Justice BREYER delivered the opinion of the Court.
Appellants, a group of Arizona voters, challenge a redistricting plan for the State's legislature on the ground that the plan's districts are insufficiently equal in population. See Reynolds v. Sims, 377 U.S. 533, 577, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964). Because the maximum population deviation between the largest and the smallest district is less than 10%, the appellants cannot simply rely upon the numbers to show that the plan violates the Constitution. See Brown v. Thomson, 462 U.S. 835, 842, 103 S.Ct. 2690, 77 L.Ed.2d 214 (1983). Nor have appellants adequately supported their contentions with other evidence. We consequently affirm a 3-judge Federal District Court decision upholding the plan.
I
In 2000, Arizona voters, using the initiative process, amended the Arizona Constitution to provide for an independent redistricting commission. See Arizona State Legislature v. Arizona Independent Redistricting Comm'n, 576 U.S. ----, ----, 135 S.Ct. 2652, 2677, 7192 L.Ed.2d 704 (2015) (upholding the amendment as consistent with federal constitutional and statutory law). Each decade, the Arizona Commission on Appellate Court Appointments creates three slates of individuals: one slate of 10 Republicans, one slate of 10 Democrats, and one slate of 5 individuals not affiliated with any political party. The majority and minority leader of the Arizona Legislature each select one Redistricting Commission member from the first two lists. These four selected individuals in turn choose one member from the third, nonpartisan list. See Ariz. Const., Art. IV, pt. 2, §§ 1 (5)-(8). Thus, the membership of the Commission consists of two Republicans, two Democrats, and one independent.
After each decennial census, the Commission redraws Arizona's 30 legislative districts. The first step in the process is to create "districts of equal population in a grid-like pattern across the state." § 1 (14). It then adjusts the grid to "the extent practicable" in order to take into account the need for population equality; to maintain geographic compactness and continuity; to show respect for "communities of interest"; to follow locality boundaries; and to use "visible geographic features" and "undivided ... tracts." §§ 1 (14)(B)-(E). The Commission will "favo[r]" political "competitive[ness]" as long as its efforts to do so "create no significant detriment to the other goals." Id., § 1 (14)(F). Finally, it must adjust boundaries "as necessary"
to comply with the Federal Constitution and with the federal Voting Rights Act. § 1 (14)(A).
After the 2010 census, the legislative leadership selected the Commission's two Republican and two Democratic members, who in turn selected an independent member, Colleen Mathis. Mathis was then elected chairwoman. The Commission hired two counsel, one of whom they thought of as leaning Democrat and one as leaning Republican. It also hired consultants, including mapping specialists, a statistician, and a Voting Rights Act specialist. With the help of its staff, it drew an initial plan, based upon the gridlike map, with district boundaries that produced a maximum population deviation (calculated as the difference between the most populated and least populated district) of 4.07%. After changing several boundaries, including those of Districts 8, 24, and 26, the Commission adopted a revised plan by a vote of 3 to 2, with the two Republican members voting against it. In late April 2012, the Department of Justice approved the plan as consistent with the Voting Rights Act.
The next day, appellants filed this lawsuit, primarily claiming that the plan's population variations were inconsistent with the Fourteenth Amendment. A 3-judge Federal District Court heard the case. See 28 U.S.C. § 2284(a) (providing for the convention of such a court whenever an action is filed challenging the constitutionality of apportionment of legislative districts). After a 5-day bench trial, the court, by a vote of 2 to 1, entered judgment for the Commission. The majority found that "the population deviations were primarily a result of good-faith efforts to comply with the Voting Rights Act ... even though partisanship played some role." 993 F.Supp.2d 1042, 1046 (Ariz.2014). Appellants sought direct review in this Court. See 28 U.S.C. § 1253. We noted probable jurisdiction on June 30, 2015, and we now affirm.
