This case arises from the 2001 legislative redistricting of South Dakota. The redistricting plan (the Plan) created a 105-member state legislature that was split into thirty-five districts. Each district elected two members of the state house of representatives at-large and one member of the state senate. District 28 was an exception. It was divided into two single-member districts: District 28A and 28B. There were only two Indian-majority districts in the plan, Districts 27 and 28A. District 27, with a ninety percent Native-American population, consistently elected Indian-preferred candidates. District 28A, with a lesser majority, frequently elected Indian-preferred candidates. District 26, which neighbors District 27, had only a thirty percent Native-American population and did not elect an Indian-preferred candidate from 1982 to 2002.

At issue is whether the Plan violated Section 2 of the Voting Rights Act by packing District 27 with Native-Americans at the expense of District 26, and whether the district court redistricted South Dakota in a manner that assured Native-Americans in Districts 26 and 27 the opportunity to elect Indian-preferred candidates. The district court1 found this to be the case, and we agree.

Native-Americans make up just over nine percent of South Dakota's population and nearly seven percent of its voting-age population. Because of the well-documented history of discrimination against Native-Americans and the nature of the reservation system, much of this population is geographically compact.2 Under the Plan, only three state house seats and one state senate seat are in Indian-majority districts. Of those seats, two state house seats and a state senate seat are in District 27 where Native-Americans comprise eighty-six percent of the voting-age population.

In December 2002, Alfred Bone Shirt and three other Indian (hereinafter the plaintiffs) voters filed suit, alleging that the Plan violated Sections 2 and 5 of the Voting Rights Act of 1965, as amended, 42 U.S.C. § 1973 and 1973c.3 The plaintiffs contended that the Plan violated Section 2 because it "packed" Indian voters into District 27, which, in turn, diluted Indian voting strength in District 26 and left Indian voters in District 26 unable to elect representatives of their choice. The district court conducted a nine-day bench trial and found by a preponderance of the evidence that the Plan violated Section 2. After the defendants refused to advance a remedy, the district court imposed one of the remedial plans proposed by the plaintiffs. The defendants appeal the finding of a Section 2 violation and the imposition of the plaintiffs' remedial plan.

The district court found that the plaintiffs had met the three preconditions listed under Thornburg v. Gingles, 478 U.S. 30, 106 S. Ct. 2752, 92 L. Ed. 2d 25 (1986), and concluded that the totality of the circumstances indicated that a Section 2 violation existed. The district court gave the defendants forty-five days to propose a remedy. The state rejected this opportunity and asked the district court to certify a legal question of whether the legislature had the power to redistrict the state in a non-census year to the South Dakota Supreme Court. Certification was granted and the defendants were given thirty days after the state supreme court's decision to propose a remedy, if necessary. Although the South Dakota Supreme Court decided the legislature did indeed have the continuing power and duty to redistrict when the past apportionment resulted in a Section 2 violation, Bone Shirt v. Hazeltine, 700 N.W.2d 746, 755 (S.D.2005), the defendants stated they would not propose a remedial plan. The district court then adopted one of the plaintiffs' proposed redistricting plans, Plan E,4 and entered judgment in favor of the plaintiffs. Bone Shirt v. Hazeltine, 387 F. Supp. 2d 1035 (D.S.D.2005). The court subsequently denied the defendant's motion to alter or amend the remedial order, and this appeal followed.

The defendants advance two basic arguments on appeal: (1) that the district court clearly erred in finding a Section 2 violation, and (2) that the district court abused its discretion in imposing the plaintiff's redistricting plan. We review the district court's factual findings for clear error, including the district court's factual determination of whether the Section 2 requirements are satisfied. League of United Latin Am. Citizens v. Perry, ___ U.S. ___, ___, 126 S. Ct. 2594, 2614, 165 L. Ed. 2d 609, ___ (2006). Legal questions and mixed questions of law and fact are also reviewed de novo. Harvell v. Blytheville Sch. Dist., 71 F.3d 1382, 1386 (8th Cir.1995) (en banc). The district court's remedial order is reviewed for an abuse of discretion. See Rodriguez v. Bexar County, 385 F.3d 853, 870 (5th Cir.2004).

I. ESTABLISHMENT OF THE GINGLES PRECONDITIONS

"The essence of a § 2 claim is that a certain electoral law, practice, or structure interacts with social and historical conditions to cause an inequality in the opportunities enjoyed by [minority] and white voters to elect their preferred candidates." Cottier v. City of Martin, 445 F.3d 1113, 1116 (8th Cir.2006) (quoting Gingles, 478 U.S. at 47, 106 S. Ct. 2752). A denial of the right to vote under Section 2 occurs when:

based on the totality of circumstances, it is shown that the political processes leading to nomination or election . . . are not equally open to participation by members of a [a racial group] in that its members have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice.

League of United Latin Am. Citizens, 126 S.Ct. at 2613-14 (quoting 42 U.S.C. § 1973(b)).

