Shirley Harvell and other voters in the Blytheville School District appeal from the district court’s order and supplemental findings of fact dismissing their Voting Rights Act complaint following our remand in Harvell v. Ladd, 958 F.2d 226 (8th Cir.1992). The defendants cross-appeal from the district court’s denial of their motion for attorneys’ fees and Rule 11 sanctions. We affirm in part and reverse in part.
I.
The Blytheville School District (the “district”) encompasses the city of Blytheville, Arkansas, and adjacent rural areas outside the city limits. According to the 1980 federal census, the district has a population of 23,-500, of whom approximately 64% are white and 35% are black. The voting age population, the pertinent population for Voting Rights Act purposes, is 14,500, of whom approximately 70% are white and 29% are black. The district court found that the black population in the district is geographically compact, located on the south side of the city of Blytheville, and is a politically cohesive group.
The Blytheville School Board (“the board”) consists of eight members. Each member serves a four-year term, and two terms expire each year. Under the election scheme that was in place until 1987, the candidate who received the most votes was elected to the board, whether or not that candidate received a majority vote. ‘When several candidates would run for one slot, only one of them black, the white vote would be split among the white candidates, while the black vote would concentrate on the black candidate, and the black candidate would be elected.” Harvell, 958 F.2d at 228.1 In 1987, this voting scheme was changed by statute to require board members to be elected by majority vote. Ark.Code Ann. § 6-14-121. Thus, unless one candidate receives a clear majority of the votes on the first round, there will be a run-off election between the two candidates who have received the most votes in the first round. No run-off elections have occurred since 1987 because all successful candidates have been elected by a majority of votes cast in the first round.
Prior to the 1970s, Blytheville voters had picked few black candidates to represent them on the Blytheville School Board. Beginning in 1974, however, with the election of *912Ayre E. “Pop” Lester, there has always been at least one black board member.2 From 1975 through 1991, two of the eight board members were black. All but two of the black members were elected to the board through unopposed races or bullet voting. Dr. Helen Nunn defeated a white candidate in 1982, then was re-elected in unopposed races in 1986 and 1990. Norvell Moore was elected through bullet voting in 1975. He was re-elected in unopposed races in 1979 and 1983. After winning re-election in 1987, Moore chose not to run for re-election in 1991.
Harvell, an unsuccessful black candidate for the board, and four black citizens3 of the district brought suit under Section 2 of the Voting Rights Act in the fall of 1989, after two elections under the new scheme. Har-vell challenged the at-large election of board members under the 1987 majority vote scheme. Harvell proposed an eight district scheme, under which one member of the board would be elected from each district. The district court found that the sustained electoral success of black candidates in filling two out of eight board positions precluded a finding of a Section 2 violation. Harvell v. Ladd, 759 F.Supp. 525, 529 (E.D.Ark.1991). Accordingly, the district court held that Har-vell had not set forth a prima facie case for a violation of Section 2 of the Voting Rights Act, dismissed Harvell’s complaint, and entered judgment in favor of the defendants. Id. at 529-30.
Harvell appealed, contending that the district court had erred in finding that a sustained minority presence on the board precluded a finding of a violation of the Act. Harvell, 958 F.2d at 228. Harvell further contended that the district court had failed to make findings sufficient to satisfy the requirements of Buckanaga v. Sisseton Independent School District, No. 54-5, 804 F.2d 469, 472 (8th Cir.1986). Id. The defendants cross-appealed, contending that the district court had erred in denying their motion for sanctions and attorneys’ fees and in refusing to dismiss the case on the basis of laches and equitable principles. Id.
We affirmed the denial of sanctions, but reversed the judgment dismissing the complaint and remanded to the district court for entry of further factual findings concerning the nine factors contained in the Senate Report accompanying the Voting Rights Act and set forth in Thornburg v. Gingles, 478 U.S. 30, 36-37, 106 S.Ct. 2752, 2758-59, 92 L.Ed.2d 25 (1986). Ladd, 958 F.2d at 230. Because of the change from a plurality to a majority vote scheme in the 1988 election and thereafter, we cautioned that “successes pri- or to the 1988 majority vote requirement do not necessarily reflect the black voters’ present ability to elect representatives of their choice under the current election scheme.” Id.
On remand, the district court entered findings with respect to each of the nine Senate Report factors. See Dist.Ct.Order, No. J-C-89-225 (E.DArk. Dec. 18, 1992). The court again dismissed Harvell’s complaint, this time based upon its finding that Harwell had failed to satisfy the third Gingles precondition because she did not “prove that the white majority votes such as to enable it ‘usually to defeat the minority’s preferred candidate.’ ” Id. at 9 (quoting Ladd, 958 F.2d at 229) (emphasis added by district court). The court held that Harvell had failed to meet her burden because the post-1987 low minority voter turnout could indicate that the black candidates were not the minority’s preferred candidates.