II
A
The Fourteenth Amendment's Equal Protection Clause requires States to "make an honest and good faith effort to construct [legislative] districts ... as nearly of equal population as is practicable." Reynolds, 377 U.S., at 577, 84 S.Ct. 1362. The Constitution, however, does not demand mathematical perfection. In determining what is "practicable," we have recognized that the Constitution permits deviation when it is justified by "legitimate considerations incident to the effectuation of a rational state policy." Id ., at 579, 84 S.Ct. 1362. In related contexts, we have made clear that in addition to the "traditional districting principles such as compactness [and] contiguity," Shaw v. Reno, 509 U.S. 630, 647, 113 S.Ct. 2816, 125 L.Ed.2d 511 (1993), those legitimate considerations can include a state interest in maintaining the integrity of political subdivisions, Mahan v. Howell, 410 U.S. 315, 328, 93 S.Ct. 979, 35 L.Ed.2d 320 (1973), or the competitive balance among political parties, Gaffney v. Cummings, 412 U.S. 735, 752, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973). In cases decided before Shelby County v. Holder, 570 U.S. ----, 133 S.Ct. 2612, 186 L.Ed.2d 651 (2013), Members of the Court expressed the view that compliance with § 5 of the Voting Rights Act is also a legitimate state consideration that can justify some deviation from perfect equality of population. See League of United Latin American Citizens v. Perry, 548 U.S. 399, 518, 126 S.Ct. 2594, 165 L.Ed.2d 609 (2006) (SCALIA, J., concurring in judgment in part and dissenting in part, joined in relevant part by ROBERTS, C.J., THOMAS & ALITO, JJ.);
id., at 475, n. 12, 126 S.Ct. 2594 (Stevens, J., concurring in part and dissenting in part, joined in relevant part by BREYER, J.); id ., at 485 n. 2, 126 S.Ct. 2594 (Souter, J., concurring in part and dissenting in part, joined by GINSBURG, J.); see also Vieth v. Jubelirer, 541 U.S. 267, 284, 124 S.Ct. 1769, 158 L.Ed.2d 546 (2004) (plurality opinion) (listing examples of traditional redistricting criteria, including "compliance with requirements of the [Voting Rights Act]"). It was proper for the Commission to proceed on that basis here.
We have further made clear that "minor deviations from mathematical equality" do not, by themselves, "make out a prima facie case of invidious discrimination under the Fourteenth Amendment so as to require justification by the State." Gaffney, supra, at 745, 93 S.Ct. 2321. We have defined as "minor deviations" those in "an apportionment plan with a maximum population deviation under 10%." Brown, 462 U.S., at 842, 103 S.Ct. 2690. And we have refused to require States to justify deviations of 9.9%, White v. Regester, 412 U.S. 755, 764, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973), and 8%, Gaffney, 412 U.S., at 751, 93 S.Ct. 2321. See also Fund for Accurate and Informed Representation, Inc. v. Weprin, 506 U.S. 1017, 113 S.Ct. 650, 121 L.Ed.2d 577 (1992) (summarily affirming a District Court's finding that there was no prima facie case where the maximum population deviation was 9.43%).
In sum, in a case like this one, those attacking a state-approved plan must show that it is more probable than not that a deviation of less than 10% reflects the predominance of illegitimate reapportionment factors rather than the "legitimate considerations" to which we have referred in Reynolds and later cases. Given the inherent difficulty of measuring and comparing factors that may legitimately account for small deviations from strict mathematical equality, we believe that attacks on deviations under 10% will succeed only rarely, in unusual cases. And we are not surprised that the appellants have failed to meet their burden here.
B
Appellants' basic claim is that deviations in their apportionment plan from absolute equality of population reflect the Commission's political efforts to help the Democratic Party. We believe that appellants failed to prove this claim because, as the district court concluded, the deviations predominantly reflected Commission efforts to achieve compliance with the federal Voting Rights Act, not to secure political advantage for one party. Appellants failed to show to the contrary. And the record bears out this conclusion. Cf. Anderson v. Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) (explaining that a district court's factual finding as to whether discrimination occurred will not be set aside by an appellate court unless clearly erroneous).
