
    Nicholas ANDERSON, a minor, by his parent and next friend, Ellen DOWD; Kayleigh Barry-Meltzer, a minor, by her parents and next friends, Cathleen Barry and George Meltzer; John P. Feeney, Jr., a minor, by his parents and next friends, Ena and John Feeney; Michael Gattozzi, a minor, by his parents and next friends, Joseph and Patrice Gattozzi; Jamie Lee Higgins, a minor, by her parents and next friends, Kerry Ann and Joseph Higgins; John K. O’Toole, Jr., a minor, by his parents and next friends, John and Rose O’Toole; Kathleen McCoy, a minor, by her parents and next friends, Carol and John Mccoy; Andrew Sharaffa, a minor, by his parents and next friends, David and Mae Sharaffa; Sean J. and Thomas E. Stoddard, minors, by their parents and next friends, Mary K. and Stephen Stoddard, Plaintiffs, Appellants, Boston’S Children First, Plaintiff, v. CITY OF BOSTON; Thomas Menino, Mayor of the City of Boston; Thomas W. Payzant, Superintendent of the Boston Public Schools; Boston School Committee; Elizabeth Reilinger, Boston School Committee Chairperson; Alfreda J. Harris, School Committee Vice-Chairperson; Felix D. Arroyo, School Committee Member; Robert P. Gittens, School Committee Member; Susan Naimark, School Committee Member; Marchelle Raynor, School Committee Member; William Spring, School Committee Member, Defendants, Appellees.
    No. 03-2021.
    United States Court of Appeals, First Circuit.
    Heard Jan. 6, 2004.
    Decided July 12, 2004.
    
      Michael Williams, with whom Robert J. Roughsedge, Chester Darling, and Citizens for the Preservation of Constitutional Rights, Inc., were on brief, for appellants.
    Frances S. Cohen, with whom Erica L. Hovani, Matthew M. Lyons, and Dechert LLP, were on brief, for appellees.
    Sharon L. Brown on brief for amicus curiae Pacific Legal Foundation.
    Before BOUDIN, Chief Judge, and LYNCH and LIPEZ, Circuit Judges.
   LIPEZ, Circuit Judge.

At the outset of its penultimate ruling in this protracted litigation, the district court observed: “This case may possibly be the concluding chapter in thirty years of litigation over the effort to desegregate the Boston Public Schools.” Boston’s Children First v. Boston School Comm., 260 F.Supp.2d 318, 319 (D.Mass.2003). That cautious prediction may be accurate.

Boston’s Children First, a non-profit advocacy group, and parents of several white students sued the City of Boston, Boston Mayor Thomas Menino, Boston Public Schools (BPS) Superintendent Thomas Payzant, and members, of the Boston School Committee (collectively, the defendants), claiming that .BPS’s now-defunct race-conscious assignment system violated their children’s rights under the Fourteenth Amendment’s Equal Protection Clause, 42 U.S.C. §§ 1981 and 1983, 42 U.S.C. § 2000d (commonly known as Title VI), and Article 111 of the Amendments to the Massachusetts Declaration of Rights. Prompted at least in part by the lawsuit against them, the Boston School Committee, at the recommendation of Superintendent Payzant, voted to remove the racial guidelines from the assignment system on July 14, 1999. After BPS adopted a facially race-neutral assignment plan in November 1999, the plaintiffs continued to press their suit, seeking declaratory relief, several forms of injunctive relief, compensatory damages, and nominal damages. Over the course of four rulings, the district court denied all of plaintiffs’ claims save one: an award-of nominal damages of $1:00 each to the two students who would have been assigned to the school of their choice under the old system but for their race. Plaintiffs appeal. Finding no error, we affirm the district court rulings in all respects.

I.

With four published district court decisions setting out the factual background of this case in considerable detail, we limit ourselves here to a recitation of the facts most pertinent to the issues before us on appeal. For greater detail, we refer readers to Boston’s Children First v. City of Boston, 62 F.Supp.2d 247 (D.Mass.1999) (“BCF I”); Boston’s Children First v. City of Boston, 98 F.Supp.2d 111 (D.Mass.2000) (“BCF II ”); Boston’s Children First v. Boston School Comm., 183 F.Supp.2d 382 (D.Mass.2002) (“BCF III”); and Boston’s Children First v. Boston School Comm., 260 F.Supp.2d 318 (D.Mass.2003) (“BCF IV”). Additionally, the majority and dissenting opinions in Wessmann v. Gittens, 160 F.3d 790 (1st Cir.1998), provide a useful historical overview of BPS’s desegregation-related litigation in federal court.

In quick review, thirty years ago the Massachusetts federal district court held that the City of Boston promoted and maintained a racially segregated dual public school system in violation of constitutionally guaranteed rights. Morgan v. Hennigan, 379 F.Supp. 410, 482 (D.Mass.1974). After twelve years of supervision by the district court, the court returned control over student assignments to BPS, declaring that BPS’s student assignment system had achieved unitariness, Morgan v. Nucci 831 F.2d 313, 318 (1st Cir.1987), “i.e. a fully integrated, non-segregated system.” Id. at 316. At that point, BPS adopted an assignment system known as the Controlled Choice Student Assignment Plan, (the “Old Plan”), which went into effect for the 1989-90 academic year.

A. The Old Plan

BPS assigns students to schools at the transition grades during students’ public school careers, each of which corresponds to a student’s advancement to a new type of school: kindergarten 1 (programs for 4-year-olds), kindergarten 2 (programs for five-year-olds), first grade (elementary school), sixth grade (middle school), and ninth grade (high school). While high school assignments are made on a citywide basis, Boston is divided into three Attendance Zones — the North, East, and West Zones — for purposes of the elementary and middle school assignments at issue in this case. These zones were drawn by the district court as part of its desegregation orders, and the lines largely hew to major transportation routes to keep traditional neighborhoods intact as much as possible. Students are eligible to attend any of the schools located in the Attendance Zone in which the students reside.

As part of the assignment process, students rank their preferences for the schools within their Attendance Zone, as well as for the few schools that accept students from any part of the city without regard to Attendance Zone lines. Students whose siblings attend a school receive a preference for that school during the assignment process. Similarly, students who live within the walk zone of a given school receive a preference for seats at that school. Finally, every student receives a randomly assigned lottery number, with the lower numbers being considered more advantageous.

Under the Old Plan, BPS assigned students to schools using the following criteria: the student’s rank preference for the school; whether a sibling already attended the school; whether the student lived within the school’s walk zone; whether the student had already matriculated at the school on a temporary basis; and, as a tie-breaker, the student’s random number, with a lower random number winning out over higher numbers. Assignments under the Old Plan operated with one additional constraint — -the “ideal racial percentage” for each grade’s population, as calculated by the racial and ethnic composition of the student population in that grade within each of the three Attendance Zones. If admitting a student would cause a deviation of more than 15% from the “ideal racial percentage,” that student would not be admitted. The Old Plan operated largely without change for ten years, from 1989 through 1999.

B. Boston’s Exam School Assignment System and Related “Reverse Discrimination” Lawsuits

In June 1999, the first four of what ultimately became ten individual plaintiffs, along with Boston’s Children First, filed this lawsuit, prompted in part by the successful “reverse discrimination” lawsuits brought by the families of two white children who were denied admission to their choice of one of BPS’s three competitive exam schools. See McLaughlin v. Boston School Comm., 938 F.Supp. 1001 (D.Mass.1996); Wessmann v. Gittens, 160 F.3d 790 (1st Cir.1998). These exam schools admit students using a different system than that used by the other schools in the BPS system. At the' time Julia McLaughlin applied to Boston Latin School, admissions were based on a combination of an applicant’s grade point average and standardized test scores (collectively called the “z-score”), subject to a 35% minority set-aside previously imposed by the federal desegregation order and still in effect at that time. After McLaughlin filed suit and obtained a preliminary injunction admitting her to Boston Latin, BPS voluntarily discontinued use of the 35% quota, admitted students similarly situated to McLaughlin, and commissioned a consulting company to devise a new admissions policy.

The replacement exam school admission policy eventually adopted by BPS defined the “qualified applicant pool” -for each exam school as the 50% of students with z-scores above the mean in any given year. Then, BPS filled half of each exam school’s seats based on the students’ expressed preferences for each school and their rank order z-scores. The remainder of the seats were also allocated by students’ school preferences and rank order z-scores, subject to mirroring the racial composition of the remaining qualified applicant pool not yet admitted. Sarah Wessmann was denied admission to Boston Latin under the new exam school admission system, sued, and ultimately prevailed on appeal. We found the admission system unconstitutional because its use of racial classifications was not narrowly tailored to meet a compelling state interest. See Wessmann, 160 F.3d at 807-09.

