EDMONDSON, Circuit Judge:
Plaintiffs, black citizens of DeSoto County, brought suit, alleging that the current at-large method of electing the county school board and county commission unlawfully dilutes black-minority voting strength, under section 2 of the Voting Rights Act and the Fourteenth and Fifteenth Amendments. After a trial, the district court found that Plaintiffs had failed to prove vote dilution and entered judgment for Defendants. We affirm the judgment.
BACKGROUND
The DeSoto County commission and school board, pursuant to Florida law,
are each composed of five members. The members of each board, who serve four-year staggered terms, are required to live in five separate residency districts but are elected by an at-large, countywide vote. The elections are partisan, with a majority requirement in the primaries but not in the general election. No black person has ever run for a seat on the commission; only one has run (unsuccessfully) for the school board.
At the time of the 1990 census, blacks comprised 15.6 percent of the county’s total population and 13.7 percent of the total voting age population.
The county, however, contains a substantial nonvoting, mostly nonresident population, housed in a state prison and a state mental institution: few of the mental institution patients are county residents; and the inmates, convicted felons, cannot vote under Florida law.
See
Fla. Const. art. 6, § 4; Fla. Stat. § 97.041(2)(b). Removing these institutionalized members of the population from the total voting age population, blacks — in 1990 — comprised only 11.8 percent of the potential voters in the county.
At trial, Plaintiffs’ experts testified that, using 1990 census data, Plaintiffs could produce election plans for the county, consisting of five single-member districts for each board with blacks constituting a majority of the noninstitutionalized voting population in one of the districts. But Defendants introduced evidence that, because of changes in the black and white populations since 1990, the creation of a majority-black district was no longer possible in 1998. One of Defendants’ experts compared the 1990 census data with 1991 voter registration data and calculated ratios of registered voters to voting age population in each proposed district; he then extrapolated, from 1998 voter registration data, the voting age population in 1998. From these calculations, he testified that blacks in 1998 could constitute only about 46 percent of the voting age population of Plaintiffs’ proposed black-majority district. Another defense expert testified that considerable growth had occurred in the county since 1990, but not in the black population of the proposed black-majority district.
Defendants also offered other evidence (not based on voter registration data) of the county’s population growth. For example, a member of the county commission testified that, based on the commission’s approval of new subdivisions, the southwest corner of the county was the major growth area: according to the witness, this area was not one with a high black population.
The district court entered judgment for Defendants, finding that Plaintiffs failed to establish their vote dilution claims. In particular, the district court found that Plaintiffs failed to show “discriminatory effects”: failed to show that the county’s at-large election system resulted in blacks having less opportunity to participate in the political process and elect candidates of their choice. Plaintiffs appeal.
THE VOTING RIGHTS ACT CLAIM
An electoral system violates section 2 of the Voting Rights Act if the system causes the members of a distinct racial group to “have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice.” 42 U.S.C. § 1973(b). The Supreme Court has said that, to satisfy section 2’s standard in a vote dilution case, plaintiffs must show (at a minimum) that: (1) “the minority group ... is sufficiently large and geographically compact to constitute a majority in a single-member district;” (2) the minority group is politically cohesive; and (3) the white majority votes as a bloc sufficiently to defeat the minority group’s preferred candidates.
Thornburg v. Gingles,
478 U.S. 30, 106 S.Ct. 2752, 2766, 92 L.Ed.2d 25 (1986). The district court, in this case, found that Plaintiffs failed to establish the first
Gin-gles
factor: “[Wjhile the Plaintiffs demonstrated the existence of the first
Gingles
precondition as of 1990, the Defendants have established by a preponderance of the evidence that as of the date of trial it is no longer possible to create a minority-
controlled district in DeSoto County.” The district court, therefore, rejected Plaintiffs’ statutory claim. Plaintiffs contend that the district court’s finding that Plaintiffs failed to establish the first
Cin-gles
factor was error because the district court should have never considered Defendants’ evidence of post-1990 population changes. We cannot accept Plaintiffs’ contention.
A.
Plaintiffs first contend that the district court should have excluded Defendants’ evidence of post-1990 population changes because the evidence contradicted a stipulation and several admissions agreed to by Defendants before trial.