To establish a Section 2 violation, the plaintiffs must prove by a preponderance of the evidence three elements, often referred to as the "Gingles preconditions":

(1) [T]he racial group is sufficiently large and geographically compact to constitute a majority in a single-member district; (2) the racial group is politically cohesive; and (3) the majority votes sufficiently as a bloc to enable it usually to defeat the minority's preferred candidate.

League of United Latin Am. Citizens, 126 S.Ct. at 2614 (internal citations and modifications omitted); Harvell, 71 F.3d at 1385. Failure to prove each of the preconditions defeats a Section 2 claim. Clay v. Bd. of Educ., 90 F.3d 1357, 1362 (8th Cir.1996). If the three preconditions are met, the court proceeds to consider the totality of the circumstances. Cottier, 445 F.3d at 1117 (citing Harvell, 71 F.3d at 1390).

In a vote dilution claim, 42 U.S.C. § 1973(b) is violated when it is proven under Gingles that the voting strength of a politically cohesive minority is diluted by either (1) fragmenting minority voters among several districts so that a majority bloc can usually outvote the minority, or, as is in this instance, (2) packing the minority into one or several districts so that the minority's influence is minimized in its neighboring districts. See Voinovich v. Quilter, 507 U.S. 146, 154, 113 S. Ct. 1149, 122 L. Ed. 2d 500 (1993) (noting both as "usual device[s] for diluting minority voting power").

A. First Gingles Precondition: Sufficiently Numerous and Geographically Compact

At the outset, the plaintiff must show Native-Americans are "sufficiently [numerous] and geographically compact to constitute a majority in a [proposed] single member district" in order to demonstrate that a workable solution is possible. Clay, 90 F.3d at 1361. The plaintiffs submitted five redistricting plans, each of which created at least one additional majority-Indian legislative district. Plan E maintained a majority-Indian Senate District (District 27) and a majority-Indian House District (District 28A) and created a new majority-Indian House district (District 26A) by reconfiguring the boundaries of Districts 26 and 27 into a new District 26 and dividing it into Districts 26A and 26B, giving each a state representative.5 According to expert testimony, each district in the remedial plan possessed voter margins that ensured Indian-preferred candidates an opportunity to win an election. See Gingles, 478 U.S. at 50, 106 S. Ct. 2752 n. 17 (explaining justification for first Gingles precondition). Under the plaintiffs' proposed plan, Native-Americans would comprise over 65 percent of the voting-age population in District 27, and over 74 percent of the voting-age population in District 26A. Furthermore, each proposed district includes Indian-preferred incumbents, which increases the opportunity of Native-American voters to elect their preferred candidates.

The defendants argue the plaintiffs must prove that the minority group will enjoy sufficient super-majority status in the proposed remedial district.6 This court recently held that at the initial stage of the Gingles precondition analysis, the plaintiffs are only required to produce a potentially viable and stable solution. Cottier, 445 F.3d at 1117: see also Gingles, 478 U.S. at 50, 106 S. Ct. 2752 n. 17 ("[T]he ultimate end of the first Gingles precondition is to prove that a solution is possible, and not necessarily to present the final solution to the problem.") As the district court correctly noted, the Gingles preconditions are designed to establish liability, and not a remedy. Because the first Gingles precondition seeks to establish whether a workable solution is possible, "the Supreme Court [at this stage] requires only a simple majority of eligible voters in the single-member district. The court may consider, at the remedial stage, what type of remedy is possible .... But this difficulty should not impede the judge at the liability stage of the proceedings." Dickinson v. Ind. State Election Bd., 933 F.2d 497, 503 (7th Cir.1991) (citations omitted).

The defendants also argue the district court violated the equal protection clause because it accepted a proposed remedial plan primarily based on race. We disagree. A redistricting plan violates the equal protection clause only if race is the predominant factor in placing voters within or outside of a particular district. Easley v. Cromartie, 532 U.S. 234, 241, 121 S. Ct. 1452, 149 L. Ed. 2d 430 (2001). Strict scrutiny does not apply where, as here, race was merely a factor in redistricting. Harvell, 126 F.3d at 1041 (8th Cir.1997); see also Bush v. Vera, 517 U.S. 952, 958, 116 S. Ct. 1941, 135 L. Ed. 2d 248 (1996) (plurality opinion).

The borders proposed in the remedial plan easily pass muster. They are compact and respect traditional boundaries. Under the remedial plan, District 27 consists of four counties, plus the Pine Ridge Reservation, as well as its off-reservation trust lands. District 26 also is made up of four counties, the Rosebud Reservation, and its off-reservation trust lands. Geographic boundaries were also considered. The proposed District 27 uses the Cheyenne River as a northern boundary and the proposed District 26 uses the Missouri River as its eastern boundary. This is consistent with traditional districting criteria, including respect for political and administrative boundaries, geographic considerations, and communities of interest. See S.D. Codified Laws 2-2-32; Abrams v. Johnson, 521 U.S. 74, 91-92, 117 S. Ct. 1925, 138 L. Ed. 2d 285 (1997); Cottier, 445 F.3d at 1118. The plaintiffs' redistricting plan also is not so irregularly shaped that it seems the primary principle in shaping the district was to include or exclude Native-Americans from any one particular district. Cottier, 445 F.3d at 1117-18. In fact, as the district court notes, the plaintiffs' plan coincides in great detail with the previous state districting plan while creating a greater opportunity for Indian voters to elect representatives of their choice. Thus, the remedial plan was not based solely on race, and survives constitutional scrutiny. Id. at 1118.