C. The New Plan

Based in no small part on Superintendent Payzant’s frank assessment' to the School Committee- that, in light of Wess-mann and other reverse discrimination lawsuits, plaintiffs, in this case would almost certainly prevail in their challenge to the Old Plan, the School Committee voted on July 14, 1999, to discontinue the use of the racial classifications in the Old Plan. See BCF IV, 260 F.Supp.2d at 324 n. 10. At the time of this vote, the School Committee also charged the Superintendent with developing a new student assignment plan that did not consider “race as a factor in making student assignments” and would also reflect “other changes necessary to maximize access to choice, to support diversity, and promote quality education for the children of the City of Boston.” BCF IV, 260 F.Supp.2d at 325.

On October 20 and November 3, 1999, the Superintendent recommended that the Old Plan be further modified in two salient ways: by reducing the percentage of available seats allocated for students within a school’s walk zone from 100% to 50%, and by treating students who did not actually live within the walk zone of any school as though they had a walk-zone preference for their first or second choice school. On November 10, the School Committee adopted the Superintendent’s recommendations to the Controlled Choice Student Assignment Plan with the modification that students lacking a walk-zone school would be given a walk-zone preference for both their first and second choice schools. For convenience, we refer to the modified Controlled Choice Student Assignment Plan as the “New Plan.”

Under the New Plan, which went into effect for the 2000-01 school year, students still rank their choice of schools and receive random numbers. Students are sorted by their school choice and ordered by their random number, with the lowest numbers put at the top of the list. BPS then computes the number of available seats at each school and sets aside 50% of those seats for students who live within the school’s walk zone. The seats at each school are then filled according to the following priorities: first priority to students within the school’s walk zone and with a sibling already in attendance; second priority to students outside the school’s walk zone but with a sibling already in attendance; and third priority to students within the school’s walk zone but with no sibling already in attendance. If there are more students in a priority tier than seats available, the seats will go to the students with the better random numbers. As students are admitted, the system updates the number of walk zone seats that are available. Once those walk zone seats are filled, a student’s walk-zone status drops out of consideration and students are assigned in accordance with the school preferences by the rank of their random number. Finally, the applications and assignments are done in rounds; if a student fails to meet the first round application deadline, she can submit her preferences in the second round, and so on.

D. Course of Litigation Below

As previously mentioned, four plaintiffs and Boston’s Children First filed suit in federal district court on June 21, 1999, claiming that the Old Plan violated the Equal Protection Clause, which provides that no State shall “deny to any person within its jurisdiction the equal protection of the laws”; 42 U.S.C. §§ 1981 and 1983, which collectively prohibit deprivations of constitutional rights under color of state law; Title VI, which prohibits institutions receiving federal funds from engaging in racial discrimination; and Article 111 of the Amendments to the Massachusetts Declaration of Rights, which states that “[n]o student shall be assigned to or denied admittance to a public school on the basis of race, color, national origin or creed.” Plaintiffs sought injunctive relief and class certification to represent all similarly situated white children.

On July 14, 1999, the School Committee voted to discontinue the use of race in assignments. On August 10, 1999, the district court denied plaintiffs’ request for injunctive relief that would have, inter alia, ordered BPS to cease using race or ethnicity in any phase of the school assignment process and to re-open the assignment process to students who attempted to transfer schools the previous year, as well as those entering kindergarten and first grade. BCF I, 62 F.Supp.2d at 262.

Some time after BCF I, six other plaintiff children joined the suit, and plaintiffs’ claims for relief expanded considerably. Plaintiffs now sought at least six forms of injunctive relief, including (1) admitting plaintiffs to their schools of choice, (2) enjoining defendants from the use of any race-based practice in all aspects of school assignments and governance, (3) requiring all students in the BPS system to reapply under the terms of the New Plan, (4) dismantling the Attendance Zones, (5) granting Boston’s Children First access to BPS records to monitor compliance, and (6) retaining jurisdiction in federal court for three years to monitor compliance. Plaintiffs also sought declaratory relief stating that the New Plan violated their rights under the relevant federal and state laws, nominal damages for all plaintiffs, and compensatory damages for five plaintiffs. On October 29, BPS moved to dismiss plaintiffs’ claims, arguing that the suit was moot in light of its voluntary discontinuance of the Old Plan.

On May 19, 2000, the BCF II court ruled that all of these claims survived defendants’ motion to dismiss, with one exception. Finding that five “of the plaintiffs did not seek assignments in the 1999-2000 school year and have not indicated any present intention to seek an assignment in the 2000-01 school year,”- the district court held that “injunctive relief is unnecessary to redress the injuries of these [five] plaintiffs as they have not indicated that they will even participate in the future school assignment plan.” BCF II, 98 F.Supp.2d at 117. Accordingly, the court granted defendants’ motion to dismiss in so far as it related to the injunctive relief of those five plaintiffs, and. otherwise denied the motion. Id.

In BCF III, the court disposed of additional claims. First, the court dismissed as moot the remaining five plaintiffs’ request for injunctive relief admitting them to their school of choice because three plaintiffs (Sharaffa, O’Toole, and Feeney) left the BPS system prior to the 2001 admissions season, and the final two plaintiffs (Higgins and Thomas Stoddard) chose to remain at their current schools. BCF III, 183 F.Supp.2d at 395. Second, the court rejected plaintiffs’ claims that the three Attendance Zones were “racially gerrymandered,” explaining that “[because the zones today, whatever role race may have played in their creation, serve administrative, rather than racial balancing purposes, I conclude that no viable ‘case or controversy’ exists regarding their current configuration.” Id. at 397-99. This holding disposed of both the injunc-tive request related to dismantling the Attendance Zones and the declaratory relief request to the extent that it rested on the allegedly racial purpose of the Attendance Zones. Third, the court denied plaintiffs’ request for an injunction requiring every student in the BPS system to reapply under the New Plan, explaining that

even if a showing could be made that one or more of the plaintiffs might derive an advantage from a system-wide reprocessing of all student assignments, any benefit conferred would be outweighed by the consequent demoralization of a school system that has yet to fully absorb the effects of a quarter-century effort to bring itself into compliance with court-ordered desegregation.

Id. at 401. Fourth, the court held that Boston’s Children First lacked standing as an organizational plaintiff to press the lawsuit. Id. at 403. The BCF III court reserved all of the other claims in the suit pending further discovery, briefing, and trial. Id.

Following a bench trial on the merits, the district court issued a ruling in BCF IV on April 23, 2003. The BCF FV court found that (1) the New Plan, with its change in the walk zone preference from 100% to 50% of seats, was facially race-neutral, (2) there was no evidence that the policy was applied in a discriminatory manner, and (3) plaintiffs did not show that the policy was adopted with a discriminatory intention and applied in a way that had a discriminatory effect. BCF TV, 260 F.Supp.2d at 331-32. Accordingly, the district court declined to apply strict scrutiny to the New Plan. Id. at 333. Instead, it evaluated the New Plan under rational basis review and found that it “satisfied] the reasonableness test.” Id. The court also held that plaintiffs’ “[m]ere skepticism ... about the defendants’ future intentions! 1 cannot justify” an injunction prohibiting the school system from using race as a factor in the assignment system in the future. In consequence, the court entered judgment for defendants, id. at 334, and noted that it would address the bifurcated claims for nominal damages separately. Id. at n. 28.

On May 27, 2003, the court issued a short memorandum and order awarding nominal damages of $1.00 each to Feeney and McCoy because, as BPS admitted, those plaintiffs “were denied seat assignments at their preferred schools because of their race” under the Old Plan. Boston’s Children First v. Boston School Comm., No. 99-11330-RGS (D.Mass. May 27, 2003) (unpublished) (“BCF V”). The court also held that “[a]s the remaining plaintiffs can make no showing of a deprivation under Texas v. Lesage, 528 U.S. 18, 21, 120 S.Ct. 467, 145 L.Ed.2d 347 (1999) (per curiam), no damages, nominal or otherwise, may be awarded.” BCF V, at 1.

II.