Harvell now appeals from the district court’s finding that she failed to satisfy her burden in proving the third Gingles precom-dition. Harvell also contends that the court’s findings with respect to a number of the Senate Report factors are clearly erroneous. Defendants cross-appeal, reiterating their re*913quest for sanctions under Federal Rule of Civil Procedure 11 and for attorneys’ fees under 42 U.S.C. § 1988.
II.
In 1982, Congress amended Section 2 of the Voting Rights Act to repudiate the “intent test” of City of Mobile, Alabama v. Bolden, 446 U.S. 55, 100 S.Ct. 1490, 64 L.Ed.2d 47 (1980). Gomez v. City of Watsonville, 863 F.2d 1407, 1411 (9th Cir.1988), cert. denied, 489 U.S. 1080, 109 S.Ct. 1534, 103 L.Ed.2d 839 (1989). Absent a showing that an electoral scheme was intentionally designed or maintained for a discriminatory purpose, the Mobile plurality did not permit a Section 2 challenge to the scheme. Mobile, 446 U.S. at 62-65, 100 S.Ct. at 1497-99. The 1982 amendments replaced the intent test with a “results test.” Gomez, 863 F.2d at 1411. Section 2, as amended, prohibits any state or political subdivision from using any “voting qualification or prerequisite to voting or standard, practice, or procedure ... which results in a denial or abridgement of the right of any citizen ... to vote on account of race or color.” 42 U.S.C. § 1973(a). But see Holder v. Hall, — U.S.-, 114 S.Ct. 2581, 129 L.Ed.2d 687 (1994) (holding that the size of a governing body is not subject to a Section 2 vote dilution challenge).
To establish a violation of Section 2, the plaintiff must show, based on the totality of the circumstances, that “members [of a protected class] have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice.” Id. § 1973(b). In Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986), the Supreme Court delineated three preconditions that the plaintiff must establish to show that a multi-member district violates Section 2.
First, the plaintiff must show that the minority group is sufficiently large and geographically compact to constitute a majority in a single-member district. Id. at 50, 106 S.Ct. at 2766. Second, the plaintiff must show that the minority group is politically cohesive. Id. at 51, 106 S.Ct. at 2766-67. Third, the plaintiff must show that the white majority votes sufficiently as a bloc to enable it, in the absence of special circumstances, usually to defeat the minority’s preferred candidate. Id.; see also Growe v. Emison, — U.S.-,-, 113 S.Ct. 1075, 1084, 122 L.Ed.2d 388 (1993).
In Gingles, the Supreme Court also set forth nine factors that the Senate mentioned in its report accompanying the Voting Rights Act to guide a court in determining whether the challenged electoral scheme dilutes the minority’s voting strength. Gingles, 478 U.S. at 36. These include (1) the history of voting-related discrimination in the state or political subdivision; (2) the extent to which voting in the state or subdivision is racially polarized; (3) the extent to which the state or subdivision has used voting practices or procedures that tend to enhance opportunities for discrimination against the minority group; (4) whether minority candidates have been denied access to any candidate slating process; (5) the extent to which minorities have borne the effects of past discrimination in relation to education, employment, and health; (6) whether local political campaigns have used overt or subtle racial appeals; (7) the extent to which minority group members 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 members of the minority group; and (9) whether the policy underlying the use of voting qualifications is tenuous. Id. 478 U.S. at 36-37, 106 S.Ct. at 2758-60.
III.
We apply the clearly erroneous standard of review to a district court’s ultimate finding of fact that a Voting Rights Act violation has not occurred. Gingles, 478 U.S. at 78-79, 106 S.Ct. at 2780-81; Ladd, 958 F.2d at 229. We will, however, “correct errors of law, including those that may infect a so-called mixed finding of law and fact, or a finding of fact that is predicated on a misunderstanding of the governing rule of law.” Gingles, 478 U.S. at 79, 106 S.Ct. at 2781 (quoting Bose Corp. v. Consumers Union, Inc., 466 U.S. 485, 501, 104 S.Ct. 1949, 1959-60, 80 L.Ed.2d 502 (1984)). When a district court’s findings are set aside because they *914rest on an erroneous view of the law, the case is usually remanded so that the district court can determine the issue using the correct legal standard. Gomez, 863 F.2d at 1411 (citing Pullmam-Standard v. Swint, 456 U.S. 273, 292, 102 S.Ct. 1781, 1792, 72 L.Ed.2d 66 (1982)). Remand is not necessary, however, when the record “permits only one resolution of the factual issue.” Id. (quoting Pullman-Standard, 456 U.S. at 287, 102 S.Ct. at 1789).