In 1991, Defendants admitted that Plaintiffs’ proffered plans indeed created five single-member districts with one majority-black district.
And, in an April 1998 pretrial statement, the parties stipulated that Plaintiffs had drawn two electoral schemes with a black-majority district.
Defendants never amended these admissions or the stipulation. Based on the admissions and stipulation, Plaintiffs contend that Defendants’ evidence of post-census changes is barred because Defendants conclusively admitted that Plaintiffs could establish the required majority-minority district.
Before filing the April pretrial statement, Defendants disclosed that they expected to call two expert witnesses at trial. On 1 May 1998, pursuant to the preexisting pretrial order, Defendants informed Plaintiffs that, given new 1998 voter registration data, Defendants’ experts would challenge the continued validity of the 1990 census figures in their testimony. Defendants explained that their experts would testify that blacks, by 1998, were no longer sufficiently geographically concentrated to permit the creation of a black-majority district. After this disclosure, Plaintiffs filed a motion in limine to exclude Defendants’ proffered evidence; the district court — after a hearing — denied the motion.
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EDMONDSON, Circuit Judge:
Plaintiffs, black citizens of DeSoto County, brought suit, alleging that the current at-large method of electing the county school board and county commission unlawfully dilutes black-minority voting strength, under section 2 of the Voting Rights Act and the Fourteenth and Fifteenth Amendments. After a trial, the district court found that Plaintiffs had failed to prove vote dilution and entered judgment for Defendants. We affirm the judgment.
BACKGROUND
The DeSoto County commission and school board, pursuant to Florida law,
are each composed of five members. The members of each board, who serve four-year staggered terms, are required to live in five separate residency districts but are elected by an at-large, countywide vote. The elections are partisan, with a majority requirement in the primaries but not in the general election. No black person has ever run for a seat on the commission; only one has run (unsuccessfully) for the school board.
At the time of the 1990 census, blacks comprised 15.6 percent of the county’s total population and 13.7 percent of the total voting age population.
The county, however, contains a substantial nonvoting, mostly nonresident population, housed in a state prison and a state mental institution: few of the mental institution patients are county residents; and the inmates, convicted felons, cannot vote under Florida law.
See
Fla. Const. art. 6, § 4; Fla. Stat. § 97.041(2)(b). Removing these institutionalized members of the population from the total voting age population, blacks — in 1990 — comprised only 11.8 percent of the potential voters in the county.
At trial, Plaintiffs’ experts testified that, using 1990 census data, Plaintiffs could produce election plans for the county, consisting of five single-member districts for each board with blacks constituting a majority of the noninstitutionalized voting population in one of the districts. But Defendants introduced evidence that, because of changes in the black and white populations since 1990, the creation of a majority-black district was no longer possible in 1998. One of Defendants’ experts compared the 1990 census data with 1991 voter registration data and calculated ratios of registered voters to voting age population in each proposed district; he then extrapolated, from 1998 voter registration data, the voting age population in 1998. From these calculations, he testified that blacks in 1998 could constitute only about 46 percent of the voting age population of Plaintiffs’ proposed black-majority district. Another defense expert testified that considerable growth had occurred in the county since 1990, but not in the black population of the proposed black-majority district.
Defendants also offered other evidence (not based on voter registration data) of the county’s population growth. For example, a member of the county commission testified that, based on the commission’s approval of new subdivisions, the southwest corner of the county was the major growth area: according to the witness, this area was not one with a high black population.
The district court entered judgment for Defendants, finding that Plaintiffs failed to establish their vote dilution claims. In particular, the district court found that Plaintiffs failed to show “discriminatory effects”: failed to show that the county’s at-large election system resulted in blacks having less opportunity to participate in the political process and elect candidates of their choice. Plaintiffs appeal.
THE VOTING RIGHTS ACT CLAIM
An electoral system violates section 2 of the Voting Rights Act if the system causes the members of a distinct racial group to “have less opportunity than other members of the electorate to participate in the political process and to elect representatives of their choice.” 42 U.S.C. § 1973(b). The Supreme Court has said that, to satisfy section 2’s standard in a vote dilution case, plaintiffs must show (at a minimum) that: (1) “the minority group ... is sufficiently large and geographically compact to constitute a majority in a single-member district;” (2) the minority group is politically cohesive; and (3) the white majority votes as a bloc sufficiently to defeat the minority group’s preferred candidates.