On this factually rich and comprehensively litigated background, we are now presented with plaintiffs’ appeal from a variety of adverse rulings. Although we find some confusion in the record and the briefs over both the exact nature of the relief sought on appeal and whether certain claims for injunctive relief sought by plaintiffs were dismissed for mootness or lack of standing, or instead resolved on the merits, we ultimately understand that plaintiffs seek three forms of relief on appeal. First, plaintiffs seek a declaratory judgment that the New Plan is unconstitutional. Second, plaintiffs seek an injunction prohibiting BPS from using race in any way in a modified school assignment system. Third, plaintiffs request nominal damages for the eight plaintiffs to whom nominal damages were previously denied. After discussing the standards of review which guide our analysis of the issues, we will address these three claims seriatim.

III.

A. Standards of Review

“We accord deferential review to specific findings of fact emanating from a bench trial.” Wessmann, 160 F.3d at 795 (citing Fed.R.Civ.P. 52(a)). However, when the issues on appeal “raise[ ] either questions of- law or questions about how the law applies to discerned facts,” such as whether the proffered evidence establishes a discriminatory purpose or a disproportionate racial impact, “our review is essentially plenary.” Id. at 795. Similarly, we review de novo the district court’s other legal conclusions, Cohen v. Brown Univ., 101 F.3d 155, 192 (1st Cir.1996), including the level of scrutiny it applied when evaluating the constitutionality of the New Plan and, in the context of denying eight plaintiffs nominal damages, its interpretation of Texas v. Lesage, 528 U.S. 18, 120 S.Ct. 467, 145 L.Ed.2d 347 (1999) (per curiam). Dispositions of a request for injunctive relief are typically “review[ed] only to ensure that the district court did not abuse its discretion in granting, or failing to grant, such relief,” Caroline T. v. Hudson School Dist., 915 F.2d 752, 754 (1st Cir.1990), although related legal determinations, such as mootness, are reviewed under the usual de novo review afforded to all conclusions of law. See Cotter v. City of Boston, 323 F.3d 160, 166 (1st Cir.2003).

3B. The Constitutionality of the New Plan

A key question in analyzing the constitutionality of the New Plan is whether strict scrutiny or rational basis review applies. Plaintiffs present several arguments that strict scrutiny applies, including that the unconstitutionality of the Old Plan requires a presumption that the New Plan is unconstitutional and that the defendants’ stated goal of diversity requires a finding that the New Plan is unconstitutional. Even if those arguments fail, plaintiffs contend, the New Plan has a discriminatory effect from which a discriminatory intent can be inferred. ■

1. , Adoption of the New Plan

When designing and choosing among methods for assigning students to schools, school boards seek to promote certain values and policies, and they operate within certain historical, political, financial, and legal constraints. Defendants in this case are no exception. As they considered the adoption of the New Plan in 1999, they saw a system burdened with a significant inequity in the number of walk zone schools available to students' in different parts of the city. For example, while about 30% of elementary school students had only one to three walk zone choices, approximately 37% had six to ten. In fact, when the New Plan was adopted in November 1999, 1772 students were not within the walk zone of any school. Furthermore, at' the neighborhood level, some areas of the city had an excess capacity of school seats compared to the number of school-age children, while other areas faced significant shortages. For example, Roxbury and South Dorchester both faced shortages of around 2500 seats, while Jamaica Plain and Allston/Brighton collectively had excess capacity of around 1600 seats. Additionally, some schools in significant demand were over-chosen by parents and students, while others lacked enough applicants to fill the available seats. In the East Zone, where plaintiffs reside, Everett Elementary had 7.3 applicants for each available seat for the 2002-03 academic year, while Lee Elementary had just 0.6 applicants for each available seat.

The substantial disparities among the Boston neighborhoods regarding school quality and capacity, numbers of resident students, and walk zone choices were significant considerations in the adoption of the New Plan and its reduction of the walk zone preference to 50% of the seats. Additionally, BPS compiled statistics showing that of the parents and students ranking their school choices, approximately 50% chose a walk zone school as their first choice, while the other 50% chose as their first choice a school whose walk zone did not include the student.

BPS also had been concerned about the potentially resegregative impact of removing the racial guidelines of the Old Plan and simultaneously leaving the 100% walk zone preference in place. Apparently, though, BPS’s analysis allayed those concerns, showing that there would be little immediate resegregative effect of removing the racial guidelines. Superintendent Payzant explained to the Massachusetts Board of Education that when the School Committee was considering changes to the Old Plan, BPS

did some simulations to see what the impact would be as a result of removing race from the plan, and based on the data we had to work with at the time, ... the result of removing race was really very, very small. In fact, we found out we only had three additional schools that would not meet the racial guidelines in one or more grades....

Although the immediate racial impact of removing the racial guidelines would be “very small,” BPS was still concerned about the impact on access and choice that would flow from a 100% walk zone preference. Accordingly, BPS simulated the-results of leaving the walk zone preference at 100%, reducing it to 75%, and reducing it to 50%. Ultimately, Superintendent Payzant recommended the 50% reduction in an October 20, 1999, memo to the School Committee.

RATIONALE

One hundred percent walk zone preference in a controlled choice plan without racial guidelines could result in all available seats being assigned to students within the walk zone. The result would limit choice and access for all students, including those who have no walk zone or live in walk zones where there are insufficient seats to serve the students residing in the walk zone....
Until more neighborhoods without schools or with insufficient numbers of schools have [more schools], [a] one hundred percent walk zone preference would limit choice and access for too many families to the schools they want their children to attend. On the other hand, the policy also should and does recognize the interests of families who want to choose a walk zone school.

Superintendent Payzant concluded the memo by stating that a 50% walk zone preference “provides a fair balance and enables the School Committee to establish a policy which will result in progress in meeting the goal[s] of excellence, equity and diversity through access and educational opportunity throughout the Boston Public Schools.”

The evidence supports the conclusion that the racial impact of removing the racial guidelines was not significant, and the School Committee adopted the 50% reduction in walk-zone seats primarily because they were concerned about limited choice and equity for students with an insufficient number of walk-zone schools. Additionally, Superintendent Payzant and the School Committee concluded that the 50% reduction was consistent with progress towards BPS’s existing goals of excellence, equity, and diversity.

2. Applicability of Strict Scrutiny Review

“The central purpose of the Equal Protection Clause of the Fourteenth Amendment is the prevention of official conduct discriminating on the basis of race.” Washington v. Davis, 426 U.S. 229, 239, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). Accordingly, “[p]roof of racially discriminatory intent or purpose is required to show a violation of the Equal Protection Clause.” Village of Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U.S. 252, 265, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977). When the government uses explicit racial classifications for the distribution of benefits, discriminatory intent is presumed, and those policies are always subjected to strict scrutiny. See, e.g., Pers. Adm’r of Mass. v. Feeney, 442 U.S. 256, 272, 99 S.Ct. 2282, 60 L.Ed.2d 870 (1979) (“A racial classification, regardless of purported motivation, is presumptively invalid and can be upheld only upon an extraordinary justification.”); Grutter v. Bollinger, 539 U.S. 306, 326, 123 S.Ct. 2325, 156 L.Ed.2d 304 (2003) (“[AJll racial classifications imposed by government must be analyzed by' a reviewing court under strict scrutiny.”) (internal quotations and citation omitted). “We apply strict scrutiny to all racial classifications to ‘smoke out’ illegitimate uses of race by assuring that [government] is pursuing a goal important enough to warrant use of a highly suspect tool.” Grutter, 539 U.S. at 326, 123 S.Ct. 2325 (quoting City of Richmond v. J.A. Croson Co., 488 U.S. 469, 493, 109 S.Ct. 706, 102 L.Ed.2d 854 (1989) (plurality opinion).) The term racial classification “normally refers to a governmental standard, preferentially favorable to one race or another, for the distribution of benefits.” Raso v. Lago, 135 F.3d 11, 16 (1st Cir.1998).

Here, though, the New Plan does not employ racial classifications: Indeed, plaintiffs concede, as they must, that the New Plan is facially race-neutral. In contrast, then, to the automatic application of strict scrutiny to overt racial classifications, “when facially neutral legislation is subjected to equal protection attack, an inquiry into intent is necessary to determine whether the legislation in some sense was designed to accord disparate treatment on the basis of racial considerations.” Washington v. Seattle School Dist., 458 U.S. 457, 484-85, 102 S.Ct. 3187, 73 L.Ed.2d 896 (1982) (emphasis added). Although plaintiffs may also invoke strict scrutiny review by showing that the facially neutral policy is applied in a discriminatory manner, Yick Wo v. Hopkins, 118 U.S. 356, 373-74, 6 S.Ct. 1064, 30 L.Ed. 220 (1886), plaintiffs have pointed to no evidence that the New Plan is applied in a discriminatory manner, nor do we see any in the record.

