
    Volma OVERTON, et al., Plaintiffs-Appellants, and Ernesto Calderon, et al., Plaintiffs-Intervenors-Appellants, v. CITY OF AUSTIN, et al., Defendants-Appellees, and Black Citizens Task Force, Defendant-Intervenor-Appellee.
    No. 87-1805.
    United States Court of Appeals, Fifth Circuit.
    May 1, 1989.
    
      David Van Os, Austin, Tex., for Overton, et al.
    Jose Garza and Judith A. Sanders-Castro, San Antonio, Tex., for Calderon, et al.
    Iris J. Jones, Barney L. Knight, City Attys., Steve Bickerstaff and C. Robert Heath, Austin, Tex., for City of Austin.
    Terry Davis, Austin, Tex., for Black Citizens Task Force.
    Before THORNBERRY, RUBIN and JONES, Circuit Judges.
   PER CURIAM:

We are asked by black and Mexican-American plaintiffs-appellants to review whether the City of Austin’s at-large, majority place system for election of city council members violates Section 2 et seq. of the Voting Rights Act of 1965, 42 U.S.C. § 1973 et seq. (1982) (as amended). The district court performed a “searching and practical evaluation of ‘past and present reality’,” S.Rep. No. 417, 97th Cong., 2d Sess., reprinted in 1982 U.S.Code Cong. & Admin.News 177, 208, both before Thornburg v. Gingles, 478 U.S. 80, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986), and, with additional evidence, after Thornburg on remand from this Court. 798 F.2d 150. The district court found no violation.. We affirm.

I. INTRODUCTION

Austin elects six council members and a mayor by majority vote using an at-large system. Although the Texas capital city has had both a black and a Mexican-American on its council for nearly 15 years, this was not always the case. From 1924 to 1951, the city council was elected at-large without designated places by plurality vote. Black candidates ran unsuccessfully for the council in 1949, 1951, 1965, and 1969, and a Mexican-American candidate was defeated in a 1969 run-off. Building upon this skeletal electoral history, the plaintiffs, black and Mexican-American individuals, the NAACP and MALDEF, seek to prove two contentions: that the 1953 city charter amendments, which introduced a place system and majority vote requirement, were discriminatorily motivated and thus warrant Voting Rights Act relief; and that notwithstanding significant successes of minority candidates in recent years, blacks and Mexican-Americans have suffered actionable racial vote dilution. As relief, they urged upon the district court two possible forms of single-member council districts: a six council member, one mayor scheme with nearly a majority of black voting age citizens in one district; or an eight council member, one mayor plan in which blacks and Mexican-Americans would comprise a majority in two districts.

Our analysis starts with amended Section 2 of the Voting Rights Act:

(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) ... is established if, based on the totality of the 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) ... 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 (1988). Congress provided that the totality of the circumstances determines whether, because of a specific voting practice like multimember district-ing, the political processes of a State or subdivision are not equally open to participation by all races. Simultaneously, Congress rejected any requirement for proportional representation by race. See S.Rep. No. 417, supra.

The Supreme Court’s first significant interpretation of amended Section 2 is found in Thornburg v. Gingles, 478 U.S. 30, 106 S.Ct. 2752, 92 L.Ed.2d 25 (1986). The Supreme Court viewed the report of the Senate Judiciary Committee accompanying the bill that amended Section 2 as instructive of the various factors that might be probative of a Voting Rights Act claim:

The Senate Report specifies factors which typically may be relevant to a § 2 claim: the history of voting-related discrimination in the State or political subdivision; the extent to which voting in the elections of the State or political subdivision is racially polarized; the extent to which the State or political subdivision has used voting practices or procedures that tend to enhance the opportunity for discrimination against the minority group, such as unusually large election districts, majority vote requirements, and prohibitions against bullet voting; the exclusion of members of the minority group from candidate slating processes; the extent to which minority group members bear the effects of past discrimination in areas such as education, employment, and health, which hinder their ability to participate effectively in the political process; the use of overt or subtle racial appeals in political campaigns; and the extent to which members of the minority group have been elected to public office in the jurisdiction ... The Report notes also that evidence demonstrating that elected officials are unresponsive to the particularized needs of the members of the minority group and that the policy underlying the State’s or the political subdivision’s use of the contested practice or structure is tenuous may have probative value.

The Court specifically recognized that:

Although the Senate Report espouses a flexible, fact-intensive test for § 2 violations, it limits the circumstances under which § 2 violations may be proved in three ways. First, electoral devices, such as at-large elections, may not be considered per se violative of § 2. Plaintiffs must demonstrate that, under the totality of the circumstances, the devices result in unequal access to the electoral process, [citation omitted] Second, the conjunction of an allegedly dilutive electoral mechanism and the lack of proportional representation alone does not establish a violation, [citation omitted] Third, the results test does not assume the existence of racial bloc voting; plaintiffs must prove it.

Thornburg, 478 U.S. at 44-46, 106 S.Ct. at 2763-64.

Discussing the issue of multimember districts, the Court again noted that they are not per se violative of minority voters’ rights. Thornburg, 478 U.S. at 48, 106 S.Ct. at 2765. It held, “Minority voters who contend that the multimember form of districting violates § 2, must prove that the use of a multimember electoral structure operates to minimize or cancel out their ability to elect their preferred candidates. See, e.g., S.Rep. 16.” Id.

The Court then noted that,

While many or all of the factors listed in the Senate Report may be relevant to a claim of vote dilution through submergence in multimember districts, unless there is a conjunction of the following circumstances, the use of multimember districts generally will not impede the ability of minority voters to elect representatives of their choice.

Id. 478 U.S. at 47-50, 106 S.Ct. at 2765-66. The circumstances cited by the Court are that the minority group:

(1) demonstrate that it is sufficiently large and geographically compact to constitute a majority in a single-member district;
(2) show that it is politically cohesive; and
(3) 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.

See id. 478 U.S. at 50-52, 106 S.Ct. at 2766-67.

The remainder of the Court’s opinion elaborates upon the nature of the evidence relevant to these three factors.