We turn, then, to Harvell’s claim that the district court erred in finding that she had failed to prove the third Gingles precondition, namely, 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.
Courts generally examine actual election returns in analyzing the Gingles preconditions. See Gingles, 478 U.S. at 63, 106 S.Ct. at 2772-73; Collins v. City of Norfolk, 816 F.2d 932, 935 (4th Cir.1987); Smith v. Clinton, 687 F.Supp. 1310, 1317 (E.D.Ark. 1988) (three-judge court). A court analyzing the second Gingles precondition, minority political eohesiveness, should look only to actual voting patterns rather than speculating as to the reasons why many minorities are apathetic. Gomez v. City of Watsonville, 863 F.2d 1407, 1416 (9th Cir.1988), cert. denied, 489 U.S. 1080, 109 S.Ct. 1534, 103 L.Ed.2d 839 (1989). Likewise, a court analyzing the third Gingles precondition should identify the preferred minority candidate by referring to how the minority voters actually cast their ballots rather than speculating why some minority voters choose not to cast ballots. See, e.g., Collins, 816 F.2d at 937-38 (candidate who receives most minority votes is preferred minority candidate); Jeffers v. Clinton, 730 F.Supp. 196, 208-09 (E.D.Ark. 1989) (three-judge court) (examining previous election returns and considering only the preferences of the minority voters who voted), aff'd, 498 U.S. 1019, 111 S.Ct. 662, 112 L.Ed.2d 656 (1991).
The record in this case contains no persuasive evidence explaining the post-1987 decrease in minority voter turnout. Moreover, low minority voter registration and turnout often evidence electoral schemes in which minorities do not have an equal opportunity to participate in the electoral process and elect representatives of their choice. Gomez, 863 F.2d at 1416 n. 4 (citing Gingles, 478 U.S. at 38-39, 106 S.Ct. at 2759-60). The district court should have identified the preferred minority candidates by considering only how the minority voters actually voted rather than engaging in speculation concerning the causes of minority voter apathy. We conclude, therefore, that the district court erred in finding that because a threshold level of eligible minority voters did not go to the polls, the post-1987 black candidates were not preferred minority candidates. We express no opinion, however, concerning the relevance of minority voter apathy when there is compelling'^evidence directly linking such apathy to a candidate’s unpopularity among the minority voters.
Because the district court’s findings rest on an erroneous view of the law, they must be set aside. We need not remand this case, however, because the record establishes that the post-1987 minority candidates were the minority voters’ preferred choice.
We cannot assume that every minority candidate is the minority voters’ preferred choice. As the Third Circuit has held, the plaintiff must “establish on an election-by-election basis, by a preponderance of the evidence, which black candidates are minority-preferred.” Jenkins v. Bed Clay Consol. Sch. Dist. Bd. of Educ., 4 F.3d 1103, 1126 (3d Cir.1993), cert. denied, — U.S. -, 114 S.Ct. 2779, 129 L.Ed.2d 891 (1994). We find persuasive the Third Circuit’s discussion of how a plaintiff meets the burden of showing that a minority candidate is the voters’ preferred choice:
[Experience does demonstrate that minority candidates will tend to be candidates of choice among the minority community. This practical experience leads to the inference that any particular minority candidate is minority preferred, and thereby takes plaintiffs a considerable distance towards meeting their production burden on this issue. This inference, however, is not enough on its own to meet this burden. Rather, plaintiffs must introduce some ad*915ditional evidence showing that the particular minority candidate is minority-preferred. The additional evidence required to meet the threshold, however, is not very substantial, and the burden may be satisfied with a variety of evidence, including lay testimony or statistical analyses of voting patterns.
Id.; see also Jeffers, 730 F.Supp. at 208 (“The fact is that there is a strong tendency for white voters to vote for white candidates when there is a black candidate in the race. Black voters behave in exactly the same fash-ion_ [I]t is a fact in present-day Arkansas politics, and there is no reason to suppose that it will change substantially in the near future.”).