In reviewing a uniformly applied facially neutral statute, “[d]etermining whether invidious discriminatory purpose was a motivating factor [in its adoption] demands a sensitive inquiry into such circumstantial and direct evidence of intent as may be available.” Arlington Heights, 429 U.S. at 266, 97 S.Ct. 555. The Supreme Court nonexhaustively enumerated several factors relevant to the inquiry: the degree of disproportionate racial effect, if any, of the policy; the justification, or lack thereof, fpr any disproportionate racial effect that may exist; and the legislative or administrative historical background of the decision. Id. at 266-68, 97 S.Ct. 555. We will evaluate plaintiffs’ various theories supporting strict scrutiny review through the lens provided by Arlington Heights, although we take the factors in a different order to better track plaintiffs’ arguments.

a. Historical background: alleged presumption of discriminatory intent

Plaintiffs claim that because the Old Plan was unconstitutional, and the New Plan perpetuates the Old Plan’s effects in violation of defendants’ alleged “duty to eliminate their duel [sic] assignment system” of the Old Plan, we should infer that the New Plan was adopted with a discriminatory intent. To support this contention, plaintiffs quote two bedrock Supreme Court desegregation cases from the 1970s: Dayton Bd. of Educ. v. Brinkman, 448 U.S. 526, 99 S.Ct. 2971, 61 L.Ed.2d 720 (1979) (Dayton II); and Keyes v. School Dist., 413 U.S. 189, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973). The very language plaintiffs quote from these eases, as well as their significantly different facts, demonstrate the inaptness of these cases.

As plaintiffs point out, the Keyes Court held that “there is a high probability that where school authorities have effectuated an intentionally segregative policy in a meaningful portion of the school system, similar impermissible considerations have motivated their actions in other areas of the system.” Keyes, 413 U.S. at 208, 93 S.Ct. 2686. Plaintiffs quote Dayton II for the proposition that such a system is “under a continuing duty to eradicate the effects of that system, and [ ]. the system-wide nature of the violation furnished pri-ma facie proof that current segregation in the [ ] schools was caused at least in part by prior intentionally segregative official acts.” Dayton II, 443 U.S. at 536, 99 S.Ct. 2971 (internal citation omitted).

Keyes and Dayton II were ongoing school desegregation cases that involved purposeful discrimination by school systems attempting to avoid their affirmative obligation to undo systemic discrimination under Brown v. Bd. of Educ., 347 U.S. 483, 495, 74 S.Ct. 686, 98 L.Ed. 873 (1954) (Brown I) (holding that the concept of “separate but equal” has no place in public education) and Brown v. Bd. of Educ., 349 U.S. 294, 301, 75 S.Ct. 753, 99 L.Ed. 1083 (1955) (Brown II) (ordering an end to segregated public education “with all deliberate speed.”). That was the status of the Boston school desegregation case at the time of the initial liability findings in 1974 and the remedial plan in 1976. See Morgan v. Kerrigan, 509 F.2d 580, 593-94 (1st Cir.1974)(relying in part on Keyes in upholding liability); Morgan v. Kerrigan, 530 F.2d 401, 425 (1st Cir.1976)(relying in part on Keyes in upholding the remedial plan).

This case arises in a completely different context. After going through school desegregation, Boston was found in 1987 to have achieved a unitary school assignment system. See Morgan, 831 F.2d at 318. The defendants here acted not with the intent to maintain a system of de jure segregation, but with the purpose of maintaining the post-segregation unitary system. Indeed, the Old Plan, toward this end, incorporated aspects of the Boston school desegregation plan that were constitutionally compelled. Additionally, when the school committee adopted the Old Plan for the 1989 school year, the questionable constitutionality of such race-conscious efforts to minimize the tendency to resegre-gate was far from clear.

In essence, plaintiffs would like to limit the relevant history of this case to the period following the adoption of the Old Plan. However, there is 'also a relevant history of de jure discrimination against minorities that predates 1989, as the long history of the BPS desegregation litigation shows. In consequence, the present-day Boston school system really faces two “legacies” — the system.it administered for decades that intentionally discriminated against minorities to maintain an unequal and segregated system, and the system it administered for ten years that subjected seat assignments to racial guidelines to maintain the racial integration achieved during the intervening twelve years of court-ordered desegregation.

There is no gainsaying that the system still must confront the fallout from its days of over-serving what ■ were traditionally white communities and under-serving what were traditionally minority, then mostly black, communities. As the BCF IV court stated: “Any assignment plan in the Boston School system is, and will be for the foreseeable future, constrained by the mismatch between school capacity and neighborhood demand, due in part to demographic shifts, and in part to the dual system’s legacy of over-serving what were historically white neighborhoods.” BCF IV, 260 F.Supp.2d at 325.

We decline to adopt plaintiffs’ circumscribed view of history. Likewise, we decline to find that plaintiffs have established a prima facie case of discriminatory intent in the adoption of the New Plan simply because the Old Plan was constitutionally unsound. Over forty years ago, the Supreme Court advised federal courts that context matters:

[I]n dealing with claims under broad provisions of the Constitution, which derive content by'an interpretive process of inclusion and exclusion, it is imperative that generalizations, based on and qualified by the concrete situations that gave rise to them, must not be applied out of context in disregard of variant controlling facts.

Gomillion v. Lightfoot, 364 U.S. 339, 343-44, 81 S.Ct. 125, 5 L.Ed.2d 110 (1960) (evaluating the validity of a redistricting plan under, inter alia, the Equal Protection Clause). Here, BPS voluntarily discontinued use of the Old Plan once it con-eluded that the plan was constitutionally suspect — in fact, within eight months of our decision in Wessmcmn — and replaced it with a racially neutral assignment system that was designed to maximize, not minimize, the equitable distribution of seats in the public schools.

We recognize that “[bjenign intentions do not immunize government action,” Raso, 135 F.3d at 16, and we do riot suggest otherwise. There is no doubt that governmental policies that employ racial classifications for the distribution of benefits, or otherwise evince racial discrimination, should be subjected to strict scrutiny review. If plaintiffs could make such a showing, we would not hesitate to apply strict scrutiny to the New Plan. However, by declining to extend the reach of Keyes, Dayton IÍ, and similar cases beyond their facts to create a presumption of racially discriminatory purpose in the adoption of the New Plan, we simply refuse to conflate vastly dissimilar cases.

b. Historical background: inclusion of diversity as a goal of the New Plan

Plaintiffs also argue that the New Plan was adopted for racially discriminatory reasons and should be subject to strict scrutiny because Superintendent Payzant and the Boston School Committee identified diversity as one of the several goals of the student assignment system. Plaintiffs equate-this commitment to racial diversity with an illegitimate commitment to racial balancing. See Wessmann, 160 F.3d at 800 (noting the “Constitution’s general prohibition against racial balancing”). To prove their point, plaintiffs cite the testimony of Superintendent Payzant elicited on cross-examination during this litigation:

Q. So this 50% walk-to plan actually preserved the racial balance gained by the Old Plan; isn’t that correct?
A. Right, which is precisely why I didn’t want to keep 100% walk-zone preference in the New Plan after racial guidelines were withdrawn.

In addition, plaintiffs cite communications from defendants trying to convince the Racial Imbalance Advisory Council (RIAC) and the Board of Education that after the adoption of the New Plan, BPS should still qualify for funds under the Racial Imbalance Law, M.G.L. c. 71, § 37C, et seqi , (RIL). Essentially, Superintendent Payzant argued that (1) BPS qualified for funds under the Old Plan, (2) the New Plan maintained approximately the same racial balance within the schools as the Old Plan, so (3) BPS should still qualify for RIL funds, even though the New Plan lacked the explicit racial guidelines of the Old Plan.

Plaintiffs’ reliance on selected excerpts ignores the totality of the evidence. As already noted, BPS’s statistical analyses showed that, even with the elimination of the racial guidelines and a 100% walk zone preference in place, there was only a “very, very small” racial result. Superintendent Payzant testified at trial that BPS compared the results of a 100% walk zone preference applied both with and without the use of the racial guidelines called for in the Old Plan

to let the data speak for themselves and show to the Commissioner, and ultimately the State Board of Education, that the impact of the change in the student assignment plan by removing racial guidelines but keeping the other elements of the controlled choice would enable us to come very close to the same circumstances that we had that qualified us for ... meeting the standards of the Racial Imbalance Law before the policy was changed.