The Voting Rights Act, among other things, forbids the use of new reapportionment plans that "would lead to a retrogression in the position of racial minorities with respect to their effective exercise of the electoral franchise." Reno v. Bossier Parish School Bd., 520 U.S. 471, 478, 117 S.Ct. 1491, 137 L.Ed.2d 730 (1997). A plan leads to impermissible retrogression when, compared to the plan currently in effect (typically called a "benchmark plan"), the new plan diminishes the number of districts in which minority groups can "elect their preferred candidates of choice" (often called "ability-to-elect" districts). See 52 U.S.C. § 10304(b). A State can obtain legal assurance that it has satisfied the non-retrogression requirement if it submits its proposed plan to the Federal Department of Justice, and the Department does not object to the plan within 60 days. See 28 C.F.R. §§ 51.9, 51.52(b) (2015). While Shelby County struck down the § 4(b) coverage formula, that decision came after the maps in this case were drawn.
The record in this case shows that the gridlike map that emerged after the first step of the redistricting process had a maximum population deviation from absolute equality of districts of 4.07%. After consulting with their Voting Rights Act expert, their mapping consultant, and their statisticians, all five Commissioners agreed that they must try to obtain Justice Department Voting Rights Act "preclearance" and that the former benchmark plan contained 10 ability-to-elect districts. They consequently set a goal of 10 such districts for the new plan. They then went through an iterative process, involving further consultation, to adjust the plan's initial boundaries in order to enhance minority voting strength. In October 2011 (by a vote of 4 to 1), they tentatively approved a draft plan with adjusted boundaries. They believed it met their goal of 10 ability-to-elect districts. And they published the plan for public comment.
In the meantime, however, the Commission received a report from one of its statisticians suggesting that the Department of Justice might not agree that the new proposed plan contained 10 ability-to-elect districts. It was difficult to know for certain because the Justice Department did not tell States how many ability-to-elect districts it believed were present in a benchmark plan, and neither did it typically explain precisely and specifically how it would calculate the number that exist in a newly submitted plan. See 76 Fed.Reg. 7470-7471 (2011). At the same time, the ability-to-elect analysis was complex, involving more than simply adding up census figures. The Department of Justice instead conducted a "functional analysis of the electoral behavior within the particular ... election district," id., at 7471, and so might, for example, count as ability-to-elect districts "crossover" districts in which white voters combine their votes with minorities, see Bartlett v. Strickland, 556 U.S. 1, 13-14, 129 S.Ct. 1231, 173 L.Ed.2d 173 (2009). Its calculations might take into account group voting patterns, electoral participation, election history, and voter turnout. See 76 Fed.Reg., 7471. The upshot was not random decision-making but the process did create an inevitable degree of uncertainty. And that uncertainty could lead a redistricting commission, as it led Arizona's, to make serious efforts to make certain that the districts it believed were ability-to-elect districts did in fact meet the criteria that the Department might reasonably apply. Cf. Alabama Legislative Black Caucus v. Alabama, 575 U.S. ----, ----, 135 S.Ct. 1257, 1273, 191 L.Ed.2d 314 (2015) ("The law cannot insist that a state legislature, when redistricting, determine precisely what percent minority population § 5 demands [because] the standards of § 5 are complex.... [To do so would] lay a trap for an unwary legislature, condemning its redistricting plan as either ... unconstitutional racial gerrymandering [or] ... retrogressive under § 5").
As a result of the statistician's report, the Commission became concerned about certain of its proposed boundaries. One of the Commission's counsel advised that it would be "prudent to stay the course in terms of the ten districts that are in the draft map and look to ... strengthen them if there is a way to strengthen them." 993 F.Supp.2d, at 1058 (internal quotation marks omitted). Subsequently, the Commission adopted several changes to the boundaries of Districts 24 and 26. It reduced the populations of those districts, thereby increasing the percentage of Hispanic voters in each. The Commission approved these changes unanimously.
Changes in the boundaries of District 8, however, proved more controversial. District 8 leaned Republican. A Democrat-appointed Commissioner asked the mapping specialist to look into modifications that might make District 8 politically more competitive. The specialist returned with a draft that shifted the boundary line between District 8 and District 11 so as to keep several communities with high minority populations together in District 8. The two Republican-appointed Commissioners objected that doing so would favor Democrats by "hyperpacking" Republicans into other districts; they added that the Commission should either favor political competitiveness throughout the State or not at all. Id., at 1059 (internal quotation marks omitted).