In this case, the evidence establishes that the post-1987 black candidates were preferred minority candidates. Through regression analysis, Harvell’s expert determined that a very strong relationship existed between the black voting age population in a precinct and the support black candidates received in that precinct.4 The relationship between black voting age population and black candidate support was as strong in this ease as in Jenkins. In Jenkins, the plaintiffs’ expert performed a regression analysis to determine the degree of relationship between the racial composition in each political unit and the support a candidate received within that political unit. Id. at 1119 n. 10. The statistical analysis yielded a correlation coefficient of 0.91, “which represents a highly consistent association between the number of votes received by a candidate of a particular race and the racial composition of the polling place.” Id. at 1120. Because the regression analysis suggested that virtually 100% of the black voters voted for the black candidate, the Third Circuit concluded that the black candidate was the minority candidate of choice. Id. at 1127-28. Harvell’s expert testified that his regression analysis indicated that black voters overwhelmingly vote for black candidates, and there is no evidence to rebut this showing. Accordingly, we conclude that the post-1987 black candidates were the minority’s preferred candidates. See also Citizens for a Better Gretna v. City of Gretna, 834 F.2d 496, 501 n. 11, 502 (5th Cir.1987) (holding that correlation coefficients of .963 and .926 revealed a “significant number” of blacks voting for a black candidate and qualified the candidate as the black-preferred candidate), cert. denied, 492 U.S. 905, 109 S.Ct. 3213, 106 L.Ed.2d 564 (1989).
Some lay testimony indicated that Harvell and Middlebrook may have had certain qualities that some minority voters may have found unappealing. There was no evidence, however, that these qualities caused Harvell and Middlebrook not to be the minority community’s preferred candidates. Moreover, “[s]poradic lay testimony, while not irrelevant, is necessarily less indicative of black voters’ voting patterns generally than the regression analysis.” Jenkins, 4 F.3d at 1127.
As we discussed earlier, the district court emphasized the pos1>-l987 low voter turnout. The statistical evidence, however, reveals that even in those elections in which the minority voter turnout was low, black voters overwhelmingly supported black candidates and white voters supported white candidates. We find the statistical analyses of the actual election returns more reliable than speculative explanations for the low voter turnout. Moreover, we have held that a court should limit its examination to actual election returns when the record does not adequately account for the cause of a particular voting pattern. Accordingly, because the record indicates that the post-1987 black candidates were the minority’s preferred choice, we hold that Harvell has established the third angles precondition.
Recently, the Supreme Court reiterated that satisfying the three angles preconditions is not sufficient to establish a Section 2 violation. Johnson v. De Grandy, — U.S. -, 114 S.Ct. 2647, 129 L.Ed.2d 775 (1994) (finding that the district court erred by implicitly concluding that the failure to maximize the number of majority-minority districts violates Section 2). Thus, we turn to Senate Report factors to determine whether, based upon the totality of the circumstances, Harvell has shown that because of the at-large *916election scheme, minority voters “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 Supreme Court has recognized that when analyzing a Section 2 claim the two most important Senate factors are the extent to which voting is racially polarized and the extent to which minorities have been elected. Gingles, 478 U.S. at 48 n. 15, 106 S.Ct. at 2765 n. 15. Both of these factors weigh in favor of a finding of a Section 2 violation. The district court found that voting in the school board elections is racially polarized. See Harvell v. Lofton, 759 F.Supp. 525, 527-28 (E.D.Ark.1991). The city does not dispute this finding. Since the enactment of the majority vote requirement, Dr. Nunn has been the only successful black candidate. The district court found that her victory fell within the “special circumstances” the Supreme Court recognized in Gingles because she ran unopposed as an incumbent. Id. at 530.
Harvell claims that the district court’s findings on four other Senate factors are clearly erroneous. These other factors, if present, are “supportive of, but not essential to, a minority voter’s claim.” Gingles, 478 U.S. at 48 n. 15, 106 S.Ct. at 2765 n. 15. We will examine each of her arguments in turn.
The district court found that “historic discrimination in the Blytheville School District area in regards to health, education, and employment does impair the ability of some blacks to participate effectively in the electoral process.” Dist.Ct.Order, No. J-C-89-225, at 5 (E.D.Ark. Dec. 18, 1992). The district court discounted this finding, however, because “it cannot be contested that many of the impediments and economic disadvantages of over a quarter century ago have been alleviated and their effect on voting in Blytheville today is questionable.” Id. With all due respect, we conclude that the district court erred by discounting its initial finding in view of the uncontroverted evidence that the percentage of black citizens in Blytheville who live below the poverty level, who are unemployed, and who have not completed high school is significantly greater than the percentage of white citizens. Moreover, the record links the low socioeconomic status of blacks to their inability to participate effectively in the political process.