B. Second and Third Gingles Preconditions: Minority Political Cohesion and Majority Bloc Voting

The second Gingles precondition requires a showing that the Native-American minority is politically cohesive. League of United Latin Am. Citizens, 126 S.Ct. at 2614. Proving this factor typically requires a statistical and non-statistical evaluation of the relevant elections. Cottier, 445 F.3d at 1118.

Evidence of political cohesiveness is shown by minority voting preferences, distinct from the majority, demonstrated in actual elections, and can be established with the same evidence plaintiffs must offer to establish racially polarized voting, because "political cohesiveness is implicit in racially polarized voting."

Id. (quoting Sanchez v. Colorado, 97 F.3d 1303, 1312 (10th Cir.1996)).

The third Gingles precondition asks whether the white majority typically votes in a bloc to defeat the minority candidate. League of Latin Am. Citizens, 126 S.Ct. at 2614. This is determined through three inquiries: (1) identifying the minority-preferred candidates; (2) determining whether "the white majority vote as a bloc to defeat the minority preferred candidate;" and (3) determining whether "there [were] special circumstances such as the minority candidate running unopposed present when minority-preferred candidates won." Cottier, 445 F.3d at 1119-20.

Both the second and third Gingles preconditions were established through use of expert testimony, employing BERA or regression analysis and Homogenous Precinct Analysis.7 The defendants argue the district court erred in receiving this evidence. We review this evidentiary decision for an abuse of discretion. United States v. Jordan, 150 F.3d 895, 899 (8th Cir.1998). The district court reviewed the testimony under Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 113 S. Ct. 2786, 125 L. Ed. 2d 469 (1993), and found the plaintiffs' expert testimony relevant and reliable. We agree. The statistical methods used by the plaintiffs have long been accepted by the Supreme Court, see Gingles, 478 U.S. at 52-53, 106 S. Ct. 2752 (regression analysis), and other courts, see, e.g. Harvell, 71 F.3d at 1386(regression analysis); Old Person v. Cooney, 230 F.3d 1113, 1123 (9th Cir.2000) (same); Rural W. Tenn. African-American Affairs Council v. Sundquist, 209 F.3d 835, 839 (6th Cir.2000) (homogenous and regression analysis). This court recently accepted the use of these methods as reliable evidence in determining the second and third Gingles preconditions. Cottier, 445 F.3d at 1118-19. And we do so here.

Second, we agree with the district court's interpretation of the evidence and the expert testimony. Ordinarily, racially polarized voting is "the keystone of a vote dilution case." Buckanaga v. Sisseton Indep. Sch, Dist., 804 F.2d 469, 473 (8th Cir.1986). Endogenous8 and interracial elections are the best indicators of whether the white majority usually defeats the minority candidate. See Cottier, 445 F.3d at 1121; Old Person, 230 F.3d at 1127. The more recent an election, the higher its probative value. See Uno v. City of Holyoke, 72 F.3d 973, 990 (1st Cir.1995). In the only mixed-race endogenous election in District 26 in the past ten years, the Indian-preferred candidate for state senate lost even though he received 70 percent of the Native-American vote. In nine of the most recent endogenous District 26 elections between white candidates, the Indian-preferred candidate lost each time. In each election, the white majority voted as a bloc to defeat the Indian-preferred candidate even though the Indian-preferred candidate was able to carry a majority of the Native-American vote.

Although they are not as probative as endogenous elections, exogenous9 elections hold some probative value. Cottier, 445 F.3d at 1121. In two exogenous, interracial elections, the Indian-preferred candidate lost. The white majority was able to vote as a bloc in each election to defeat overwhelming Native-American voter support for the Indian-preferred candidate. It was only in exogenous elections between white candidates, that Native-Americans were finally able to elect their preferred candidate. On the basis of this record, we agree with the district court's findings that Native-Americans in South Dakota are politically cohesive and that the white majority voting bloc usually defeats the Indian-preferred candidate.

Although satisfying the three Gingles preconditions takes the plaintiff "a long way towards showing a section 2 violation," Harvell, 71 F.3d at 1390, the plaintiffs ultimately must prove that the totality of the circumstances indicates minority voters had "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 Senate Committee report that accompanied the 1982 amendment to the Voting Rights Act noted the courts should consider the following, inexhaustive, objective factors in determining whether the totality of the circumstances indicate a Section 2 violation:

(1) the extent of any history of official discrimination in the state or political subdivision that touched the right of the members of the minority group to register, to vote, or otherwise to participate in the democratic process;

(2) the extent to which voting in the elections of the state or political subdivision is racially polarized;

(3) the extent to which the state or political subdivision has used unusually large election districts, majority vote requirements, anti-single shot provisions, or other voting practices or procedures that may enhance the opportunity for discrimination against the minority group;

(4) if there is a candidate slating process, whether the members of the minority group have been denied access to that process;

(5) the extent to which members of the minority group in the state or political subdivision bear the effects of discrimination in such areas as education, employment and health, which hinder their ability to participate effectively in the political process; (6) whether political campaigns have been characterized by overt or subtle racial appeals;

(7) the extent to which members of the minority group have been elected to public office in the jurisdiction.