Neither the majority nor the dissenters in Thornburg — nor Congress itself— adopted a talismanic test for a Section 2 violation. Reliance upon either the Court’s voter dilution threshold analysis, the “totality of the circumstances,” or upon alleged intentional discriminatory acts therefore becomes a fact-bound, intensely local inquiry highly dependent upon the district court’s conclusions. As such, the clearly erroneous test applies to the district court’s findings. Thornburg, 478 U.S. at 79, 106 S.Ct. at 2781; Campos v. City of Baytown, 840 F.2d 1240 (5th Cir.1988).

Despite this deferential standard of review, we may not close our eyes to the fact that the fluidity of the Section 2 analysis, as glossed by Thornburg, may encourage litigants to aggregate statistics or facts rather indiscriminately in the hope that a district court will simply count facts rather than analyze them carefully. The district court did not fall prey to that short-coming here. Indeed, the case was well-tried on both sides and resulted in copious, comprehensive findings by the trial court. We must review those findings in some detail to lend perspective to the appellants’ assignments of error.

II. SUMMARY OF DISTRICT COURT OPINIONS

Austin’s population, updated to 1984, exceeds 362,000, approximately 12% of whom are black and 18% of whom are Mexican-American. The court’s pertinent findings may be grouped under six topics: (1) history of multimember districting; (2) slating; (3) racial appeals in past elections; (4) responsiveness of city council to minority needs; (5) tenuousness of the justification for multimember districting; (6) the Thornburg factors.

1. History of multimember district-ing.

Austin implemented an at-large election system in 1909, calling for a five member council elected at large on a plurality basis. The mayoral position was then filled by an election among the five sitting council members. In 1953, the city adopted a majority vote requirement and chose to elect councilmen by place designation. Contrary to the appellants’ contentions, which will be discussed below, the court found that the 1953 charter change did not result from a racially discriminatory intent, has not been maintained for that purpose, and has had no such result. While the court acknowledged that a black candidate ranked eighth in the number of votes received among 14 council candidates in 1951, the court found it “pure folly that a major and radical change in the entire electoral system was a reaction to the candidacy of a black man who ran for office.”

Between 1951 and 1953, a 15 member committee was created to propose changes in the Austin city charter. The amendments were the product of a year-long study by this committee, which included representatives of minority communities. The propositions voted on in 1953 represented a complete overhaul of the structure of city government. There were more than 30 separate propositions on the ballot. Issues included the power of the city manager, eligibility requirements for candidates, and the use of limited-purpose annexation.

In light of the wide-ranging changes proposed, the court was unable to conclude that racial discrimination motivated two of those changes. The court found insufficient credible evidence that any racial tension existed in Austin in 1953 or that it was “well known at the time that the change to place and majority requirements would dilute minority voting power.” Evidence was absent, the court stated, that supporters of the charter amendments or the media emphasized the potential vote dilution aspects of the change. The court noted that the city did not also adopt staggered terms or other potentially vote-diluting arrangements. Proposition 5, which effected the change to place elections, also brought about other changes, including setting the date for elections on the first Saturday in April, lowering the residence requirement for councilmen, and eliminating the requirement for a petition of 25 voters to accompany a candidate’s filing. The court concluded that the city of Austin did not intend to discriminate when it adopted a majority, at-large electoral system in 1953.

2.Slating.

The district court defined slating as the creation of a package or slate of candidates, before filing for office, by an organization with sufficient strength to make the election merely a stamp of approval of the pre-ordained candidate group. Slating could thus operate to control effective access of minorities to the ballot. The trial court found no evidence that minorities experience any such roadblocks to taking their place on the ballot for any council seat. Further, the court found that no group has the political power or financial resources to control the election of a slate of candidates.

The court accepted arguendo the appellants’ identification of the Austin Progressive Coalition (APC) as a “powerful endorsing group.” Nevertheless, the appellants failed to establish that members of minority groups were not allowed to participate in the APC or that minority candidates were denied its endorsement. On the contrary, at least one black and one Mexican-American have been endorsed by the APC and elected by the voters in every city council election since 1975. At least one black candidate was endorsed and elected in the 1971 and 1973 elections. A second Mexican-American, DeLeon, was endorsed but not elected in 1981.

The court found that minority candidates, who also received the approval of the minority community, are endorsed by the APC. It also found that minority groups participate in the APC endorsement process. In Austin, the court observed, a number of endorsing groups exist, each of which pursues its own agenda. No evidence suggested that the value or effect of an APC endorsement is more significant than that of the NAACP or the Mexican-American Democrats, or that APC endorsement is more highly coveted than that of any other group.

The court recognized that various groups donate money, time and energy to the election of candidates, but it found no single slating group to be of sufficient strength or motivated by the intent to deny meaningful access to minorities or to dilute their voting strength. In short, the court found that Austin politics are influenced by factions who form constantly shifting coalitions motivated by issues other than racial exclusivity.

3. Racial appeals.

No Austin campaign in recent memory has included issues of race or ethnicity. The court particularly dismissed appellants’ contention that subliminal racial appeals accompanied the voters’ rejection in 1985 of an amendment proposing single-member districts.

4. Responsiveness to minority needs.

The court considered the Austin city council to be especially attentive to the needs of minorities. It suggested that an at-large electoral system forces each council member to respond to the minority community, to whom he must look for support at the polls. The court considered testimony by minority council members that they felt unable fully to represent the minority community, but it found this testimony vague. The court observed that numerous city officials, including the city manager, senior assistant city manager, and seven out of 17 department heads are black or Hispanic. Among the city’s various boards and commissions, a total of 16% of the appointments in 1984-85 were black and 11.5% were Mexican-Americans. These figures were higher than those of 1976-77. The city passed antidiscrimination laws covering public accommodations, employment, and housing in 1976 and 1977. Sixty percent of the city’s $273,000,000.00 in community development bloc grant funds between 1979 and 1984 was related to housing. The city also funds a corporation to make mortgage loans to low-income persons, provides essential medical services for the poor, operates a shelter for transients and constructed a job training center. Forty-two percent of the city’s parks and recreation facilities and forty-five percent of all city facilities are located in the three of Austin’s eight fiscal districts having the highest minority populations.