The data are indeed telling. According to Superintendent Payzant’s testimony to the Board of Education, when BPS simulated the first-round transition grade assignments for the 1999-2000 year using actual parent choices but eliminating only the use of the racial guidelines, it found that just three additional schools would have one or more transitional grades falling outside the racial guidelines. Using the parental choice data to analyze the effect on individual student placements without the use of the racial guidelines revealed that only 938 out of 13,057 (or seven percent) of students would have been assigned to different schools. About fifty-three percent of those 938 individual changed assignments would have resulted in the student being assigned to a school which she had ranked higher, and, correspondingly, forty-seven percent would have been assigned to a school which she had ranked lower. Whites, Asians, and Hispanics fared slightly better as groups, while blacks and Native Americans fared slightly worse.

In sum, BPS’s analyses showed that, even after removing the racial guidelines of the Old Plan, the BPS school assignment system did not need further modification to maintain the “racial balance” required to be eligible for RIL funds. Although defendants were pressured by RIAC to continue explicit racial balancing, they refused to comply, despite the substantial RIL funds at stake.

However, the Superintendent and the School Committee were also concerned about equity of choice and access across the system, particularly for students who lived in neighborhoods with inadequate capacity or underperforming schools. In his July 14, 1999 memo to the School Committee, Superintendent Payzant commented that “it is important to note that this is not an issue of returning to neighborhood schools. That can happen in an equitable way only when new quality schools are built in neighborhoods that now have an insufficient number of schools to serve resident school age children.... ” This concern is further reflected in the summary description of the New Plan provided to the Commissioner of Education as part of BPS’s RIL compliance presentation. That document stated that the Superintendent and the School Committee

are confident that the [New Plan] continues to ensure both choice and access beyond a student’s particular neighborhood in order to preserve racial and ethnic diversity and reduce the likelihood of racial isolation within its schools. In addition, the [New Plan] retains all of the educational benefits of the original Controlled Choice Student Assignment Plan, including the promotion of school improvement, continuity and stability of placement, and equitable distribution of resources and educational opportunity district-wide.

The defendants’ public confidence that the New Plan preserved racial diversity while advancing the other values that they identified was not an admission that the New Plan was a suspect device to achieve the numerically precise racial balancing of the Old Plan.

Contrary to plaintiffs’ arguments, the mere invocation of racial diversity as a goal is insufficient to subject the New Plan to strict scrutiny. In those cases where the Supreme Court inquired whether diversity is a compelling state interest and whether the program at issue could survive strict scrutiny, the programs were all subjected to strict scrutiny because they used explicit racial classifications to achieve the goal of diversity. None of these cases, nor any other case to which our attention has been drawn, has subjected a governmental program to strict scrutiny simply because the state mentioned diversity as a goal. As the district court succinctly put it: “Motive, in other words, is not always suspect. Means, however, may be.” BCF TV, 260 F.Supp.2d at 330. The Supreme Court has explained that the motive of increasing minority participation and access is not suspect. See, e.g., City of Richmond v. JA Croson Co., 488 U.S. 469, 507, 109 S.Ct. 706, 102 L.Ed.2d 854 (1989) (approving the use of race-neutral means to increase minority participation in governmental programs). '

We said as much in Raso v. Lago,' 135 F.3d 11 (1998), where we considered an equal protection and § 1983 challenge to a facially race-neutral policy change regarding the award of housing units that, at the end of the day, resulted in fewer white residents receiving a preference for the units to which they would have otherwise been entitled because of their prior residency. After acknowledging that the change in policy was motivated by a desire to ensure that all races had equal access to the new housing, we stated that “plaintiffs are mistaken in treating ‘racial motive’ as a synonym for a constitutional violation.” Raso, 135 F.3d at 16.

Employing de novo review and placing Superintendent Payzant’s cited testimony in the context of the entire record,, we.find that the plaintiffs have not shown that the defendants’ use of the word “diversity” was simply a subterfuge for “racial balancing.” While defendants frankly acknowledged that they valued the degree of integration BPS had attained since it came under federal court order thirty years ago, their analyses using actual parental choice patterns showed that removing the racial guidelines of the Old Plan and the maintenance of a 100% walk-zone preference would not significantly erode those integration gains. BPS then resisted pressure to adhere to strict racial balancing,' even with RIL funds potentially on the table, and adopted the race-neutral New Plan. To increase the likelihood of a favorable outcome on diversity and to promote “school improvement, continuity and stability of placement, and equitable distribution of resources and educational opportunity district-wide,” as well as the system’s ongoing goals of “excellence, equity and diversity,” the defendants opted for the 50% walk-zone preference.

As the district court put it, Superintendent Payzant’s reference to diversity “simply restated his more convincing point that the revised assignment plan is intended to address issues of equity by giving parents in under-served neighborhoods fairer access to the school system’s resources.” BCF IV, 260 F.Supp.2d at 332. To the extent that the School Committee’s adoption of the New Plan promoted choice and equitable access to BPS resources for all students in the BPS system, as well as diversity, there is nothing in that mix of goals or the means of achieving them that triggers strict scrutiny under our own precedents or those of the Supreme Court.

c. Disproportionate effect

Having rejected plaintiffs’ claims that the history of the New Plan’s adoption, and its stated goal of diversity, require the application of strict scrutiny review, we now turn to their evidence regarding the impact of the New Plan. As we previously noted, a disproportionate racial effect of a policy can be evidence of an invidious discriminatory purpose. Although plaintiffs cite to “individual examples of the racial effect” of the 50% reduction in walk zone seats under the New Plan, they neither describe these examples as a “disproportionate effect” nor accept that any such disproportionate effect of the New Plan is relevant to establishing defendants’ purportedly racially discriminatory purpose. Instead, they argue that their individual examples suffice to establish an equal protection violation. Before explaining how plaintiffs apparently misunderstand the relevant case law and their resultant evi-dentiary burden in this case, we first recount the evidence they presented on the racial effect of the New Plan.

To establish the allegedly discriminatory effect of the New Plan’s reduction of the walk zone preference from 100% to 50% of available seats, plaintiffs relied exclusively on the testimony of Ann Walsh, president of Boston’s Children First. Although Walsh testified that she reviewed admissions data from “every school in the city,” she only presented data for the 2002-03 admission rounds for one class in each of three schools: a pre-kindergarten program at the Wolfgang Amadeus Mozart Elementary School, and two kindergarten programs at the Richard J. Murphy Elementary School and the Mary Lyon Elementary School. Walsh testified that she selected these particular schools because she “looked for schools with white walkers who were pushed aside by the [change to a] 50% [walk zone preference], and [these three schools were] an example of that.”

Walsh prepared one-page charts for each of these schools, comparing the racial demographics of students who were admitted to the selected classes under the New Plan, with its 50% walk zone preference, to the racial demographics of students who would have been admitted if a full 100% of the seats had been reserved for students who lived within the walk zone. Walsh’s testimony, and the charts she prepared for this litigation, show that in the three elementary schools — out of the 85 or so in the BPS system — a total of twenty white students who would have been admitted under a hypothetical 100% walk zone preference were not admitted under the actual 50% walk zone preference. In plaintiffs’ view, with this showing of “individual examples of the racial effect” of the change in the walk zone preference, there was no need to engage in any systemwide analysis of the racial impact, of the walk zone seat reduction. Indeed, Walsh did not attempt to project a systemwide impact from her three-school analysis. Walsh explicitly testified that she is “opposed to the concept that the overall impact on the school system is the issue.”

Plaintiffs erred in this minimalist approach to their evidentiary burden in this case. To be sure, the Equal Protection Clause protects individuals: “rights created by the first section of the Fourteenth Amendment are, by its terms, guaranteed to the individual. The rights established are personal rights.” Shelley v. Kraemer, 334 U.S. 1, 22, 68 S.Ct. 836, 92 L.Ed. 1161 (1948). When a governmental policy employs overt racial classifications, the impact of race on an individual outcome is clear. As we have explained, courts will then apply strict scrutiny to determine whether the use of the racial classification is narrowly tailored to serve a compelling state interest. See, e.g., Gratz v. Bollinger, 539 U.S. 244, 275-76, 123 S.Ct. 2411, 156 L.Ed.2d 257 (2003). As we discuss infra in Part III.D., the Old Plan used explicit racial guidelines, and two plaintiffs in this case — John Feeney and Kathleen McCoy — showed that they were denied seats at their schools of choice under the Old Plan because of their race and the imposition of racial caps in force at that time. Accordingly, they were awarded nominal damages in recognition of that injury.