S.R. No. 97-417 at 28-29 (1982); Gingles, 478 U.S. at 44-45, 106 S. Ct. 2752. Two additional factors are also probative in determining whether Section 2 was violated: (1) was there a significant lack of response from elected officials to the needs of the minority group, and (2) was the policy underlying the jurisdiction's use of the current boundaries tenuous. Gingles, 478 U.S. at 44, 106 S. Ct. 2752.

Two factors predominate the totality-of-circumstances analysis: "the extent to which voting is racially polarized and the extent to which minorities have been elected under the challenged scheme." Harvell, 71 F.3d at 1390. Here, the record reflects a high level of polarization in District 26, as well as an intolerable level of racial polarization in District 27, and it is clear that Native-Americans have consistently been excluded from District 26's elected positions. Moreover, the record reflects that not one Indian-preferred candidate was elected to the state legislature from the area that includes District 26 during the period of 1982 to 2002.10

The defendants opine that the actual cause of racially polarized voting in South Dakota is the establishment and continued maintenance of the reservation system. As a result, Native-Americans have a low interest in South Dakota politics. We reject this argument. The presumption that South Dakota is relieved of liability for discriminatory voting practices because the reservation system makes Native-Americans less involved in state politics and more involved in tribal matters is untenable. See United States v. South Dakota, 636 F.2d 241, 245 (8th Cir.1980). The record is clear that South Dakota's history of discrimination against Native-Americans has limited their ability to succeed in the state political process. Id. at 244-45. The vestiges of this discrimination remain, dampening Native-American interest in South Dakota politics and affecting the ability of Native-Americans to register, to vote, and to participate in the electoral process. See Westwego Citizens for Better Gov't v. City of Westwego, 872 F.2d 1201, 1211-12 (5th Cir.1989). Further, the "historic effects of discrimination in the areas of health, employment, and education impact negatively" on the ability of Indians to participate in the political process. Harvell, 71 F.3d at 1390.

When a Section 2 violation is found, the district court is responsible for developing a constitutional remedy. As required, the defendants were afforded the first opportunity to submit a remedial plan. Cottier, 445 F.3d at 1123; Williams v. City of Texarkana, 32 F.3d 1265, 1268 (8th Cir.1994). They refused, thus leaving it to the district court to fashion its own remedy or, as here, adopt a remedial plan proposed by the plaintiffs. Williams, 32 F.3d at 1268.

In formulating a remedial plan, the first and foremost obligation of the district court is to correct the Section 2 violation. See Westwego Citizens for Better Gov't, 946 F.2d at 1124. Second, the plan should be narrowly tailored, and achieve population equality while avoiding, when possible, the use of multi-member districts. Abrams v. Johnson, 521 U.S. 74, 98, 117 S. Ct. 1925, 138 L. Ed. 2d 285 (1997); Chapman v. Meier, 420 U.S. 1, 26-27, 95 S. Ct. 751, 42 L. Ed. 2d 766 (1975). Third, the plan must not violate Sections 2 or 5 of the Voting Rights Act. Finally, the plan should not "intrude on state policy any more than is necessary" to uphold the requirements of the Constitution. Upham v. Seamon, 456 U.S. 37, 41-42, 102 S. Ct. 1518, 71 L. Ed. 2d 725 (1982) (per curiam) (quoting White v. Weiser, 412 U.S. 783, 794-95, 93 S. Ct. 2348, 37 L. Ed. 2d 335 (1973)).

The defendants argue the district court committed three reversible errors in adopting the remedial plan: (1) the plan is not an appropriate remedy, since it will still result in losses for Indian-preferred candidates; (2) the court did not seek preclearance from the Department of Justice; and (3) the court ignored evidence that "reformulating a new district may result in a new dynamic." (Appellant Br. at 77-79.) We disagree. In our view, the district court's remedial plan assures Native-American voters the opportunity to elect representatives of their choice and meaningful participation in the political process. Harvell, 126 F.3d at 1041. The record reveals the remedial plan affords Native-Americans more than a 65 percent majority in District 27 and a 74 percent majority in District 26A. See Ketchum v. Byrne, 740 F.2d 1398, 1402 (7th Cir.1984) (acknowledging recognized 65 percent guideline); Neal v. Coleburn, 689 F. Supp. 1426, 1438 (E.D.Va.1988) ("[T]he general 65% guideline for remedial districts is not a required minimum which the plaintiffs must meet before they can be awarded any relief under § 2 . . . . Rather, the 65% standard is a flexible and practical guideline to consider in fashioning relief for a § 2 violation"). Furthermore, the district court correctly considered other factors, including turnout rate and incumbency in formulating the plan. Dickinson, 933 F.2d at 503. The defendants' argument that the remedial plan must provide some sort of guarantee that Indian-preferred candidates will be elected is not persuasive; all that is required is that the remedy afford Native-Americans a realistic opportunity to elect representatives of their choice. This is true here.