In 1985, the ethnic composition of the city of Austin’s work force was approximately 19% black (compared to 12.2% in total population); 20.6% Hispanic (compared to 18.7% in total population), and 59.1% Anglo (compared to approximately 68% in total population). Minority workers are employed extensively in administrative positions with the city, and their numbers and percentages in such categories have increased since 1975. In addition, the city has effectively promoted minority business enterprises through its contract awards. Furthermore, Travis County, which includes Austin, enjoys black and Mexican-American representation in the state legislature. The Austin Independent School District has had at least one black and one Hispanic member since 1972.

5. Tenuousness.

The court found that the city’s reasons for maintaining its at-large and place requirements for city council membership are not tenuous. Each time the issue of single member districts has been placed on the ballot, it has failed — most recently in January 1985. The court credited the defendants’ evidence that the at-large system enhances minority access, particularly because the minority community is substantially dispersed throughout the city. It concluded that appellants did not carry their burden of establishing that an at-large system is maintained on a tenuous basis as a pretext for discrimination.

6. Thornburg factors.

Focusing on the threshold vote dilution factors enumerated in Thornburg, the court reviewed various city council election results from 1965 through 1987 and analyzed statistics from 52 Austin precincts concerning elections involving minorities who ran for city council. The court found that city council elections in which a minority candidate ran during the 1960’s were racially polarized.

A. Size and geographical compactness.

The Thornburg analysis first requires the court to determine whether the minority population is sufficiently large and geographically compact to constitute a majority in a single-member district. Appellants furnished proposals embodying either a six-one council and mayoral election plan or an eight-one plan which expanded the city council by two members. The court agreed that in the six-one proposal, the proposed largely black district would contain an approximately 50.7% black population, but a voting age black population of only 45.8%. The Mexican-American population would be 13.9%, of which 12% were estimated to be of voting age. In the eight-one plan, a black population of 60.6% and a voting age black population of 57.2%, could occur in one district. In neither type of plan would Mexican-Americans command a voting age majority, although one district in an eight-one proposal would include a 57.5% Mexican-American population, with a voting age population of 49.8%. The Mexican-American claim to a specific electoral district therefore is inseparable, as appellants acknowledge and the court found, from its claim to be politically cohesive for Thorn-burg purposes with the black population.

The court noted that neither the black nor Mexican-American plaintiffs had submitted a six-one plan in which they would separately constitute a majority of the voting age population in the proposed districts. The court relied upon various comments in Thornburg which pointed to the requirement of a voting age majority of minority voters in a proposed single-member district. The court discounted the appellants’ request that the 1980 census figures be updated to include all members of the minority population who were eleven or older among the eligible voters in their district. The court also concluded, however, that Thornburg permits it to order an expansion of the city council to eight members — a remedy that would guarantee a black majority voting age population district and would permit adoption of a district in which Mexican-Americans, although not a majority, could be aggregated with blacks to achieve such a result. This possibility led the court to consider whether blacks and Hispanics are politically cohesive according to Thornburg’s second prong.

B. Political cohesiveness of the minority groups.

The court found that blacks and Mexican-Americans are, as individual groups, politically cohesive.

The court agreed that the black and Mexican-American communities share common concerns and have common histories of discrimination. It did not, however, rate as conclusive the appellants’ affidavits and depositions from politically active Austin citizens that reflect their perceptions of the cohesiveness between the two minority groups. First, the court noted that such perceptions were not backed up by survey or other demonstrative evidence to reinforce these conclusions. Second, the court found such testimony counter-balanced by affidavits submitted on behalf of the city of Austin which denied any systematic political cohesiveness.

By contrast, the court rated as significant the voting statistics concerning the frequency with which blacks and Mexican-Americans supported the same candidates. The aptness of such a comparison was drawn from Thornburg’s comment that “a showing that a significant number of minority group members usually vote for the same candidates is one way of proving the political cohesiveness necessary to a vote dilution claim_” 478 U.S. at 56, 106 S.Ct. at 2769. Between 1975 and 1983, the Mexican-American preferred candidate was supported by an average of 69% of Austin’s black voters, and the black preferred candidate was supported by an average of 73% of Mexican-American voters. More significantly, however, in those same elections, Anglos voted with one or the other minority groups more frequently than the two groups voted together. Thus, in elections where Anglos ran against minorities and supported a different candidate than did the minority groups, minorities voted together five times and voted differently four times. This result, the court found, is hardly evidence of cohesiveness.

The court also compared the results of a 1987 race for Place 1 in which a black, Terry Davis, and a Mexican-American, Gilbert Martinez, were candidates. In that race, Davis received 12.1% of the vote in Mexican-American precincts, to Martinez’s 46.7%. In the black precincts Martinez garnered 10.8% of the vote, compared to Davis’s 63.5%. The court held that such evidence likewise failed to support a finding of cohesiveness between blacks and Mexican-Americans. The court considered it likely that in a district with a large percentage of both minorities, black and Mexican-American candidates will oppose each other for office, and if they did so, the residual Anglo vote would determine the outcome of the election.

C. Evidence of white bloc voting.

The district court commenced its discussion of the third prong of Thornburg by observing that the Supreme Court did not reach a consensus on what type of evidence proves that a white bloc-voting majority will usually defeat the minority’s preferred candidate. Justice Brennan’s opinion for four members of the Court stated flatly that causation or intent are irrelevant in comparing the voting behavior of whites and a minority, and that the race of the candidate is irrelevant. Justice White disagreed with this portion of the opinion. Justice O’Connor’s four-member concurrence stated that although evidence of the reasons behind voting patterns could not be used to rebut a plaintiff’s showing of racial political cohesiveness, such evidence is relevant

in answering the question whether bloc voting by white voters will consistently defeat minority candidates. Such evidence would suggest that another candidate, equally preferred by the minority group, might be able to attract greater white support in future elections.

478 U.S. at 100, 106 S.Ct. at 2792.

The district court concluded that regardless of which view of white bloc voting is adopted, the appellants’ evidence failed to demonstrate it.