In contrast, when evaluating a facially race-neutral policy, the impact of race on an individual outcome is not always immediately clear. Courts can -only infer that an invidious racial purpose motivated a facially neutral policy when that policy creates disproportionate racial results. “Sometimes a clear pattern, unexplainable on grounds other' than race, emerges from the effect of the state action even when the governing legislation appears neutral on its face.” Village of Arlington Heights v. Metropolitan Housing Dev. Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977) (emphasis added). See also Washington v. Davis, 426 U.S. 229, 242, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976) (“an invidious discriminatory purpose may often be inferred from the totality of the relevant facts, including the fact, if it is true, that the law bears more heavily on one race than another.”).

In this context, showing only isolated instances of students not receiving assignments at their first choice schools is insufficient. Here, there is no clear pattern of disparate racial impact, much less the “stark” pattern contemplated by Arlington Heights. Id. (“Absent a pattern as stark as that in Gomillion or Yiek Wo, impact alone is not determinative ....”) (footnotes omitted). At most, plaintiffs have established that in three schools the reduction from 100% to 50% of seats set aside for students in the walk zone resulted in twenty white students, out of the approximately 25,000 or so elementary (K-5) students in the BPS system, not being assigned to their first choice school. More relevantly, Walsh’s own charts show that seven of the twenty students who actually were assigned to the disputed seats were white, meaning that the impact on whites as a group was a net loss of thirteen seats. Isolated examples that only show a small net loss of seats to white students in selected schools is a far cry from showing that the New Plan disproportionately affects white students in the BPS system. In fact, as the district court emphasized, even with the reduction in walk zone seats, “in the 2002-2003 school year, 80 percent of white applicants received their first choice of schools, as compared to 77 percent of black applicants.” BCF IV, 260 F.Supp.2d at 332.

Even if this showing could be characterized as evidence of a disproportionate effect, a characterization which we reject, the “individual examples of the racial effect” cited by plaintiffs are explainable “on grounds other than race.” Arlington Heights, 429 U.S. at 266, 97 S.Ct. 555. As the district court found, plaintiffs “have not been able to show [ ] that the loss was due to discrimination.... Rather, as defendants point out, white students have been denied admission to certain schools, not because they were forced to compete on a non-level playing field, but because their parents have tended to over-choose these same schools.” BCF IV, 260 F.Supp.2d at 332. If plaintiffs had been able to show that the New Plan resulted in stark systemwide racial disparities regarding assignments to first choice schools, we might — depending on the circumstances— have reached the conclusion that intentional discrimination occurred and so adopt a stricter standard of scrutiny in assessing justification. Plaintiffs chose, however, to eschew such analysis.

The BCF IV court rightly concluded that plaintiffs’ evidence fails to show any disproportionate effect of the New Policy.

[I]t was open to plaintiffs to show that the reduction in the walk zone preference has had a disproportionate impact on white children, that is, that a greater percentage of white students have found themselves shut out of their neighborhood schools. This plaintiffs have not done.

Id. at 331-32. With plaintiffs having shown no racial classification at play in the New Plan, no discriminatory purpose for its adoption, and no discriminatory effect of its application, we cannot conclude that the plan “in some sense was designed to accord disparate treatment on the basis of racial considerations.” Washington v. Seattle School Dist., 458 U.S. 457, 485, 102 S.Ct. 3187, 73 L.Ed.2d 896 (1982). Consequently, the district court correctly held that the New Plan was not subject to strict scrutiny.

3. Rational Basis Review

Instead, since race-based classifications are not in play and plaintiffs failed to show that the New Plan was adopted with a discriminatory purpose, the New Plan must only survive rational basis review; as long as the plan is rationally related to a legitimate governmental interest, it must be upheld. See, e.g., Romer v. Evans, 517 U.S. 620, 631, 116 S.Ct. 1620, 134 L.Ed.2d 855 (1996) (holding that “if a law neither burdens a fundamental right nor targets a suspect class, we will uphold the legislative classification so long as it bears a rational relation to some legitimate end").

As we have explained at some length, defendants adopted the New Plan to foster "excellence, equity and diversity through access and educational opportunity throughout the Boston Public Schools." All of those goals are legitimate state interests, and the assignment process of the New Plan is rationally related to achieving them. Plaintiffs do not contend otherwise. Again, we think the district court said it well:

Because the School Committee has rescinded the use of any form of racial classification, direct or indirect, in the New Choice Plan, its stated objectives of preserving parental choice and opportunity, particularly for parents who would otherwise be restricted in their choice of schools, and of fostering school excellence by permitting parents to vote with their feet, satisfy the reasonableness test.

BCF IV, 260 F.Supp.2d at 333.

Accordingly, we reject plaintiffs' claims that the New Plan violates their rights under the Equal Protection Clause of the Fourteenth Amendment, Title VI, or §~ 1981 and 1983.

4. Article 111 Claim

Although plaintiffs argue in their opening brief to this court that the Old Plan violated Article 111 of the Amendments to the Massachusetts Declaration of Rights, they only summarily state once that "the District Court should have subjected the New Plan to Strict Scrutiny under Article 111," (emphasis added), citing to Comfort ex rel. Neumyer v. Lynn School Comm., 283 F.Supp.2d 328 (D.Mass.2003) without comment. When a party includes no developed argumentation on a point, as is the case here, we treat the argument as waived under our well established rule. See United States v. Bongiorno, 106 F.3d 1027, 1034 (1st Cir.1997) ("We have steadfastly deemed waived issues raised on appeal in a perfunctory manner, not accompanied by developed argumentation."). We make two points, however. First, in the context of arguing that the Old Plan violated Article 111, plaintiffs claim that the "Comfort Court held that under Art. 111, school assignment plans that deny students an assignment to their neighborhood schools are subject to strict scrutiny... ." This misstates Comfort. Comfort, 283 F.Supp.2d at 366 ("I recognize . . . the need to proceed with caution.... [A]lthough I am convinced by amici that intermediate scrutiny is the correct test to apply here, my analysis below will apply the more rigorous standard which the parties have briefed, strict scrutiny.") Second, and more importantly, given our disposition of the federal claims, we would not find that the New Plan assigns students "on the basis of race, color, national origin or creed." Mass. Const. amend. art. 111.

C. Prospective Injunctive Relief

Injunctive relief is a discretionary remedy. Thus, appellate courts typically review grants or denials of such relief only for abuse of discretion. Caroline T. v. Hudson School Dist., 915 F.2d 752, 754 (1st Cir.1990). However, to the extent that the disposition of the request for an injunction turns on an issue of law, such as lack of standing or mootness, appellate courts review such determinations de novo. See Langlois v. Abington Housing Authority, 207 F.3d 43, 47 (1st Cir.2000) (observing that although injunctions are typically-reviewed for abuse of discretion, “the standard of review obviously depends on the issue under consideration. Generally speaking, pure issues of law ... are reviewed de novo, findings of fact for clear error, and ‘judgment calls’ with considerable deference depending upon the issue.”)

Plaintiffs argue that the district court erred by dismissing their request for an injunction against BPS’s future use of race because of a lack of standing, citing to BCF II, 98 F.Supp.2d at 117 and BCF III, 183 F.Supp.2d at 395, without quoting any language of the district court. Plaintiffs misread the district court’s holdings. The district court in fact did not dismiss the plaintiffs’ request for a prohibitory injunction for lack of standing. As it noted in its May 21, 2002 Memorandum and Order regarding this standing issue:

In a January 25, 2002 Memorandum and Order [BCF III], the court found that while plaintiffs lacked standing to pursue immediate injunctive relief (given the absence of any cognizable injury), there was a strong possibility that one or more plaintiffs had standing to seek prospective relief enjoining any racially-based allocation of walk zone preferences.... Consequently, the court afforded plaintiffs an opportunity “for further briefing of the Lesage issues identified in this opinion, as well as issues of a constitutional dimension raised by the School Committee’s walk zone preference policy.” [citing BCF III, 183 F.Supp.2d at 403.]

Boston’s Children First v. Boston School Comm., No. Civ. A. 99-11330-RGS, 2002 WL 1058923, at *1 (D.Mass. May 21, 2002) (citation omitted) (“May 21 Order”). The “Lesage issues” identified in this May 21 Order relate to the standing and mootness discussion in BCF III, 183 F.Supp.2d at 392-95.

In the May 21 Order, which addressed, inter alia, plaintiffs’ standing to seek the requested prohibitory injunction, the district court explained that seven of the ten plaintiffs either “attested to having applied for year 2002-2003 admission to schools within their walk zones” or “attest[ed] to their intention to remain in the Boston public school system to apply for middle school assignments within their respective walk zones.” May 21 Order at *1. The district court then concluded that “under Lesage each [of the seven] has demonstrated standing to seek forward-looking relief.” Id.