The defendants further contend that the remedial plan violates. Section 5 of the Voting Rights Act because it will result in an overall loss of representation for Native-Americans in District 27. See Beer v. United States, 425 U.S. 130, 141, 96 S. Ct. 1357, 47 L. Ed. 2d 629 (1976). Section 5 is designed to combat retrogression which, "by definition, requires a comparison of a jurisdiction's new voting plan with its existing plan [and] necessarily implies that the jurisdiction's existing plan is the benchmark against which the effect of voting changes is measured." Reno v. Bossier Parish Sch. Bd., 520 U.S. 471, 478, 117 S. Ct. 1491, 137 L. Ed. 2d 730 (1997) (internal citations omitted). The burden is on South Dakota to prove that the change does not have a discriminatory purpose or an effect that would deny or abridge the voting rights of minorities based on race when compared to the status quo of the previous plan. Reno v. Bossier Parish Sch. Bd., 528 U.S. 320, 328-29, 334, 120 S. Ct. 866, 145 L. Ed. 2d 845 (2000). The defendants have not carried this burden. A retrogressive effect is one that decreases minority voting power in comparison with a preexisting plan when it eliminates a majority minority district or otherwise reduces the voting power of a minority community.11 Beer, 425 U.S. at 141, 96 S. Ct. 1357. Here, the plan increases the number of Native-American majority districts by one, and enhances the voting power of the minority. Thus, the remedial plan is consistent with the goals of the Supreme Court, as stated in Beer, 425 U.S. at 141, 96 S. Ct. 1357: "reapportionment that enhances the position of racial minorities with respect to their effective exercise of the electoral franchise can hardly have the effect of diluting or abridging the right to vote on account of race within the meaning of § 5."

As to the defendants' claim that Section 5 was violated due to the lack of preclearance, we find no merit. Section 5 clearly states that the preclearance requirement12 applies to "legislative apportionment plans that are adopted without judicial discretion or approval." McDaniel v. Sanchez, 452 U.S. 130, 138, 101 S. Ct. 2224, 68 L. Ed. 2d 724 (1981). In this case, the plan was privately developed, and thus not subject to preclearance. Id. ("[T]he Act's preclearance requirement does not apply to plans prepared and adopted by a federal court.").

Finally, the defendants opine that the district court erred when it reformulated a plan that "may result in a new dynamic." The defendants do not describe the dynamic they fear, nor do they direct us to any evidence in support of their position. Moreover, we have found no case law suggesting that a district court must analyze the changing political dynamics of remedial districts. Therefore, we find that the district court did not abuse its discretion in implementing the plaintiffs' remedial plan.

For each of the reasons noted herein, we affirm the decision of the district court and find that the preponderance of the evidence shows that the plaintiffs met their burden in proving a Section 2 violation. We also affirm the district court's decision to impose the plaintiffs' proposed remedial plan.

GRUENDER, Circuit Judge, concurring in the judgment.

Because I do not find that the district court clearly erred in the essential holdings of its opinion, I concur in the judgment. I write separately because my analysis of the district court's findings and my application of the clearly erroneous standard differs from that of the Court.

We review the district court's factual findings for clear error. Harvell, 71 F.3d at 1386. "Using this standard, we will overturn a factual finding only if it is not supported by substantial evidence in the record, if it is based on an erroneous view of the law, or if we are left with the definite and firm conviction that an error was made." United States v. Vertac Chemical Corp., 453 F.3d 1031, 1039 (8th Cir.2006) (quotation omitted). Under this standard, affirmance may be proper regardless of whether "we agree with the district court's interpretation of the evidence and the expert testimony." Ante at 1021; see also ante at 1016, 1020, 1021. We instead review the district court's factual findings only to ascertain whether the district court's interpretation of the facts is a permissible one, as "[a] district court's choice between two permissible views of the evidence cannot be clearly erroneous." Vertac, 453 F.3d at 1039 (qutoation omitted); see also Cottier, 445 F.3d at 1123-24 (Colloton, J., dissenting) ("To preserve the benefit of the trial court's particular familiarity with the indigenous political reality, we apply a clear error standard of review both to the predicate factual determinations and to the ultimate finding regarding vote dilution.") (internal quotations and alterations omitted).

The Court's opinion adequately describes the Gingles preconditions. See ante at 1017-21. While I cannot join the Court's analysis of the Gingles preconditions, I concur in its conclusion. I set forth what I find to be the proper analysis of the issues below.