The district court first pointed out that all members of the Court in Thornburg agree that consistent, sustained minority electoral success is presumptively “inconsistent with ... [an] allegation that the ability of black voters ... to elect representatives of their choice is not equal to that enjoyed by the white majority.” 478 U.S. at 77, 106 S.Ct. at 2780. Since 1971, there has consistently been a black representative on the city council, and since 1975 there has been a Mexican-American representative on the city council. The court held that while Thornburg suggests that the occasional election of minority candidates owing to special circumstances such as lack of opposition or incumbency may not rebut the existence of racially polarized voting, such circumstances may not be permitted to support a Section 2 claim when there is otherwise a lack of racially polarized voting. In Austin, as noted, the court found no racial polarized voting since the late 1960’s. The court found no “gentleman’s agreement” that minorities might prevail only in Places 5 and 6 on the city council, allowing the racial polarization of the remaining council seats. To support this conclusion, the court observed that in 1985 and 1987, Gilbert Martinez obtained a majority of votes in certain Anglo precincts even while running for Place 1.

Second, the court found no persuasive evidence of white bloc voting. Between 1975 and 1983, the winning candidate in Austin council races was the black preferred candidate 85.7% of the time and was the Mexican-American preferred candidate 80% of the time. Since 1975 anglo voters have given from 47% to 84% of their vote to minority candidates who have prevailed in city council elections.

The court explained in detail why it did not accept as probative the testimony of appellants’ expert Dr. Miller whose bivari-áte ecological regression analysis was a cornerstone of the appellants’ polarization proof. Even assuming that Dr. Miller’s results are reliable and indicate that some recent elections have been polarized, the court found that those results do not necessarily show that the white majority will usually vote as a bloc to defeat the minority preferred candidates. Additionally, the court found Dr. Miller’s statistical analysis to be seriously flawed. The court said:

the analysis of Dr. Miller is highly suspect for several reasons. Dr. Miller used different measures to determine Black and Mexican-American voting strength. He failed to take into account the difference in population sizes of voting precincts. His analysis resulted in impossible results [in some instances]_ In addition, he completely failed to establish a confidence level for the results of his regression analysis.... Without such a measure, there is no way to determine if the results are statistically significant.

The court, in short, felt it could not accept the expert’s analysis at face value.

III. DISCUSSION

Appellants take issue with virtually every factual and legal conclusion of the district court.

We need not address all of their contentions, however, because failure to establish any singlé criterion of Thornburg is fatal to their case. Thornburg, 478 U.S. 30, 48-51, 106 S.Ct. 2752, 2765-67 (1986). We conclude that the trial court was not clearly erroneous in its finding that the white majority in Austin did not vote sufficiently as a bloc to enable it to defeat the minorities’ preferred candidates. We must also address the appellants’ contention that Austin’s multimember district plan was enacted and perpetuated with an intent to discriminate against minority groups.

A. Evidence of Racially Polarized Voting.

A most perplexing aspect of Thornburg is its discussion of what constitutes evidence of legally significant, racially polarized voting. The third prong of the plurality opinion requires proof that the white majority votes sufficiently as a bloc to enable it usually to defeat the minority’s preferred candidate. The “usual predictability of the majority’s success distinguishes structural dilution from the mere loss of an occasional election.” Thornburg, 478 U.S. at 51, 106 S.Ct. at 2767. Justice Brennan’s opinion for four members of the Court holds that statistical evidence that different races vote differently, by itself — without proof of causation or intent — establishes racially polarized voting. 478 U.S. at 62, 106 S.Ct. at 2772-73. Justice White disagreed with this portion of the opinion and particularly took issue with its statement that the race of the candidate preferred by minority voters is irrelevant to racial bloc voting analysis. 478 U.S. at 83, 106 S.Ct. at 2783. Justice O’Connor, representing four members of the Court, agreed with Justice White on this point and further suggested that evidence of factors other than statistical racial voting patterns should be considered in assessing minority vote dilution. 478 U.S. at 101, 106 S.Ct. at 2792.

The district court responded conservatively to this uncertainty, by focusing on statistical evidence of election contests involving minority candidates and by relying largely on election results, rather than extrinsic factors, in drawing its conclusions on racial vote polarization. In the absence of further Supreme Court guidance, we do not criticize this methodology, although it is not the only permissible way to approach § 2 claims. Cf. Houston v. Haley, 859 F.2d 341 (5th Cir.1988), vacated on other grounds, 869 F.2d 807 (5th Cir.1989). Two findings are critical to the trial court’s decision. It declined to grant much weight to the analysis performed by appellants’ expert Dr. Miller, and it found that the sustained history of electoral success by black and Mexican-American candidates, which has yielded proportional (or greater) representation on the Austin council for over 10 years, refuted the contention of racially polarized voting.

Attempting to breathe force into their expert’s opinion that Austin elections have been racially polarized, the appellants assert that Dr. Miller’s analysis used precisely the same methodology as that of the Thornburg expert at the trial level. Bivar-iate ecological regression analysis was used by both experts, but that does not suffice to establish the reliability of the conclusions of the expert in this case. As we have earlier recounted, the district court found those conclusions suspect primarily because of the expert’s failure to achieve meaningful correlation coefficients and his use of inconsistent measures of minority voter strength.

Both criticisms are valid. Bivariate ecological regression analysis has been frequently employed in Section 2 cases after Thornburg. See, e.g., Campos v. City of Baytown, Texas, supra; Citizens For a Better Gretna v. City of Gretna, La., 834 F.2d 496 (5th Cir.1987), reh. denied 849 F.2d 1471 (5th Cir.1988). Crucial to the validity of regression analysis are the values for “r” and “r”, which measure the strength of the correlation and linear relationship of the variables being examined, in this case the race of the voter and the candidate he supports.