Although the district court acknowledged that it should take judicial notice of the history of official racial discrimination in the electoral process in Arkansas, it gave this factor little weight because of state and national efforts to end racial discrimination. Id. at 3. We have consistently found that “[t]he state has a history of official discrimination in its electoral process.” Whitfield v. Democratic Party of State of Ark., 890 F.2d 1423, 1424 (8th Cir.1989), cert. denied, 498 U.S. 1126, 111 S.Ct. 1089, 112 L.Ed.2d 1193 (1991). As the Fifth Circuit has noted, because “Congress was concerned not only with present discrimination, but with the vestiges of discrimination which may interact with present political structures to perpetuate a historical lack of access to the political system[,] ... the court must provide a sounder basis for its conclusion than its personal opinion that discrimination has been eradicated in the recent past.” Westwego Citizens for Better Government v. City of Westwego, 872 F.2d 1201, 1211-12 (5th Cir.1989). Because the district court did not provide any reason other than its opinion concerning recently taken steps to eradicate discrimination, however laudable and salutary those steps may be, we agree with Harvell that the district court erred by giving insufficient weight to the history of racial discrimination in Arkansas. ■
When analyzing the extent to which the voting practices and procedures in Blythe-ville School District may enhance the opportunity for discrimination, the district court considered, as provided by the Senate Report, the majority vote requirement. The district court found that the Arkansas majority vote requirement might enhance the opportunity for discrimination against black voters. Dist.Ct.Order, No. J-C-89-225, at 4 (E.D.Ark. Dec. 18, 1993). The court noted, however, that there had been no run-off elections since the enactment of the majority vote requirement and that no black candidate would have been successful under the preexisting plurality system. Id. Although the implication of the district court’s finding is *917that black voters are no worse off under the majority vote system than they were under the pre-existing plurality system, we believe that the voting pattern established under the new system requires a contrary finding. Under the prior system, black candidates may have had a chance of electoral success; under the new system, given the voting patterns of post-1987 elections, they appear to have almost none. The district court found that the electorate is racially polarized because the “majority of black voters vote for black candidates and the majority of white voters vote for white candidates.” Harvell v. Lofton, 759 F.Supp. at 527 (E.D.Ark.1991). If only twenty-nine percent of the voters (the black voting age population) vote for a black candidate, it is mathematically impossible for that candidate, absent the “special circumstances” the Supreme Court recognized in Gingles, to receive a majority of the votes.
Although there is some evidence to the contrary, the district court’s finding that the board is responsive to the complaints and needs of the minority community is not clearly erroneous. As we have noted, however, this factor is not essential to Harvell’s claim. Indeed, the Senate Report states that a lack of responsiveness by elected officials to the needs of the minority community would be a factor of only “limited relevance.” 1982 U.S.C.C.A.N. 177, 206-07; see also Westwego Citizens for Better Government v. City of Westwego, 946 F.2d 1109, 1123 (5th Cir.1991) (finding a Section 2 violation when the plaintiff did not prove a lack of responsiveness); Jeffers v. Clinton, 730 F.Supp. 196, 213-14 (E.D.Ark.1989) (three-judge court) (same), aff'd, 498 U.S. 1019, 111 S.Ct. 662, 112 L.Ed.2d 656 (1991).5
In summary, we hold that the district court erred by finding that Harvell did not satisfy the third Gingles precondition. The record establishes that the post-1987 black candidates were the preferred minority candidates. After considering the totality of the circumstances, we conclude that the at-large electoral scheme dilutes the minority’s voting strength. Accordingly, we reverse the district court’s judgment dismissing Harvell’s claim and remand for implementation of a plan that comports with the requirements of Section 2.
Our holding that plaintiffs are entitled to relief on their claim perforce forecloses defendant’s application for sanctions pursuant to Federal Rule of Civil Procedure 11 and attorneys’ fees pursuant to 42 U.S.C. § 1988. Accordingly, we affirm the district court’s denial of sanctions and attorneys’ fees.
The judgment is affirmed in part and reversed in part, and the ease is remanded to the district court for the entry of an appropriate remedial decree.
. This process is referred to colloquially as "bullet voting” or "single-shot voting.”
. The successful black candidates and their respective terms of service on the board are as follows: Ayre E. "Pop” Lester (1974-82); Norvell Moore (1975-91); Dr. Helen Nunn (1982- ).
. The five named plaintiffs are Shirley M. Har-vell, Rev. Emmanuel Lofton, Hattie Middlebrook, Mary Alice Jones, and Jacquelin Henton. Har-vell was an unsuccessful candidate for the board in 1989, 1990, and 1991. Middlebrook was defeated in her attempt to run for the board in 1991, after this suit was initiated. For the sake of convenience, we refer to the plaintiffs in this opinion collectively as “Harvell.”
. Appendix II contains the results of the expert’s statistical analysis.
. Because Harvell has not challenged the district court's findings with respect to the other Senate Report factors, we need not address them,