Under the first Gingles precondition, Bone Shirt must show that Indians constitute a minority that is sufficiently large and geographically compact to constitute a majority in a single-member district. Gingles, 478 U.S. at 50, 106 S. Ct. 2752. This first precondition focuses upon whether the district court can "fashion a permissible remedy in the particular context of the challenged system." Sanchez v. Colorado, 97 F.3d 1303, 1311 (10th Cir.1996) (quoting Nipper v. Smith, 39 F.3d 1494, 1530-31 (11th Cir.1994)). If no "proper and workable remedy exists," then a plaintiff's claims fail as a matter of law. Cottier, 445 F.3d at 1117. In Cottier, this Court sustained redistricting plans under the first Gingles precondition so long as the proposed plans offered Indians a "more reasonable opportunity" to elect representatives of their choice. Id.

The State contends that the district court erroneously determined that Indians need not have a supermajority in the newly-created district. This Court rejected a similar argument in Cottier. Id. The question is whether the minority population has an "equal opportunity" to elect its preferred candidate, not whether it will actually muster the votes to do so. League of United Latin Am. Citizens v. Perry, ___ U.S. ___, ___-___, 126 S. Ct. 2594, 2615-16, 165 L. Ed. 2d 609, ___-___ (2006). In any event, the State's argument is beside the point, as Bone Shirt demonstrated that there were five potential remedial plans that gave Indians a supermajority of over 65 percent in the new District 26, the remedial district. As such, I cannot say that the district court clearly erred when it concluded that Indians constituted a minority that was sufficiently large and compact to constitute a majority in a single-member district. In addition, the Court accurately described the proposed remedial districts, ante at 1019, and I likewise conclude that the proposed remedial districts are not themselves racial gerrymanders.

B. The Second and Third Gingles Preconditions

Gingles's second precondition required Bone Shirt to show that Indians are politically cohesive. Gingles, 478 U.S. at 51, 106 S. Ct. 2752. "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, and, consequently, establishes minority bloc voting within the context of § 2." Id. (internal citation omitted). The third Gingles precondition requires a plaintiff to demonstrate that "the white majority votes sufficiently as a bloc to enable it—in the absence of special circumstances, such as the minority candidate running unopposed — usually to defeat the minority's preferred candidate." Gingles, 478 U.S. at 51, 106 S. Ct. 2752 (internal citation omitted).

Much of the argument before the district court and in this Court addressed whether the statistical methods employed by Bone Shirt's expert, Dr. Steven Cole, were sufficiently reliable. Cole employed bivariate ecological regression analysis ("BERA") and homogenous precinct analysis ("HPA"). The State's expert, Dr. Zax, employed ecological inference ("EI") or "King's Method." Using BERA and HPA, Cole determined that Indian voters are highly cohesive; that is, Indians tend to vote for the same candidates. The district court accepted Cole's BERA-based statistical analysis, even though "Cole admitted that [his] equation contains an error [and that] the effect of that error is unknown." 336 F. Supp. 2d at 1001-02. The Court points out that BERA has "long been accepted" by the courts. Ante at 1020-21.

I find it difficult to rely upon a statistical method that incorporates an admittedly erroneous equation that yields a result with an error of unknown quantity and effect. Daubert specifically requires a district court to consider "the known or potential rate of error" of the scientific method utilized by testifying experts. 509 U.S. at 594, 113 S. Ct. 2786. It is difficult to weigh this factor in Daubert's analysis if "the effect of that error is unknown." 336 F. Supp. 2d at 1002. Nor am I persuaded that previous acceptance of BERA results permanently decides the matter. Science evolves, and scientific methods that were once considered unassailable truths have been discarded over time. Unreliable testimony based upon those outdated theories and methods must be discarded as well, lest scientific stare decisis ensure that such theories survive only in court. It may be that the validity of some scientific methods need not be constantly reestablished in case after case, but a statistical method that contains an apparently unquantified error would not be one of them. If Cole's BERA-based testimony were the only basis for the district court's opinion, I would likely hold that its conclusions were unsupported by competent evidence.

Nevertheless, I do not find that the district court clearly erred when it found that Indians vote sufficiently cohesively and the white majority voted as a bloc to usually defeat the minority preferred candidate ("MPC"), thereby establishing the second and third Gingles preconditions. As the district court correctly noted, "all three methods employed by the parties' experts in this case generate sufficiently similar results." Id. at 1004. In other words, Cole's BERA and HPA-based results and Zax's EI-based results are substantially similar. While the State contends that this is not the case, the analysis it presents in its brief is based upon a misunderstanding of the proper approach to the issue.

First, the State's expert used an approach that conflates the second and third Gingles preconditions. According to the State's brief, "dilution may be found when there is first, racial polarization and, second, in a case in which there is racial polarization, the minority candidate loses." The State further refines its approach by arguing that a particular race does not qualify as "polarized" unless at least 60 percent of Indians voted for the MPC and at least 60 percent of the white majority voted against him. But there is no support for this approach, as no Gingles precondition asks whether the white majority is also cohesive. To the contrary, the questions under Gingles's second and third preconditions are whether the minority votes cohesively and whether "the white majority votes sufficiently as a bloc" in most elections to defeat the candidate that the cohesive minority population prefers. Gingles, 478 U.S. at 51, 106 S. Ct. 2752. Nothing in the case law prescribes that the white majority bloc must be of a certain size beyond the requirement that the bloc be large enough to defeat the MPC. As such, Dr. Zax's assumption that only races where at least 60 percent of the white majority votes for the same candidate improperly skews his results.