In this case, Dr. Miller calculated “r” values mainly between 0.5 and 0.7 for the 43 races the plaintiffs claim are polarized, and “r” values above 0.8 in only 6 cases. Consequently, squaring these “r” values to calculate coefficients of determination demonstrates that race explains more than half of the variance in voting in only six of the races relied on by the plaintiffs. In context, and in view of the district court’s finding that “Dr. Miller’s methodology contains so many questionable practices that the Court cannot place much weight in the results,” we cannot reject the court’s finding of a lack of polarized voting as clearly erroneous.

The trial court also properly recognized the limitations inherent in Dr. Miller’s differing measures of the ethnic composition of precincts. Explaining that his base data were the most reliable supplied to him, Dr. Miller extrapolated the number of black voters in a precinct from census data on black population, without regard to age levels or voter registration. He estimated the number of Mexican-American voters, on the other hand, from the number of Spanish surnames on precinct voter registration lists. These estimates tend to overstate minority vote results unless minority voter turnout is as high or higher than that of the rest of a precinct. This overstatement is magnified by Dr. Miller’s calculation of the Anglo vote as the remainder after subtracting minority votes from total votes in each precinct. Consequently, these measures tend to inflate the level of minority support for a candidate. In this case, a number of the expert’s computations reflected such difficulties, yielding figures of Mexican-American support of over 100% in some instances and, for Ang-los and Mexican-Americans, support levels of less than 0% for various candidates. Although we agree that absolute perfection in the base statistical data is not to be expected, a trial court should not ignore the imperfections of the data used nor the limitations of statistical analysis.

Appellants also fault the trial court’s reference to results from the 1985 and 1987 races involving Gilbert Martinez as evidence refuting the alleged racial polarization of the Anglo vote. The court, however, relied on the city’s “extreme case” or “homogeneous precinct” analysis in concluding that Martinez performed extremely well in certain predominantly Anglo precincts. The court did not suggest that the precinct percentages reflected the overall vote. This type of analysis — the limitations of which the court expressly recognized — has been utilized in other Voting Rights Act cases. See, e.g., Gingles v. Edmisten, 590 F.Supp. at 367-68 n. 29; Citizens For a Better Gretna, 834 F.2d 496; Campos v. City of Baytown, 840 F.2d 1240.

Simply put, the district court’s findings regarding the presence of racially polarized voting were not clearly erroneous. Austin has repeatedly elected black and Mexican-American council members during the past 17 years. Even according to appellants’ voting analysis, the winning minority candidates frequently received well over fifty percent (50%) of the Anglo vote and were also the preferred candidates of the minorities. Minority candidates have routinely been elected to other posts in Austin and the surrounding Travis County. To adopt appellants’ position that racial bloc voting nonetheless inhibits minority participation in Austin’s government, we would at least have to ignore the 14 successful races by four different minority candidates in recent years, a fact the Supreme Court holds “presumptively inconsistent” with a Section 2 claim. To ignore those elections, we would have to find, contrary to the district court, that they were the product of a slating process that essentially rigged Austin’s elections against minority access. However, ample evidence in the record supports the trial court’s finding that the wide-open and vigorous Austin political system is not manipulated by any one group, and is certainly not manipulated for racial reasons.

B. Intentional Discrimination.

Appellants alternatively contend that the City of Austin inaugurated its at-large majority place system with the intent to discriminate against blacks and Mexican-Americans. They contend that the court’s findings regarding the 1953 charter revision which introduced the present system are clearly erroneous; that those findings were not evaluated according to the appropriate legal standard; and that where discriminatory intent underlying a statute’s original enactment is proven, it is unnecessary to demonstrate that, years later, the statute continues to have a discriminatory effect in order to invalidate it. We reject these contentions.

When evaluating the historical background of the city’s 1953 charter revision, the trial court did not cite Village of Arlington Heights v. Metropolitan Housing Development Corporation, 429 U.S. 252, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977). That decision identifies five factors that are pertinent to determine the discriminatory intent of a regulation that continues to have a disparate racial impact. Those factors include: (1) the historical background of the decision, (2) the specific sequence of events leading up to the decision, (3) departures from the normal procedural sequence, (4) substantive departures, and (5) legislative history, especially where there are contemporary statements by members of the decision-making body. 429 U.S. 252, 267-68, 97 S.Ct. 555, 564-65. Of course, as the City points out, Arlington Heights does not suggest that these factors are exhaustive. 429 U.S. at 268, 97 S.Ct. at 565. Moreover, the Arlington Heights evaluation of original legislative intent only supports a Fourteenth Amendment challenge where a facially neutral state law has been shown to produce disproportionate effects along racial lines. Hunter v. Under wood, 471 U.S. 222, 228, 105 S.Ct. 1916, 1920, 85 L.Ed.2d 222 (1985). In this case, however, the record of sustained minority representation on Austin’s city council for over a decade belies a finding of present-day discriminatory impact from the numbered-place system.

Even if Arlington Heights governs this case, the district court’s findings were not inadequate to reach its ultimate conclusion that the 1953 charter revision did not result from intentional discrimination. Those findings, recited in more detail at the outset of this opinion, implicitly treated each of the factors listed by Arlington Heights.

The trial court’s findings describe the historical background of the revision as part of a general overhaul of the Austin city charter. The revision to a numbered-place system of council member elections was proposed by a citizens’ committee, on which racial minorities were represented, after more than a year of effort. Thirty-two propositions were voted on. Other revisions put to the voters at the same time ran the gamut from changes in the council-city manager relations to a prohibition on council members’ having an interest in city contracts, to changes in municipal annexation, personnel, and taxing policies. While the court acknowledged that the proposals for charter revision followed on the heels of a city council election in which a black candidate finished eighth in a field of fourteen candidates competing for six council positions, the court found no other evidence to support discrimination post hoc, propter hoc. The court did not consider that two or three contemporary references to allowing “minorities” to take control of city government were probative, because such terminology was not at that time an equivalent for racial minorities. Additionally, the City offered numerous contemporary news articles which describe the thirty-two charter revisions in detail without ever alluding to a possible impact of the change on “minorities.” The court’s findings are shielded by the clearly erroneous standard of review. We are simply not left with a definite and firm conviction that they are wrong.