Thornburg v. Gingles,
478 U.S. 30, 106 S.Ct. 2752, 2766, 92 L.Ed.2d 25 (1986). The district court, in this case, found that Plaintiffs failed to establish the first
Gin-gles
factor: “[Wjhile the Plaintiffs demonstrated the existence of the first
Gingles
precondition as of 1990, the Defendants have established by a preponderance of the evidence that as of the date of trial it is no longer possible to create a minority-
controlled district in DeSoto County.” The district court, therefore, rejected Plaintiffs’ statutory claim. Plaintiffs contend that the district court’s finding that Plaintiffs failed to establish the first
Cin-gles
factor was error because the district court should have never considered Defendants’ evidence of post-1990 population changes. We cannot accept Plaintiffs’ contention.
A.
Plaintiffs first contend that the district court should have excluded Defendants’ evidence of post-1990 population changes because the evidence contradicted a stipulation and several admissions agreed to by Defendants before trial.
In 1991, Defendants admitted that Plaintiffs’ proffered plans indeed created five single-member districts with one majority-black district.
And, in an April 1998 pretrial statement, the parties stipulated that Plaintiffs had drawn two electoral schemes with a black-majority district.
Defendants never amended these admissions or the stipulation. Based on the admissions and stipulation, Plaintiffs contend that Defendants’ evidence of post-census changes is barred because Defendants conclusively admitted that Plaintiffs could establish the required majority-minority district.
Before filing the April pretrial statement, Defendants disclosed that they expected to call two expert witnesses at trial. On 1 May 1998, pursuant to the preexisting pretrial order, Defendants informed Plaintiffs that, given new 1998 voter registration data, Defendants’ experts would challenge the continued validity of the 1990 census figures in their testimony. Defendants explained that their experts would testify that blacks, by 1998, were no longer sufficiently geographically concentrated to permit the creation of a black-majority district. After this disclosure, Plaintiffs filed a motion in limine to exclude Defendants’ proffered evidence; the district court — after a hearing — denied the motion. Plaintiffs never moved for a continuance.
Defendants did not seek to amend or to withdraw the admissions or stipulation. Instead, Defendants argued that their evidence of population changes did not contradict Defendants’ earlier admissions and stipulation because the admissions and stipulation were tied to and, thus, limited to the 1990 census figures. The district court agreed with Defendants. The district court found that the admissions and stipulation inherently were based on the use of 1990 census data.
The district court’s conclusion that the pretrial stipulation was defined by the 1990 census data was no abuse of discretion.
See generally Pulliam v. Tallapoosa County Jail,
185 F.3d 1182, 1185 (11th
Cir.1999) (noting that trial court’s interpretation of pretrial order is reviewed for abuse of discretion). The trial court is in the best position to interpret the scope of stipulations in the pretrial statement.
See Morrison v. Genuine Parts Co.,
828 F.2d 708, 709 (11th Cir.1987) (noting that district court has broad discretion to decide whether to hold party to stipulation). We note that, in the April pretrial statement, Defendants expressly contended that Plaintiffs had not established the first
Gin-gles
factor because the 1990 census might not reflect the county’s population in 1998. Therefore, in the light of the pretrial statement as a whole, the district court’s decision that the stipulation was based on and limited to the 1990 census figures was not error.
Nor do we think the district court erred in construing the admissions as limited to the 1990 census.
We think, at the very least, ambiguity did exist about whether the admissions were absolute or limited to the 1990 census figures, figures which might or might not accurately describe the county’s population at the time of trial.
See Woods v. Robb,
171 F.2d 589, 541-42 (5th Cir.1948). For example, one admission stated: “[I]n making [this] admission Defendants assume that Plaintiffs have accurately reported the figures for each of the districts.... If the figures shown in [the exhibit] turnout to be other than those Plaintiffs have shown, then Defendants reserve the right to supplement this answer accordingly.” And, Plaintiffs’ requests for admission specifically relied on exhibits created with figures from the 1990 census.
See Rolscreen Co. v. Pella Prods. of St. Louis, Inc.,
64 F.3d 1202, 1210 (8th Cir.1995) (noting that conclusive effect of ad
mission “may not be appropriate where requests for admissions or the responses to them are subject to more than one interpretation” and that “[ijssues change as a case develops, and the relevance of discovery responses is related to their context in the litigation”).