Second, the State diluted the proper analysis by relying heavily upon election results in races in other districts and for other offices, known as exogenous elections. As we have held previously, endogenous results are preferable to exogenous ones. Cottier, 445 F.3d at 1121. Moreover, the district court clearly found that endogenous results were preferable to exogenous results, and the State did not attack that finding in its appeal.

The State also relied heavily upon results from District 27 when arguing that the white majority does not usually defeat the MPC. But it is hardly shocking that the white population usually cannot vote as a bloc sufficient to defeat the MPC in District 27—a district created to ensure that Indians could elect their MPC and where Indians enjoy a large supermajority. Contrary to the State's argument, the precedent addressing this issue makes clear that courts must focus on election results from the majority-white district. See, e.g., Gingles, 478 U.S. at 51, 106 S. Ct. 2752 (holding that the minority proves the third precondition by showing that "submergence in a white multimember district impedes its ability to elect its chosen representatives" because the district's "white majority" votes sufficiently as a bloc) (emphases added); see also League of United Latin Amer. Citizens, 126 S.Ct. at 2616 ("The Court has rejected the premise that a State can always make up for the less-than-equal opportunity of some individuals by providing greater opportunity to others."); De Grandy, 512 U.S. at 1003-04, 114 S. Ct. 2647 (holding that the third precondition was satisfied by "a tendency of non-Hispanic whites to vote as a bloc to bar minority groups from electing their chosen candidates except in a district where a given minority makes up a voting majority") (emphasis added).

If the State's approach were correct, packing would be both the problem and the solution—i.e., having illegally packed Indians into one district, the State could then point out that Indians are sometimes able to elect their preferred candidate in the packed district. See Old Person, 230 F.3d at 1122 (noting that this approach "would permit white bloc voting in a majority-white district to be washed clean by electoral success in neighboring majority-Indian districts"). As the case law illustrates, the State's approach to the issue is inappropriate.

In this case, then, the elections that speak to this critical issue are those in District 26, the "white majority" district in question. And, at bottom, when analyzed under the proper framework, both experts' analyses using all three methods—BERA, HPA and EI—support the conclusion that the Indians vote cohesively in that district and that the white majority usually votes as a bloc to defeat the MPC. As such, the district court did not clearly err when it held that the second and third Gingles preconditions had been met.

The district court analyzed all the Senate factors, as well as two additional factors often considered in Section 2 cases. See ante at 1021-22. The district court's weighing of the totality of the circumstances, like its factual findings, is subject to clear error review. Stabler, 129 F.3d at 1023.

The Court's opinion analyzes only two of the Senate factors, the extent of racially polarized voting and the extent to which minorities have been elected, reasoning that these two factors "predominate" the analysis. Id. at 1022-23. Without analyzing the remainder of the factors, the Court then cites a 1981 case from this Circuit involving South Dakota and holds that "[t]he record is clear that South Dakota's history of discrimination against Native-Americans has limited their ability to succeed in the state political process." Id. at 1023. After reviewing the district court's Senate-factor findings and its weighing of those factors, I believe that the issue of whether the totality of the circumstances indicates that South Dakota violated Section Two is a closer call than reflected in the Court's opinion. Nevertheless, I conclude that the district court did not clearly err when it determined that "based on the totality of the circumstances, it [has been] shown that . . . [members of a protected group] 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).

I would, however, find that the district court's analysis of several of the Senate factors was clearly erroneous. First, the district court erroneously concluded that South Dakota uses voting procedures that enhance the opportunity for discrimination. The district court first found that South Dakota "has taken measures to simplify voting procedures and promote access to the political process [and that] these laws and practices decrease opportunities for discrimination." 336 F. Supp. 2d at 1037. Nevertheless, the district court concluded that South Dakota's use of multimember districts in District 26 and District 27 outweigh South Dakota's efforts to ensure Indian access to the polls. Id. The district court's conclusion on this factor is unsupported by any analysis or evidence. Moreover, it is difficult to see how the use of multimember districts in District 27, which has a supermajority of Indians, hurts Indian efforts to elect their preferred candidates. As the lack of Indian voters in District 26 forms the basis for Bone Shirt's claim, it is unclear from the evidence whether the use of multimember districts in fact adds to that injury, as there may just be too few Indians in District 26 irrespective of whether it is a single or multimember district. As the district court's opinion does not represent a choice between two permissible views of the evidence, but is instead a conclusion unsupported by substantial evidence, I would hold that it clearly erred when analyzing this factor.

