Treating the suggestion for rehearing en banc as a petition for panel rehearing, it is ordered that the petition for panel rehearing is DENIED. No member of the panel nor Judge in regular active service of this Court having requested that the Court be polled on rehearing en banc (Federal Rules of Appellate Procedure and Local Rule 35), the suggestion for Rehearing En Banc is DENIED.

PATRICK E. HIGGINBOTHAM, Circuit Judge, special concurrence:

I concur in the denial of the petition for rehearing but add a caution about the issue of polarized voting lest our decision be read as an endorsement of the techniques here used in its proof. Care must be taken in the factual development of the existence of polarized voting because whether polarized voting is present can pivot the legality of at-large voting districts. The inquiry is whether race or ethnicity was such a determinant of voting preference in the rejection of black or brown candidates by a white majority that the at-large district, with its components, denied minority voters effective voting opportunity. In answering the inquiry, there is a risk that a seemingly polarized voting pattern in fact is only the presence of mathematical correspondence of race to loss inevitable in such defeats of minority candidates. The point is that there will almost always be a raw correlation with race in any failing candidacy of a minority whose racial or ethnic group is as small a percentage of the total voting population as here. Yet, raw correspondence, even at high levels, must accommodate the legal principle that the amended Voting Rights Act does not legislate proportional representation. More complex regression study or multi-variate mathematical inquiry will often be essential to gauge the explanatory power of the variables necessarily present in a political race. Nor will math models always furnish an answer. A healthy dose of common sense and intuitive assessment remain powerful components to this critical factual inquiry. For example, a token candidacy of a minority unknown outside his minority voting area may attract little non-minority support and produce a high statistical correspondence of race to loss. Yet, one on the scene may know that race played little role at all. In sum, detailed findings are required to support any conclusions of polarized voting. These findings must make plain that they are supported by more than the inevitable by-product of a losing candidacy in a predominately white voting population. Failure to do so presents an unacceptable risk of requiring proportional representation, contrary to congressional will.

Because "polarized voting" was not so prominent in voting cases we have given it little attention, including the dicta of Nevett v. Sides, 571 F.2d 209, 223 n. 18 (5th Cir.1978), cert. denied, 446 U.S. 951, 100 S. Ct. 2916, 64 L. Ed. 2d 807 (1980). The footnote discussion there is misleading; indeed, if read in an overly literal manner its validity is questionable.1

The proof in this case has given me concern. Little more has been shown than that the percentage of votes for minority candidates in any given precinct enjoyed a mathematical correspondence with the percentage of minorities living in the precinct. Further, according to the plaintiffs' expert, such a voting pattern proves polarized voting, which he defined as the tendency of members of a particular ethnic or racial group to vote in a similar manner and differently from other ethnic or racial groups.

As Judge Randall observes, at the first trial plaintiff's expert, Dr. Charles Johnson, testified that minority candidates received an average of 11% of the vote in predominantly anglo precincts compared to a 63% average in minority areas. Yet, such figures are inevitable in losing minority candidacies when the minority carries the minority voting areas. At the second trial, the evidence presented by plaintiff's expert, Dr. Robert Brischetto, was little more than a sophisticated version of the raw correspondence evidence presented at the first trial.

Although in its briefs on appeal the City relies almost completely on its assertion that the district court's finding of responsiveness undercut the statistical showing of polarized voting, the City at the second trial also disputed the statistical studies. The City's expert, Dr. Delbert A. Taebel, strongly contested both Dr. Brischetto's method and conclusion.

Dr. Brischetto's method consisted of analyzing the percentage of minority voters in each precinct for correlation with the percentage that voted for the minority candidate. By doing this for each precinct, a pattern of the mathematical relationship between the racial or ethnic composition of precincts and their voting was formed. A value ("r") was then assigned to this overall correlation, ranging from 0, where there would be no correlation, to an exact direct correlation of 1.0, with figures of .5 or higher considered to be a high correlation. Dr. Brischetto then took the resulting correlation figure and squared it ("r²"), leaving what is termed the "coefficient of determination." This figure was said to explain the proportion of variation in a candidate's support accounted for by the ethnic and racial composition of a precinct. Dr. Brischetto studied the 1970-1982 City Council and School District races containing minority candidates, consisting of 22 races in all. Nineteen races had r values of .9 or higher, and the lowest was .75. Similarly, the lowest r² value was .56, and thirteen races had an r² value of .75 or higher.

These high values seem to present solid proof of polarized voting. Yet, when looked at more closely, much of their force is lost. The most striking aspect of Dr. Brischetto's study is that no other variables than race or ethnicity were tested. In other words, Dr. Brischetto did not test for other explanatory factors than race or ethnicity as intuitively obvious as campaign expenditure, party identification, income, media use measured by cost, religion, name identification, or distance that a candidate lived from any particular precinct. There are well-established statistical methods, such as step-wise multiple regressions, to test for the relative importance of such multiple factors. Significantly, the inference of bloc voting from this model builds on an assumption that race or national origin is the only explanation for the correspondence. It ignores the reality that race or national origin may mask a host of other explanatory variables.

By modeling his study so simply in a situation where minority voters voted overwhelmingly for minority candidates, Dr. Brischetto's study inevitably showed polarized voting. A high correlation figure would show up even if the white voters split their vote 50-50, as long as the minority voters voted as a bloc. Such a voting pattern obviously would not constitute polarized voting for our purposes. In Dr. Taebel's words, this posed "a serious problem" in Dr. Brischetto's study. In practice this failing worked to show polarized voting according to Dr. Brischetto even in one School District race involving one minority and two anglo candidates where the minority candidate won not simply a plurality but a majority of the votes, carrying every single precinct. This race does not approach any realistic legal standard of polarized voting. This general failure puts at issue the relevance of Dr. Brischetto's methodology.

There were other problems with Dr. Brischetto's study, including his general use of census data as a substitute for the racial and ethnic makeup of the actual voters in a precinct in any given race. This is termed the "ecological fallacy," meaning the use of aggregate data in an attempt to explain the actual behavior of individuals. The problem is illustrated by precinct 4 in the 1982 Mayor's race. According to the stipulated 1980 census data in the record, precinct 4 had a total population of 4,735. Of the 4,735 total population, there were only 2,914 eligible voters (over 18), 61.5% of the total. Of those people only 971, or 20.5% of the 4,735, were registered voters. On election day only 261 voted. Dr. Brischetto's study was bottomed on the assumption that this 261--5.5% of the total--was a microcosm of the 4,735. This great leap undermines the reliability of his study.

Finally, Dr. Brischetto excluded two races involving victorious minority candidates from his study. A minority was elected in a 1970 School District election; voting figures were unavailable before 1972, however, so Dr. Brischetto could not use this race in his study. Another minority was elected in a single-member white majority state legislative district, albeit encompassing only part of Lubbock.

The evidence here is suspect and presents a substantial risk of being wrong. It is unfortunate that a change in a city's form of government ultimately rests on such an uncertain footing. But, given that there is no evidence to rebut plaintiff's proof other than the City's criticism of Dr. Brischetto's study and its attempt to show responsiveness, I agree with Judge Randall that the record is not so barren as to render clearly erroneous the finding by the district court that bloc voting was established.