Appellants’ evidence of intentional discrimination in this case may be fruitfully compared with the evidence of discrimination in Hunter v. Underwood and Carrollton Branch of N.A.A. C.P. v. Stallings, 829 F.2d 1547, 1551 (11th Cir.1987). The latter case presented a Section 2 challenge to a single-member county commission set up in Alabama in 1951. The local representative who had sponsored the bill effecting that decrease from a three-member commission had been quoted in a related context as saying, “This is a white man’s country and we must keep it that way.” 829 F.2d at 1551. Likewise, in Hunter, counsel for the state defendants virtually conceded that the challenged statute was enacted with the intent of disenfranchising blacks. 471 U.S. at 231, 105 S.Ct. at 1921. The law had been passed as part of the state’s 1901 constitutional convention in which a “zeal for white supremacy ran rampant.” Id. Here, the record is equivocal concerning the motivation for adopting a majority-vote, numbered place charter revision. Thus, the ambit for the district court’s interpretation of the evidence was wide.

IV. CONCLUSION

A claim under Section 2 of the Voting Rights Act raises serious questions about the integrity of a political subdivision’s mode of governance. In this case, the evidence offered by both parties was voluminous and the arguments well presented. The district court in its turn conscientiously evaluated the case. For the foregoing reasons, the judgment of the district court is AFFIRMED.

EDITH H. JONES, Circuit Judge,

concurring:

I concur with our panel’s result and reasoning as far as they go, but I would also have addressed the trial court’s analysis of the first two Thornburg factors: the size and geographical compactness of the minority groups, and the political cohesiveness between these two racial groups. In light of our court’s recent decision that Section 2 of the Voting Rights Act applies to judicial elections, Chisom v. Edwards, 839 F.2d 1056 (5th Cir.1988), together with the advent of another Census-related round of legislative redistricting, we would be wise to resolve issues that are likely to recur. Additionally, our panel ought to have clarified an apparent misperception among courts as to the appropriate evaluation of statistical evidence in vote dilution cases. The district court’s thorough analysis of the case furnishes a well-documented steppingstone to these ends.

A. Size and Geographical Compactness.

The appellants’ first hurdle in the wake of Thornburg is to show that they are sufficiently numerous and geographically compact to form a majority in a single member district or districts. 478 U.S. at 50, 106 S.Ct. at 2766. In appellants’ six/one single-member plan, neither blacks nor Mexican-Americans would command a majority of the voting age population in any district. Consequently, in order to obtain legal relief, appellants propose three refinements to this prong of Thornburg: that total population figures rather than those of voting age minority citizens may be used to fulfill this test; that the court may order the council expanded from six to eight members, thus reducing the threshold population requirement in each district; and that blacks and Mexican-Americans may be aggregated as a politically cohesive minority. The district court ruled with appellants on only the second of these three refinements.

The appellants’ propositions are ill-founded. First, the raison d’etre of Thornburg and of amended § 2 is to facilitate participation by minorities in our political processes, by preventing dilution of their votes. Only voting age persons can vote. It would be a Pyrrhic victory for a court to create a single-member district in which a minority population dominant in absolute, but not in voting age numbers, continued to be defeated at the polls. Thornburg implicitly recognized this fact:

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 practice.

478 U.S. at 50-51 n. 17, 106 S.Ct. at 2766-67 n. 17 (emphasis added).

Courts which have addressed this issue have concluded that Thornburg’s first prong refers to a majority voting age population in a proposed single-member district. McNeil v. Springfield Park District, 851 F.2d 937, 944-45 (7th Cir.1988); Ketchum v. Byrne, 740 F.2d 1398, 1412-13 (7th Cir.1984); Romero v. City of Pomona, 665 F.Supp. 853, 854 (C.D.Cal.1987); Martin v. Allain, 658 F.Supp. 1183, 1204 (S.D.Miss.1987); Latino Political Action Committee v. City of Boston, 609 F.Supp. 739 (D.C. Mass.1985), aff'd, 784 F.2d 409 (1st Cir.1986); Potter v. Washington County, 653 F.Supp. 121, 129 (N.D.Fla.1986); Gingles v. Edmisten, 590 F.Supp. 345, 381 n. 3 (E.D.N.C.1984), 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). See also, Blacksher and Menefee, From Reynolds v. Sims to City of Mobile v. Bolden, 34 Hastings L.J. 1, 55-56 (1982). Our court’s previous cases have not addressed this issue, but in each of them the newly-created single-member districts contained a minority population well in excess of 50 percent, raising the inference that voting age population was also comfortably over 50 percent. See, Campos v. City of Baytown, 840 F.2d 1240 (5th Cir.1988); League of United Latin American Citizens v. Midland Indep. Sch. Dist., 812 F.2d 1494, vacated en banc 829 F.2d 546 (5th Cir.1987).

The appellants’ advocacy of an eight-member council as a means of overcoming the first prong of Thornburg is likewise deficient. The district court assumed ar-guendo that it might order an expansion of the city council to accommodate single-member districts. This reasoning puts the cart before the horse, by authorizing a remedy for voter dilution before a violation of Section 2 has been found. Actionable vote dilution must be measured against the number of positions in the existing governmental body rather than some hypothetical model based upon whatever size is necessary to accomplish proportional representation. Adding council member districts “would create a voting rights violation where none presently exists by enabling appellants to meet the necessary precondition of their Section 2 claim.” McNeil v. Springfield Park District, supra at 946. The district court should therefore have considered only whether a six-member single-district council would afford appellants a greater potential for electing candidates of their choice.

If appellants are required to utilize the six-one single-member district plan and voting age majorities to satisfy Thornburg’s first prong, they must establish that blacks and Mexican-Americans are a politically cohesive minority. It is appropriate to consider this argument in the larger context of Thornburg’s, second prong.