Second, the district court found that, although there is no formal candidate slating process in South Dakota, there is an informal one, and it worked in one instance to harm Indian interests when a Democratic committee chairman campaigned against the MPC, who was running as a Democrat. Id. Again, the district court's conclusion is unsupportable, as the factor concentrates first upon whether there is a candidate slating process. At most, the district court found that there is an informal one. Id. This then means that the process is more open than if there were a formal slating process that worked consistently against Indian interests. While it is unclear whether an informal slating process is relevant to the Senate factor, a single instance where, for whatever reason, a party chairman chose not to support his party's candidate is an insufficient basis upon which to determine that Indians have been "denied access to that [slating] process." Gingles, 478 U.S. at 37, 106 S. Ct. 2752. The district court's finding in this regard is clearly erroneous.

Third, the district court's conclusion that racial appeals have been used in South Dakota's elections, 336 F. Supp. 2d at 1041, was also clearly erroneous. As support for its conclusion, the district court primarily cited news stories concerning alleged Indian voter fraud. Id. The district court's opinion does not reflect that any of the stories originated from a particular campaign, that they were meant to incite anti-Indian sentiment or that they were meant to motivate white voters to reject Indian candidates. Moreover, the fact that the news media reported that one non-Indian politician chose an Indian running mate is not evidence of a racial appeal, much less a racial appeal that is detrimental to Indians. This evidence does not support the district court's conclusion that racial appeals have been used in South Dakota elections. Therefore, because the finding is unsupported by evidence, I would find that it was clearly erroneous.

One other portion of the district court's analysis is problematic despite its factual accuracy. A very significant portion of the district court's conclusion that there was a "long and extensive history" of discrimination that affects the voting rights of Indians in South Dakota is predicated upon early South Dakota and American history, including denial of the right of Indians to vote by Congress in the 1860s. 336 F. Supp. 2d at 1034. Because Indians have had the right to vote under particular circumstances since at least the 1890s and have had the universal right to do so for over half a century, this evidence is far from dispositive. Nor am I persuaded that particular witnesses' anecdotes about perceived slights at the polls would be sufficient to sustain the district court's opinion on this issue. Nevertheless, there was also evidence of more recent discrimination, including purposeful efforts to deny Indians the right to vote in various jurisdictions in South Dakota, id. at 1023-24, and I cannot conclude that the district court clearly erred when it determined that this factor weighed in Bone Shirt's favor.

Although the district court's conclusion with respect to three of the Senate factors was clearly erroneous, its conclusion respecting the other nine factors it analyzed was not. Importantly, this includes its conclusion concerning the two "primary factors," Harvell, 71 F.3d at 1390—the existence of polarized voting and the lack of Indian elected officials. In my view, the district court's analysis of these remaining Senate factors constitutes a "choice between two permissible views of the evidence," Vertac,453 F.3d at 1039, and I cannot therefore say that its analysis is clearly erroneous. As we have held previously, "Congress made clear . . . that the factors identified in the legislative history are not exhaustive . . . and that there is no formula for aggregating the factors." Buckanaga v. Sisseton Indep. Sch. Dist. No. 54-5, 804 F.2d 469, 471 (8th Cir.1986). In accord with this reality, no court has ever determined how many of the factors must be present or in what combination. Under these circumstances, I cannot say that the district court's overall weighing of the totality of the circumstances was clearly erroneous.

After South Dakota declined to submit a remedial plan, the district court adopted the ACLU's "Remedial Plan 1." 387 F. Supp. 2d at 1038-39. The State argues on appeal that the remedial plan is retrogressive in that it hurts the opportunity of Indians in District 27 to elect the candidates of their choice, it is facially impermissible under Section Five of the Voting Rights Act and it must be submitted to the Department of Justice or a three judge panel for clearance.

In his brief, Bone Shirt pointed out that the State did not make its retrogression and Section Five arguments before the district court. The State did not dispute that characterization in its reply. Accordingly, I would find that the State failed to preserve these arguments for appeal. See, e.g., AIG Centennial Ins. Co. v. Fraley-Landers, 450 F.3d 761, 767 (8th Cir.2006) ("We generally do not consider arguments presented for the first time on appeal . . . .").

Nor am I persuaded that the district court was required to seek preclearance from the Department of Justice or a three judge panel for its proposed redistricting plan. As the Supreme Court interpreted Section Five in the context of a judicially-ordered redistricting plan, the redistricting plan need not be submitted for preclearance unless the plan was created by the relevant legislative body. McDaniel, 452 U.S. at 153, 101 S. Ct. 2224 ("As we construe the congressional mandate, it requires that whenever a covered jurisdiction submits a proposal reflecting the policy choices of the elected representatives of the people—no matter what constraints have limited the choices available to them—the preclearance requirement of the Voting Rights Act is applicable."). Here, the adopted plan does not reflect South Dakota's redistricting choices. Indeed, South Dakota explicitly refused to offer any remedial redistricting plan. Accordingly, the district court need not have sought preclearance.

For the foregoing reasons, I would affirm the judgment of the district court. Accordingly, I concur in the judgment.