The Democrat-appointed proponent of the change replied that District 8 had historically provided minority groups a good opportunity to elect their candidate of choice-an opportunity that the changes would preserve. The Voting Rights Act specialist then said that by slightly increasing District 8's minority population, the Commission might be able to claim an 11th ability-to-elect district; and that fact would "unquestionably enhance the submission and enhance chances for preclearance." Ibid. (internal quotation marks omitted). The Commission's counsel then added that having another possible ability-to-elect district could be helpful because District 26 was not as strong an ability-to-elect district as the others. See ibid .
Only then, after the counsel and consultants argued for District 8 changes for the sake of Voting Rights Act preclearance, did Chairwoman Mathis support those changes. On that basis, the Commission ultimately approved the changes to District 8 by a vote of 3 to 2 (with the two Republican-appointed commissioners dissenting). The total population deviation among districts in this final map was 8.8%. While the Commission ultimately concluded that District 8 was not a true ability-to-elect district, the State's submission to the Department of Justice cited the changes to District 8 in support of the argument for preclearance. On April 26, 2012, the Department of Justice precleared the submitted plan.
On the basis of the facts that we have summarized, the District Court majority found that "the population deviations were primarily a result of good-faith efforts to comply with the Voting Rights Act ... even though partisanship played some role." 993 F.Supp.2d, at 1046. This conclusion was well supported in the record. And as a result, appellants have not shown that it is more probable than not that illegitimate considerations were the predominant motivation behind the plan's deviations from mathematically equal district populations-deviations that were under 10%. Consequently, they have failed to show that the Commission's plan violates the Equal Protection Clause as interpreted in Reynolds and subsequent cases.
C
The appellants make three additional arguments. First, they support their claim that the plan reflects unreasonable use of partisan considerations by pointing to the fact that almost all the Democratic-leaning districts are somewhat underpopulated and almost all the Republican-leaning districts are somewhat overpopulated. That is likely true. See 993 F.Supp.2d, at 1049 (providing a chart with percentage deviation figures by district). But that fact may well reflect the tendency of minority populations in Arizona in 2010 to vote disproportionately for Democrats. If so, the variations are explained by the Commission's efforts to maintain at least 10 ability-to-elect districts. The Commission may have relied on data from its statisticians and Voting Rights Act expert to create districts tailored to achieve preclearance in which minority voters were a larger percentage of the district population. That might have necessitated moving other voters out of those districts, thereby leaving them slightly underpopulated. The appellants point to nothing in the record to suggest the contrary.
Second, the appellants point to Cox v. Larios, 542 U.S. 947, 124 S.Ct. 2806, 159 L.Ed.2d 831 (2004), in which we summarily affirmed a district court's judgment that Georgia's reapportionment of representatives to state legislative districts violated the Equal Protection Clause, even though the total population deviation was less than 10%. In Cox, however, unlike the present case, the district court found that those attacking the plan had shown that it was more probable than not that the use of illegitimate factors significantly explained deviations from numerical equality among districts. The district court produced many examples showing that population deviation as well as the shape of many districts "did not result from any attempt to create districts that were compact or contiguous, or to keep counties whole, or to preserve the cores of prior districts." Id ., at 949, 124 S.Ct. 2806. No legitimate purposes could explain them. It is appellants' inability to show that the present plan's deviations and boundary shapes result from the predominance of similarly illegitimate factors that makes Cox inapposite here. Even assuming, without deciding, that partisanship is an illegitimate redistricting factor, appellants have not carried their burden.
Third, appellants point to Shelby County v. Holder, 570 U.S. ----, 133 S.Ct. 2612, 186 L.Ed.2d 651 (2013), in which this Court held unconstitutional sections of the Voting Rights Act that are relevant to this case. Appellants contend that, as a result of that holding, Arizona's attempt to comply with the Act could not have been a legitimate state interest. The Court decided Shelby County, however, in 2013. Arizona created the plan at issue here in 2010. At the time, Arizona was subject to the Voting Rights Act, and we have never suggested the contrary.
* * *
For these reasons the judgment of the District Court is affirmed.
It is so ordered.