further noted that, just as the policies embodied in Fed.R.Evid. 606(b) prohibit “federal courts from inquiring into the validity of a jury verdict[,]” so too “the policies underlying the ‘secret ballot’ prevent courts from inquiring into the votes of the electorate.” Id. at 574. We therefore “h[e]ld that absent a referendum that facially discriminates racially, or one where although facially neutral, the only possible rationale is racially motivated, a district court cannot inquire into the electorate’s motivations in an equal protection clause context.” Id.7
*816In light of these principles, the district court was correct to reject plaintiffs’ equal protection argument. 9X is not racially discriminatory on its face, and the repeal of PR in favor of 9X was supported by numerous rationales that had nothing to do with race. Defendants presented significant evidence that PR was an administrative botch that often left voters feeling confused and powerless. Although we rely on Arthur to decide this issue, this evidence was strong enough to support a holding that the district court did not clearly err when it found there were in fact neutral explanations for the replacement of PR with 9X.
AFFIRMED.
. Plaintiffs suggest that white candidates cannot be included among "blacks' preferred candidates,” but we disagree. Although some courts have cautioned that a candidate who receives the support of a majority of black voters in a multi-member election might not be a "preferred” candidate of blacks, see Collins v. City of Norfolk, Va., 883 F.2d 1232, 1238 (4th Cir.1989) (noting that other candidates may be " 'preferred by a significantly higher percentage of the minority community' " when each voter's ballot " ‘may contain votes for more than one candidate’ ”), cert. denied, 498 U.S. 938, 111 S.Ct. 340, 112 L.Ed.2d 305 (1990), courts generally have understood blacks’ preferred candidates simply to be those candidates who receive the greatest support from black voters. See, e.g., Jenkins v. Red Clay Consol. School Dist. Bd. of Educ., 4 F.3d 1103, 1127 (3rd Cir.1993) ("Since approximately 100% of the black voters of Red Clay supported Mitchell, he was clearly their candidate of choice."), cert. denied, - U.S. -, 114 S.Ct. 2779, 129 L.Ed.2d 891 (1994); Smith v. Clinton, 687 F.Supp. 1310, 1315-16 (E.D.Ark.1988) (three-judge panel). See also Sanchez v. Bond, 875 F.2d 1488, 1495 (10th Cir.1989) ("Nothing in the [Voting Rights Act] indicates that the chosen representative of a minority group must be a minority.”), cert. denied, 498 U.S. 937, 111 S.Ct. 340, 112 L.Ed.2d 305 (1990).
. Given this conclusion, we need not consider whether a showing that the minority-preferred candidates' lack of success is "somehow tied to race,” League of United Latin Am. Citizens v. Clements, 999 F.2d 831, 850 (5th Cir.1993) (en banc), cert. denied, - U.S. -, 114 S.Ct. 878, 127 L.Ed.2d 74 (1994), is a prerequisite to a finding of “legally significant white bloc voting.” Gingles, 478 U.S. at 56, 106 S.Ct. at 2769 (emphasis supplied). See generally Clements, 999 F.2d at 850-63 (concluding that such a showing is necessary).
. We note that a contrary holding would punish , the city for its commendable efforts to increase black representation on the city council by means of the appointment process.
. Those factors include: (1) “the extent of any history of official discrimination in the state or political subdivision that touched the right of the members of the minority group to register, to vote, or otherwise to participate in the democratic process”; (2) whether the challenged election district is "unusually large”; (3) "if there is a candidate slating process, whether members of the minority group have been denied access to that process"; (4) "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”; (5) "whether political campaigns have been characterized by overt or subtle racial appeals”; (6) "whether there is a significant lack of responsiveness on the part of elected officials to the particularized needs of the members of the minority group”; and (7) "whether the policy underlying the state or political subdivision’s use of [the electoral system] is tenuous.” Gingles, 478 U.S. at 36-37, 106 S.Ct. at 2759.
. We also note that the Senate Judiciary Committee report for § 2, upon which the Gingles Court heavily relied, cites with approval a 1978 Justice Department study which concluded, after a detailed investigation, that 9X did not dilute the voting power of black Cincinnatians. S.Rep. No. 205, 97th Cong., 2nd Sess. 35 (1982), reprinted, in 1982 U.S.C.C.A.N. 213.
. Although plaintiffs’ complaint also alleged that 9X violated the Fifteenth Amendment, plaintiffs have made no Fifteenth Amendment argument before this court.
. Plaintiffs suggest that this rule and the lengthy discussion that preceded it were dicta because *816the Arthur court went on to observe that racially neutral rationales supported the electorate’s decision in the referendum examined in that case. See 782 F.2d at 574. But that observation was necessary to show that the referendum in Arthur could be supported by a rationale that was not racially motivated. Our observation thus was made in the course of applying the rule quoted in the text, not in the course of supplanting it. Moreover, even if that rule somehow were dicta, we reaffirm it today.