The scope and effect of admissions (like the scope and effect of stipulations) is a matter for determination by the trial court, in the exercise of its broad discretion.
Given the circumstances of this case, the district court did not abuse its discretion in interpreting the admissions and stipulation as limited to the 1990 census figures.
B.
Plaintiffs also contend that, even if the admissions and stipulation did not bar the introduction of Defendants’ post-census evidence, the district court erred in allowing Defendants’ evidence to oppose the census figures.
No one challenges the initial accuracy of the 1990 census; the trial, however, was in 1998. At trial, Defendants pointed to the lapse of time since the census and to the changed circumstances. The presumption is that census figures are continually accurate.
See Valdespino v. Alamo Heights Indep. Sch. Dist.,
168 F.3d 848, 853-54 (5th Cir.1999). But this presumption is not irrebuttable.
The continuing accuracy of census figures is presumed only until the party challenging the census data overcomes the presumption with competent evidence to the contrary.
See id.
Although a burden rests on the party challenging the continuing accuracy of the census to introduce evidence to the contrary, we stress that the burden to establish the first
Gingles
factor remains, throughout the case, with the plaintiff.
See Gingles,
106 S.Ct. at 2764. We conclude that the district court did not err in considering non-census data.
Plaintiffs claim that the district court erred in considering non-census evidence based on voter registration figures because, Plaintiffs say, registration data is an inherently unreliable measure of voting age population and cannot be used to contradict census figures. First, we note that there is no per se rule against the use of voter registration data in voting rights cases.
Although the Supreme Court has
written that voter registration data may be less probative than pure population data in voting cases, the Court has treated voter registration evidence as credible and as reliable.
See Burns v. Richardson,
384 U.S. 73, 86 S.Ct. 1286, 1297, 16 L.Ed.2d 376 (1966). We also have recognized the competence of this kind of data.
See Wyche v. Madison Parish Police Jury,
635 F.2d 1151, 1161-62 (5th Cir.1981). Like most evidence presented by expert testimony, we think its admissibility has to be determined on a case-by-case basis by the district court.
See generally Daubert v. Merrell Dow Pharmaceuticals Inc.,
509 U.S. 579, 113 S.Ct. 2786, 2796-98, 125 L.Ed.2d 469 (1993). And, this court has previously said, in a voting rights case, that statistical evidence derived from a sampling method, using reliable statistical techniques, is admissible on the question of determining the relevant population.
See Negron v. City of Miami Beach, Fla.,
113 F.3d 1563, 1570 (11th Cir.1997). We see no reason why the evidence presented in this ease — calculations of the county’s population in 1998 derived from voter registration information — should be subject to a different analysis.
Whether evidence derived from voter registration figures is' sufficiently reliable to be admitted and considered is a determination in the discretion of the district court.
See generally Allison v. McGhan Medical Corp.,
184 F.3d 1300, 1306 (11th Cir.1999) (citing
General Elec. Co. v. Joiner,
522 U.S. 136, 118 S.Ct. 512, 517, 139 L.Ed.2d 508 (1997)) (discussing review of admissibility of expert testimony). If the evidence is admissible, that voter registration data might not be as reliable as some other measures of population goes to the weight of the evidence, but does not preclude use of the figures by the district court.
Here, the district judge was presented with expert testimony, from both sides, on the reliability of Defendants’ evidence. Defendants’ expert spoke to the reliability of the registration data for the county, pointing, out the lack of obstacles to registration. He stated that he believed that registration data would not underrepre-sent the black population in 1998 because the passage of the Motor Voter law,
if anything, would increase registration rates since 1991.
The district court’s receipt and consideration of evidence on the demographic changes in. the county was no abuse of discretion. The kinds of evidence introduced in this case are not unfit for the purpose of challenging the continuing accuracy of census data.
C.
Next, we inquire whether the district court erred in finding no vote dilution for the section 2 claim in this case. We review the district court’s finding of no vote dilution for clear error only.