Here, then, the district court explicitly held that seven of the plaintiffs had standing to seek an injunction prohibiting BPS from the unconstitutional use of race in future assignment systems. As can be seen from both the May 21 Order and the treatment of plaintiffs’ request for forward-looking relief in BCF IV, which we discuss next, the district court did not dismiss this claim for want of standing. Accordingly, we can dispense with any further analysis on that ground.

After a bench trial on the merits, the district court denied plaintiffs’ requests to enjoin defendants from the future use of race and to retain jurisdiction over the assignment system. BCF IV, 260 F.Supp.2d at 333-34. Plaintiffs claim that the district court misapplied City of Mesquite, v. Aladdin’s Castle, Inc., 455 U.S. 283, 102 S.Ct. 1070, 71 L.Ed.2d 152 (1982) in so ruling. There was no such error.

We discussed City of Mesquite in New England Regional Council of Carpenters v. Kinton, 284 F.3d 9 (1st Cir.2002), where we held that when a governmental entity revised a challenged policy to remove the offending language, plaintiffs’ claim for in-junctive relief was mooted. Id. at 18. Directly addressing the Supreme Court’s decision in City of Mesquite, we explained that the Supreme Court had “held that ‘a voluntary cessation of a challenged practice does not deprive a federal court of its power to determine the legality of the practice.’ ” Id. (quoting City of Mesquite, 455 U.S. at 289, 102 S.Ct. 1070).' This is precisely the City of MesqvAte language upon which plaintiffs rely. As we made clear in Kinton, though, this reliance is misplaced: “Under circuit precedent ... the City of Mesquite exception applies ‘only when there is a reasonable expectation that the challenged conduct will be repeated following dismissal of the case.’ ” Kinton, 284 F.3d at 18 (quoting D.H.L. Assocs., Inc. v. O’Gorman, 199 F.3d 50, 55 (1st Cir.1999)). There is no such reasonable expectation here. As the district court observed in BCF IV: “Mere skepticism ... about the defendants’ future intentions[ ] cannot justify the type of judicial intervention that plaintiffs seek.” BCF IV, 260 F.Supp.2d at 333.

Whether this ruling is characterized as one based on mootness concerns (reviewed de novo) or on the merits (reviewed for abuse of discretion), we find that the district court did not err in denying plaintiffs’ claims for an injunction prohibiting BPS from the unconstitutional use of race in future student assignment plans. Defendants have voluntarily abandoned the unconstitutional use of race in all of its student assignment systems, and they have expressed in testimony and in letters to the Racial Imbalance Advisory Council and the Board of Education their strong desire to comply with constitutional requirements in all future assignment systems. As we have discussed supra in Part III.B.2.b, the defendants’ commitment to diversity is not per se constitutionally suspect. While there is ample evidence that defendants will continue to monitor relevant school demographics and will consider modifying the current assignment system to meet all of their stated goals, including diversity, plaintiffs have been unable to show any reasonable expectation that.defendants will return to unconstitutional means to achieve those goals. Accordingly, we see no reason to overturn the district court’s denial of the requested prohibitory injunction.

D. Nominal Damages

Finally, in BCF V, the district court found that only two plaintiffs were denied their preferred choice of schools because of their race under the Old Plan, and to those two plaintiffs the district court awarded nominal damages. BCF V, at 2 (awarding $1.00 each to John Feeney and Kathleen McCoy). On appeal, the eight remaining plaintiffs seek nominal damages as well, claiming that the district court erred in two regards.

First, plaintiffs state that

[i]t is impossible to deconstruct what assignments would have been made under the Old Plan had race not been a factor. The BPS Director of Records Management admitted that he could not simulate for how [sic] choices would have changed had the racial caps and set asides of the Old Plan not been in place.

Plaintiffs provide no citation to support this contention, and the district court found as a matter of fact that BPS did indeed demonstrate that the other eight plaintiffs were not denied seats at their preferred schools because of race. See BCF III, 183 F.Supp.2d at 387-91 (detailing the assignment histories of each plaintiff); see also BCF V! As we review factual determinations for clear error, Wessmann, 160 F.3d at 795, and plaintiffs have pointed to no record evidence to contradict the district court’s relevant factual findings, we leave them undisturbed on appeal.

Second, plaintiffs claim that the district court misread Texas v. Lesage, 528 U.S. 18, 120 S.Ct. 467, 145 L.Ed.2d 347 (1999) (per curiam). In Lesage, the University of Texas denied a Caucasian applicant admission to a Ph.D. program while admitting at least one minority candidate. The parties agreed that “the school considered the race of its applicants at some stage during the review process.” Id. at 19, 120 S.Ct. 467. The University showed that “even if the school’s admissions process had been completely colorblind, Lesage would not have been admitted.” Id. The Supreme Court held that if a defendant “conclusively established that [plaintiff] would have been rejected under a race-neutral policy,” damages are not available. Id. at 20, 120 S.Ct. 467. The Court could not have been clearer: “The government can avoid liability by proving that it would have made the same decision without the impermissible motive.” Id. at 21, 120 S.Ct. 467 (emphasis added).

Plaintiffs claim that the “same decision” defense set forth in Lesage is not available against claims for nominal damages for constitutional violations. Plaintiffs misread Lesage in making this argument. Lesage makes no distinction among the classes of damages that become unavailable upon defendants’ showing that they would have reached the same admissions result even in the absence of an unconstitutional use of race. Lesage, 528 U.S. at 20, 120 S.Ct. 467. Lesage is unambiguous:

Simply put, where a plaintiff challenges a discrete governmental decision as being based on an impermissible criterion and it is undisputed that the government would have made the same decision regardless, there is no cognizable injury warranting relief under § 1983.

Id. at 21, 120 S.Ct. 467. Lesage did not limit this holding to compensatory damages or qualify the type of relief in any way, other than to mention that the case arose under § 1983. There is no doubt that nominal damages are one of the forms of relief available under § 1983. See Farrar v. Hobby, 506 U.S. 103, 112, 113 S.Ct. 566, 121 L.Ed.2d 494 (1992) (stating that in a § 1983 action, Supreme Court precedent “obligates a court to award nominal damages when a plaintiff establishes the violation of his right to procedural due process but cannot prove actual injury.")

As Farrar explains, where there is a deprivation of constitutional rights that do not result in an "actual injury" giving rise to compensatory damages, nominal damages are the appropriate remedy. See also Carey v. Piphus, 435 U.S. 247, 266, 98 S.Ct. 1042, 55 L.Ed.2d 252 (1978). However, Lesage makes clear that when the governmental entity would have made the same decision even without the impermissible consideration of race-as it did here for eight of the plaintiffs-there is no deprivation of constitutional rights at all. Lesage, 528 U.S. at 21, 120 S.Ct. 467. Without a deprivation of constitutional rights, liability will not attach, and damages-nominal, compensatory, or otherwise-cannot be imposed. Id.

In sum, we find no error in the district court's factual findings that the eight plaintiffs seeking nominal damages on appeal would not have been admitted to the school of their choice even if BPS had not impermissibly considered race under the Old Plan. Further, we find no error in the district court's application of Lesage and other relevant precedent to the plaintiffs' claims for nominal damages.

Iv.

This case comes to us in the semi-centenary year of Brown v. Board of Education, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954). There, the Supreme Court described the importance of public education:

Today, education is perhaps the most important function of state and local governments. Compulsory school attendance laws and the great expenditures for education both demonstrate our recognition of the importance of education to our democratic society. It is required in the performance of our most basic public responsibilities, even service in the armed ~forces. It is the very foundation of good citizenship. Today it is a principal instrument in awakening the child to cultural values, in preparing him for later professional training, and in helping him to adjust normally to his environment. In these days, it is doubtful that any child may reasonably be expected to succeed in life if he is denied the opportunity of an education.

Brown, 347 U.S. at 493, 74 S.Ct. 686. Given these high stakes in the access to public education, it is not surprising that this case and those that preceded it have inspired deep passions among the parties and their supporters. Indeed, in histories already written about the aftermath of Brown in our large cities, Boston has often been cited as a city that resisted fiercely the mandate of Brown and the measures required to dismantle a public school system segregated by government action.