B. The Political Cohesiveness of the Minority Groups.

It is uncontested that blacks and Mexican-Americans, as individual groups, are politically cohesive within the understanding of Thornburg. The parties dispute vigorously, however, whether blacks and Mexican-Americans may be aggregated into one politically cohesive minority. If this is not possible, there is an insufficient Mexican-American population to obtain § 2 relief under Thornburg's requirements for size and geographical compactness. This court has previously held (although I participated in the dissent from the denial of rehearing en banc), that minorities may be aggregated for purposes of establishing § 2 voter dilution claims if, in addition to otherwise demonstrating a violation of § 2, they show that they are politically cohesive. Campos v. City of Baytown, 840 F.2d 1240; see also, Campos v. City of Baytown, 849 F.2d 943 (5th Cir.1988) (dissent from denial of rehearing en banc). The issue before us is whether blacks and Mexican-Americans in Austin, as a single group, have proven themselves politically cohesive.

The principal evidence underlying the district court’s conclusion is a chart, prepared by the City from appellants’ expert’s figures, depicting the estimated votes of minority candidates in 19 city council races between 1975 and 1983. Appellants contend that this chart demonstrates consistent support by blacks and Mexican-Americans for the same minority candidates. At the very least, however, the district court was not clearly erroneous in reading the chart differently and finding that in eight of the 19 races, whites voted with both minorities for minority candidates; in two races a minority candidate failed to receive a plurality from either minority group; and in the remaining nine races, blacks and Mexican-Americans voted for the same candidate only five times. Appellants misstate the proof necessary to support their position of mutual cohesiveness by considering those races in which both minority groups voted the same way as white voters. Even as such evidence tends to show black-Hispanic political solidarity, it simultaneously refutes any notion that the white vote was racially polarized. Although there was testimonial evidence of similar political goals espoused by blacks and Mexican-Americans in Austin, the fact remains that the appellants’ statistical analysis demonstrated a more complex pattern of voting by race and ethnicity than appellants would portray. Thus, while black voters were extremely cohesive and Mexican-American voters were somewhat cohesive among themselves in races where a minority candidate ran, they did not usually combine to support candidates who were usually disfavored by Anglo voters. Thornburg, 478 U.S. at 56, 106 S.Ct. at 2769-70.

C. The Significance of the Statistical Evidence Presented.

In part IIA of our opinion we said, “Crucial to the validity of regression analysis are the values for “r” and “r”, which measure the strength of the correlation and linear relationship of the variables being examined, in this case the race of the voter and the candidate he supports. In this case, Dr. Miller calculated “r” values mainly between 0.5 and 0.7 for the 43 races the plaintiffs claim are polarized, and “r” values above 0.8 in only 6 cases.”

By contrast, in Gingles v. Edmisten, 590 F.Supp. 345 (E.D.N.C.1984), 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), Dr. Grofman’s bivariate ecological regression yielded “r” values ranging from 0.7 to 0.98; most exceeded 0.9. 590 F.Supp. at 368 n. 30. The expert’s regression analysis relied on in Campos yielded “r” values generally above 0.68, and three out of five “r” values exceeded 0.84. To date courts have based vote polarization conclusions on data yielding “r” values of 0.8 or higher for the majority of elections examined. See, e.g., Campos, 840 F.2d at 1246; Solomon v. Liberty County, Fla., 865 F.2d 1566 (11th Cir.1988); Jackson v. Edgefield County, 650 F.Supp. 1176, 1197 (D.S.C.1986).

Whether a given “r” value should be regarded as statistically significant must be determined on a case by case basis since the value signifying statistical significance is dependent upon sample size (e.g., the number of precincts studied in each election). See generally D. Barnes & J. Conley, Statistical Evidence in Litigation (1986). A review of the existing case law beginning with Major v. Treen, 574 F.Supp. 325 (E.D.La.1983), suggests that courts have often failed to appreciate this important fact. On several occasions courts have made the seemingly unqualified assertion that “r” values at or above 0.5 are statistically significant. See Major v. Treen, 574 F.Supp. at 338; Gingles v. Edmisten, 590 F.Supp. at 368 (“In experience, correlations above an absolute value of .5 are relatively rare and correlations above .9 extremely rare.”). Cf. Solomon v. Liberty County, Fla., 865 F.2d at 1575 (“r” values become statistically significant at 0.3). Statistical theory simply precludes such universal conclusions.

In contrast, a careful reading of the Campos opinion indicates that the district court was presented with, and took note of, expert testimony as to the level at which the “r” value became statistically significant for the regression analysis of the election yielding the lowest correlation coefficient. Our court was careful to note that, “[f]or the Campos race, the court found that the “r” value of .52, slope of .33 and significance of .0456 were the lowest values introduced but, as testified by [the plaintiffs’ expert] Brishetto, they were still statistically significant.” Campos, 840 F.2d at 1247. We ought to encourage district courts and litigants alike to pay close attention to the signifcance of the “r” values generated by regression analysis. Statistics are a mischievous tool, especially in court, if they are not prepared and offered with a convincing explanation of their mathematical characteristics and limitations. The absence here of customary levels of statistical reliability was rightly acknowledged by the district court.

CONCLUSION

Previous cases and the above discussion establish three propositions regarding the first two Thornburg prongs that should be explicitly recognized by our circuit. First, voting age majority in a proposed single-member district, rather than population majority, should determine whether a minority group is sufficiently numerous. Second, the Thornburg analysis should be conducted according to the existing number of districts in a political subdivision, not according to a larger number tailored to accommodate a single-member district racial majority. Third, although we have now held that two racial minorities may prove that they are jointly politically cohesive under Thornburg, this factual determination in one or two cases does not suggest that in every case blacks and Mexican-Americans will satisfy their burden of proof. Finally, courts should insist not only on the provision of “r” values generated by the regression analyses, but also on evidence as to the level at which those “r” values become significant. Courts should continue to investigate these issues carefully, as the district court did here. 
      
      . The NAACP and MALDEF stand for National Association for the Advancement of Colored People and Mexican-American Legal Defense Fund, respectively.
     
      
      . The Black Citizens Task Force intervened in this case and participated on the side of the City of Austin.
     
      
      . As previously noted, the district court, on remand from this Court, took additional evidence and amended its findings in light of Thornburg. We recite the facts and reasoning on which the district court ultimately relied in concluding that there was no § 2 violation.
     