See Gingles,
106 S.Ct. at 2781. In the present case, Plaintiffs, using the 1990 census, proffered (at best) majority-minority districts with a black voting age majority of only about 54-57 percent. No one dis
putes that there has been substantial population growth in the county since the 1990 census. Defendants showed that a considerable amount of that growth has been within the white population. Based on the post-census population data derived from voter registration figures, Defendants’ experts concluded that the creation of a black-majority district was not feasible in 1998: (1) movement of the district lines would include more whites in the district, thus decreasing the black majority; and (2) the black population growth was geographically distant from the proposed district and could not be included to make a black-majority district.
Defendants also offered other evidence, not derived from voter registration figures, of the population changes and growth in the county.
In
Valdespino,
the Fifth Circuit upheld a district court’s finding that the plaintiffs had failed to establish the first
Gingles
factor. 168 F.3d at 856. There, even though, according to the 1990 census, the plaintiffs could create a majority-minority district, the
Valdespino
defendants presented evidence, at the 1997 trial, that demographic changes since the 1990 census had made the creation of such a district impossible. The defendants’ presentation included evidence that a large apartment complex in the district had closed and reopened with fewer residents, while, at the same time, residential development outside the district increased.
See id.
at 850-51. The Fifth Circuit concluded that the district court did not err in deciding that the defendants’ figures demonstrated sufficient post-census demographic changes to raise considerable doubt that a majority-minority district could still be created and in deciding that the plaintiffs had not carried their burden of proof.
See id.
at 854, 856.
The record, in this case, presents ample evidence of population growth in the county since 1990, particularly outside of Plaintiffs’ proposed district. And, even using the 1990 census, Plaintiffs’ proffered black-majority district was not one that was overwhelmingly black. Thus, we cannot say that the district court erred in this finding that Defendants’ evidence undercut the presumption that the 1990 census reflected the truth about the county’s population and population distribution in 1998.
On this record, the district court (considering all the evidence including the 1990 census) did not clearly err in finding and in concluding that Plaintiffs failed to show the existence of the black-majority district needed to establish their prima facie case of vote dilution.
THE CONSTITUTIONAL CLAIMS
Plaintiffs contend that, even if their statutory claim fails, the district court erred in rejecting their constitutional vote dilution claims.
Plaintiffs point out
that the district court found that a discriminatory purpose underlies the county’s current at-large voting scheme. And, Plaintiffs assert that the record shows that the county’s black population lacks an equal opportunity to participate in the political process and elect candidates of its choice. Plaintiffs argue that they, therefore, have sufficiently established claim's under the Fourteenth and Fifteenth Amendments.
We disagree.
As an initial matter, we doubt that any plaintiff, challenging an electoral system like DeSoto County’s, can establish a constitutional vote dilution claim where his section 2 claim has failed. Plaintiffs say that, after a claimant has proved discriminatory intent, he need only produce minimal evidence of injury resulting from the challenged electoral scheme to prevail under the Constitution. But, the Supreme Court, historically, has articulated the same general standard, governing the proof of injury, in both section 2 and constitutional vote dilution cases; plaintiffs, in both cases, must show that “there is evidence that excluded groups have ‘less opportunity to participate in the political process and to elect candidates of their choice.’ ”
Compare Davis v. Bandemer,
478 U.S. 109, 106 S.Ct. 2797, 2809, 92 L.Ed.2d 85 (1986) (quoting
Rogers v. Lodge,
458 U.S. 613, 102 S.Ct. 3272, 3279, 73 L.Ed.2d 1012 (1982)),
with Gingles,
106 S.Ct. at 2763,
and
42 U.S.C. § 1973(b). The pertinent issues seem the same (or almost the same) in both cases. And, even if the standards are not completely identical in application, we know that section 2 was intended to be more permissive than the constitutional standard.
See Sobmon,
899 F.2d at 1015 (Kravitch, J., specially concurring);
see also Lee County Branch of NAACP v. City of Opelika,
748 F.2d 1473, 1478 n. 7 (11th Cir.1984) (“[I]f the plaintiffs cannot prevail under the generally more easily proved ‘results’ standard of section 2, it is unlikely that they could prevail on their constitutional claims in any event.”). The parties have cited (and we have found) -no case in which a circuit court has concluded that an at-large or multi-member-district electoral system, although not in violation of section 2, unconstitutionally dilutes minority voting strength.