      
      . The city council was enlarged in 1967 by an amendment to the city charter providing for six council members. In 1969, the charter was again amended to provide for the separate election of a mayor. Apparently, neither of these steps is challenged by appellants.
     
      
      . The district judge recognized the inherent limitation of relying on results generated from such a small proportion of the total votes, but he observed that no other more reliable method of estimating the ethnic breakdown of the vote had been provided. Among the 52 precincts, seven were classified as predominantly Mexican-American, because they contained a 60-89% Mexican-American population. Nine precincts containing a 50-85% black population were identified as predominantly black, and the rest in the sample had a 90% or greater Anglo population.
     
      
      . Between 1975 and 1983 a minority was a candidate in 19 races. Anglos supported the minority in eight of those 19 races. Thus, in those eight races, the entire city voted cohesively. In two of the 19 races, the minority candidate did not receive plurality support of either community. In the remaining nine races, blacks and Mexican-Americans supported a different candidate than did Anglos. Significantly, the court found that in four of these nine races, the black-supported candidate did not receive a majority of Mexican-American votes and the Mexican-American-supported candidate did not receive a majority of black votes.
     
      
      . See, e.g., the court’s conclusions at n. 6 supra, drawn from Dr. Miller’s data.
     
      
      . Earlier, the opinion explained the significance of minority electoral results on the vote dilution process as follows:
      Consequently, if difficulty in electing and white bloc voting are not proven, minority voters have not established that the multi-member structure interferes with their ability to elect their preferred candidates.
      478 U.S. at 49 n. 15, 106 S.Ct. at 2766 n. 15.
     
      
      . Contrary to appellants’ assertion, the district court did not impermissibly require them to prove that Anglos vote as a bloc because of ethnicity or that multi-variate (as opposed to bivariate) regression analysis is required. Rather, the court explained that it was viewing Dr. Miller's results consistently with Justice O'Con-nor's admonition that factors other than race might be relevant in the overall decision whether white voters will usually defeat minority candidates.
     
      
      .In this connection, the district court properly held that consistent minority electoral success does not as a matter of law foreclose a Section 2 claim, Thornburg, 478 U.S. at 76 and 100-01, 106 S.Ct. at 2780 and 2793 (O’Connor, J., concurring), but is "presumptively inconsistent” with a claim. The court thus accorded considerable but not conclusive significance to these electoral successes.
     
      
      . The "r" value expresses the percentage of variance in the vote that is explained by the race of the voters.
     
      
      . Insistence upon the statistical significance of results in bivariate ecological regression analysis is particularly important because of the inherent limitations of that methodology. Briefly stated, it premises correlations not upon facts about individual voter behavior but upon assumptions usually developed from precinct election returns. Estimating the ethnic composition of precincts, the analyst then assumes that the voters in most precincts voted according to their ethnicity. The piling on of assumptions may easily fall prey to more sophisticated statistical errors. Wildgen, Adding Thornburg to the Thicket: The Ecological Fallacy and Parameter Control in Vote Dilution Cases, 20 Urban Law. 155 (1988).
     
      
      . Cf. Gingles v. Edmisten, 590 F.Supp. at 368.
     
      
      . Ignoring those races leaves the five races in which minority candidates failed to win elections. Two of those candidates have previously been conceded by appellants not to have been serious city-wide contenders. Finally, appellants' emphasis on losing candidacies, especially in the face of overwhelming minority support for the winning minority candidates, conflicts with Thornburgs admonition that occasional minority defeat simply does not equate with racial polarization. 478 U.S. at 56, 106 S.Ct. at 2770.
     
      
      . A city exhibit at trial showed that 27 different groups endorsed candidates in Austin elections.
     
      
      . Appellants additionally suggest that the district court erred by excluding testimony of their witness Ed Wendler, Sr., who would have provided-background on the attitude of "the whites" during the discussions on charter revision. The court excluded this testimony on grounds that it was repetitious. Wendler had already testified at length, the court had received in evidence many articles and exhibits regarding that era, and it had heard other live testimony. We cannot say that the court abused its discretion.
     
      
      .Even if total populations may be considered and an eight-member city council is the yardstick for a § 2 violation, appellants’ population figures still yield districts that barely assure the possibility of electing a black council member. The Mexican-American population does not by itself generate such a potential even in an eight-member district plan. The City observes, with some justification, that minorities would not necessarily find themselves better represented if they achieve one single-member district on a six-person council, where they now enjoy two representatives; or two members comprising a smaller proportion of an expanded eight-person council.
     
      
      . But see, Houston v. Haley, 859 F.2d 341 (5th Cir.1988) (Brown, J., dissenting) (arguing that voting age must be the determinative factor), vacated, 869 F.2d 807 (5th Cir.1989).
     
      
      . Thornburg notes that "... if, although geographically compact, the minority group is so small in relation to the surrounding white population that it could not constitute a majority in a single-member district, these minority voters cannot maintain that they would have been able to elect representatives of their choice in the absence of the multi-member electoral structure.” 478 U.S. at 50 n. 17, 106 S.Ct. at 2766 n. 17.
     
      
      . The district court found that Dr. Miller's analysis yielded highly questionable results. But even if these results are entitled to credence, the trial court found that they do not support appellants' arguments.
     
      
      . Cf. Thornburg, 478 U.S. at 56, 106 S.Ct. at 2769-70 (the same evidence of racial polarization will be probative both to establish the political cohesiveness of the minority group and to show white racial polarization).
     
      
      . In three of the five races in which blacks and Mexican-Americans supported the same minority candidate in opposition to the majority of Anglos, those candidates actually won election because they received a sizeable percentage of the Anglo vote — in no instance less than forty-seven percent (47%). This reinforces the inference that Austin’s voting patterns are not racially correlated in a politically meaningful sense and that blacks and Mexican-Americans have no monopoly on supporting minority candidates.
     
      
      .The comment in Major v. Treen may have been based on testimony from Dr. Henderson. If so, this statement — indicating a threshold significance for "r" — is obviously confined to the specific evidence presented in that case.
     