In the absence of Supreme Court direction, therefore, we question, as a legal proposition, whether vote dilution can be established under the Constitution when the pertinent record has not proved vote dilu
tion under the more permissive section 2. But, we need not resolve this question today.
Even if we assume that it is possible, as a matter of law, to prevail on a constitutional claim where no section 2 violation can be in fact established, Plaintiffs here have not proved their constitutional claim. Briefly stated, to establish a constitutional vote dilution claim, Plaintiffs must show that: (1) the county’s black population lacks an equal opportunity to participate in the political process and elect candidates of its choice; (2) this inequality of opportunity results from the county’s at-large voting scheme; and (3) a racially discriminatory purpose underlies the county’s voting scheme.
Lucas v. Townsend,
967 F.2d 549, 551 (11th Cir.1992);
see also Bandemer,
106 S.Ct. at 2809. We will accept, for the purposes of this appeal, the district court’s finding that Plaintiffs have shown discriminatory intent.
And, we will assume, for the sake of argument, that Plaintiffs’ evidence demonstrates the absence of equal opportunity.
Plaintiffs, nonetheless, failed to establish their constitutional claims because the record fails to show that the inequality of opportunity results from the county’s current electoral system. In other words, Plaintiffs have failed to establish causation.
That a plaintiff, claiming a violation of his voting rights under the Fourteenth and Fifteenth Amendments, must show that an injury is caused by the government conduct he seeks to challenge is hardly a novel proposition.
See Kirksey v. Bd. of Supervisors of Hinds County,
554 F.2d 139, 148 (5th Cir.1977) (inquiring whether reapportionment plan “will in fact have the effect of perpetuating the denial of access to the political process that was proved by plaintiffs to exist”);
Personnel Adm’r of Mass. v. Feeney,
442 U.S. 256, 99 S.Ct. 2282, 2293, 60 L.Ed.2d 870 (1979)
(requiring that claimant show discriminatory impact traceable to discriminatory purpose);
see also Allen v. Wright,
468 U.S. 737, 104 S.Ct. 3315, 3327, 82 L.Ed.2d 556 (1984) (requiring equal protection plaintiff to show causation as element of standing). To show that inequality of opportunity is caused by a particular electoral system, a plaintiff must establish that “an alternative election scheme exists that would provide better access to the political process.”
Burton v. City of Belle Glade,
178 F.3d 1175, 1199 (11th Cir.1999);
see also Reno v. Bossier Parish Sch. Bd.,
520 U.S. 471, 117 S.Ct. 1491, 1498, 137 L.Ed.2d 730 (1997);
Holder v. Hall,
512 U.S. 874, 114 S.Ct. 2581, 2585, 129 L.Ed.2d 687 (1994);
Nipper v. Smith,
39 F.3d 1494, 1533 (11th Cir.1994) (en banc).
As we have explained, “[I]f a minority cannot establish that an alternative election scheme exists that would provide better access to the political process, then the challenged voting practice is not responsible for the claimed injury.”
Burton,
178 F.3d at 1199;
see also Gingles,
106 S.Ct. at 2766 (explaining if first
Gingles
factor is not shown, then “the multi-member form of the district cannot be responsible for minority voters’ inability to elect its candidates”).
Here, Plaintiffs failed to make the requisite showing of causation: Plaintiffs did not establish that an alternative system of districting could exist whereby the black-minority vote could elect its preferred candidates. The district court found that the creation of a black-majority district, in 1998, was not feasible. Plaintiffs, on appeal, argue that a black-majority district is not required; according to Plaintiffs, a “black-influence district,” where a substantial black minority is coupled with sufficient white cross-over voting so that the black minority in fact can elect candidates of its choice, is sufficient. We, however, need not decide whether Plaintiffs’ “influence district” theory is correct.
Plaintiffs never argued this theory to the district court.
Plaintiffs have failed to establish causation. Plaintiffs’ contention that the district court erred in rejecting their constitutional claims, therefore, must fail.
CONCLUSION
The district court dealt with the evidence without error. The case was fully tried. The district court was the finder of fact. The district court did not err in determining that Plaintiffs showed no lack of equal political opportunity that was caused by the county’s electoral system! Plaintiffs failed to meet their burden. The judgment of the district court is AFFIRMED.