Hopefully, future histories will also tell the rest of the story. Attitudes in Boston have evolved, policies have changed, institutions have reorganized. In many ways, the social fabric has been re-knit. But this healing has not lowered the stakes in public education. People of good faith, harboring only the best of intentions, can- and do-disagree about the ultimate resolution of the difficult legal and social issues that surround public education generally and school assignment systems specifically. These continuing disagreements do not diminish all that has been accomplished.

In the end, we are grateful to the parties and their attorneys, as well as the amicus curiae, whose advocacy has illuminated the difficult issues before us. We also express our appreciation to the able district court judges who thoughtfully and thoroughly addressed the many complex and difficult issues in this case. The fact-finding and careful reasoning set forth in the four published opinions in this case have significantly aided our review on appeal.

For all of the foregoing reasons, the judgments of the district court are AFFIRMED in all respects. No costs shall be awarded.

So ordered. 
      
      . All of the plaintiffs here reside in the East Zone. While plaintiffs challenged the Attendance Zone concept earlier in this litigation, they do not press any claim related to the Attendance Zones on appeal.
     
      
      . Each Attendance Zone contains approximately 30 elementary schools; while students are free to rank all of those schools, along with the citywide programs, in order of their preference, most students actually rank only five to six schools.
     
      
      . For elementary schools, the walk zone includes the geocodes, or smaller geographic units within each Attendance Zone, within a one-mile radius of the school. For middle schools, the walk zone radius increases to 1.5 miles.
     
      
      . This criterion applied when a school had more kindergarten seats than first grade seats. Students with "permanent” kindergarten seats were assured placement in that school's first grade, while students with “tem-poraiy” seats had to apply for a first grade seat. BCF III, 183 F.Supp.2d at 386-87.
     
      
      . Plaintiffs-appellants in this case are now ten individual minor children, represented by their respective parent(s). Boston’s Children First was the organizational plaintiff when the case was initially filed. However, the district court found that Boston's Children First had no standing to bring suit. BCF III, 183 F.Supp.2d at 403. This ruling was not appealed. Accordingly, Boston’s Children First is not a party before this court on appeal, and we refer to the individual minors collectively as "plaintiffs” throughout the opinion.
     
      
      . From what we can glean from the record, it appears that the assignment system virtually always accommodates the sibling priority.
     
      
      . Because there is no dispute that the defendants are subject to Title VI, § 1981, and § 1983, all of plaintiffs' claims under these provisions turn on the resolution of the equal protection claim. See General Building Contractors Assn., Inc. v. Pennsylvania, 458 U.S. 375, 389-390, 102 S.Ct. 3141, 73 L.Ed.2d 835 (1982) (purposeful discrimination that violates the Equal Protection Clause also will violate § 1981); Baker v. McCollan, 443 U.S. 137, 144 n. 3, 99 S.Ct. 2689, 61 L.Ed.2d 433 (1979) (§ 1983 "is not itself a source of substantive rights, but a method for vindicating federal rights elsewhere conferred”); Alexander v. Sandoval, 532 U.S. 275, 281, 121 S.Ct. 1511, 149 L.Ed.2d 517 (2001) (Title VI proscribes only those racial classifications that would violate the Equal Protection Clause or the Fifth Amendment). Accordingly, we, like the parties, direct our analysis to the Equal Protection Clause arguments. We treat the Article 111 claim separately in Part III.B.4.
     
      
      . The plaintiffs seeking compensatory damages were Jamie Lee Higgins, John O'Toole, Andrew Sharaffa, and Sean and Thomas Stoddard.
     
      
      . These five plaintiffs are Michael Gattozzi, Kathleen McCoy, Nicholas Anderson, Rayleigh Bariy-Meltzer, and Sean Stoddard.
     
      
      . Although plaintiffs do not explicitly request reversal of the district court’s denial of a declaratory judgment holding the New Plan unconstitutional, they claim that they have standing to seek such a declaratory judgment. Further, they argue at length in their briefs that the New Plan is unconstitutional. We cannot read these arguments as anything other than a request that the New Plan be declared unconstitutional.
     
      
      . According to their brief, plaintiffs explicitly “no longer seek relief in the form of individual reassignments to their schools of choice.” Furthermore, plaintiffs apparently no longer seek compensatory damages or any of the myriad forms of injunctive relief once requested, save the injunction prohibiting the use of race in future school assignment systems.
     
      
      . Although the district court never explicitly described the Old Pian as unconstitutional, it awarded nominal damages to two plaintiffs who had been denied school assignments under the Old Plan because of their race; and nominal damages in this context require a constitutional violation. Since the defendants neither appealed from the award nor sought to defend the constitutionality of the Old Plan, we accept for purposes of our analysis the colorable premise that the Old Plan was unconstitutional.
     
      
      . As the BCF IV court noted, only one school deviates from the 50% walk zone preference: the new K-8 Orchard Gardens School, located in the predominately minority neighborhood of Roxbury, Crossing, uses a 75% walk zone preference. BCF IV, 260 F.Supp.2d at 331. Although the district court called this deviation ''troubling,” id. at n. 24, it noted that the Orchard Gardens School is located in an area that has traditionally had too few schools to serve the resident student population. Id. at 331. Also, Orchard Gardens School is one of only three K-8 pilot schools, which are subject to fewer restrictions than the vast majority of non-pilot schools in the BPS system, and one of only two schools with a walk zone that crosses Attendance Zone lines. More to the' point, plaintiffs do not argue on appeal that the Orchard Gardens School walk zone preference is proof of BPS applying the facially neutral walk zone policy in a discriminatory manner.
     
      
      . At the time that the BPS student assignment system was declared unitary, it included the following court-ordered racial guidelines: The enrollment guidelines are based upon the racial/ethnic composition of the public , school population within each community district and at each grade level: elementary, middle, and high school.... [AJssignment totals at a particular school may diverge from the community district standard within a range established by adding and subtracting 25% from each racial/ethnic group’s proportion.... Thus, for example, if 48% of the elementary school students residing in a subdistrict consisted of a particular racial/ethnic group, 25% of 48, i.e., 12, would be added and subtracted to result in an allowable range from 36% to 60% for the assignment of these students to each elementary school in the community district.
      
        Morgan v. Nucci, 620 F.Supp. 214, 221 (D.Mass.1985).
     
      
      . This council advises the Massachusetts Commissioner of Education and the Massachusetts Board of Education on issues related to the development and maintenance of school desegregation and integration in public schools within the Commonwealth. Much of that communication and testimony related to BPS's eligibility for funding under the Racial Imbalance Law. See footnote 16, infra.
      
     
      
      . The RIL, inspired by Title VI and adopted in 1965, states a policy "to encourage all school committees to adopt as educational objectives the promotion of racial balance and the correction of existing racial imbalance in the public schools.” M.G.L. c. 71, § 37C. To be eligible for funds under the RIL, school boards must provide the State Board of Education with statistics demonstrating their compliance with the racial balancing requirements of the RIL. Id. § 37D. BPS last received RIL funds in November 2001 because the Massachusetts legislature defunded the program for 2002. The program remains unfunded, and its validity is currently being challenged in the federal courts. Comfort ex rel. Neumyer v. Lynn School Comm., 283 F.Supp.2d 328 (D.Mass.2003) appeal docketed, No. 03-2415 (1st Cir. Oct. 17, 2003).
     
      
      . See Regents of Univ. of Cal. v. Bakke, 438 U.S. 265, 311-12 & 319, 98 S.Ct. 2733, 57 L.Ed.2d 750 (1978) (noting that a "diverse student body ... is a constitutionally permissible goal for an institution of higher education” but striking down a two-track medical school admissions system that used "explicit racial classification[s]”) (opinion of Powell, J.); Gratz v. Bollinger, 539 U.S. 244, 123 S.Ct. 2411, 156 L.Ed.2d 257 (2003) (striking down as not narrowly tailored an undergraduate admissions system that automatically awarded twenty points in admissions scoring to members of under-represented ethnic and racial minority .groups); Grutter v. Bollinger, 539 U.S. 306, 334 & 328, 123 S.Ct. 2325, 156 L.Ed.2d 304 (2003) (holding that "[u]niversities can ... consider race or ethnicity more flexibly as a 'plus’ factor in the context of individualized consideration of each and every applicant” and that a diverse student body is a sufficiently compelling interest to justify such use of race).
     
      
      . Walsh has a Master’s Degree in mathematics and was enrolled in law school while the trial was ongoing. BCF IV, 260 F.Supp.2d at 328. She also was "a couple of courses short a Master’s Degree in computer science." Id. (quoting the trial transcript). Walsh “has never worked as a statistician," id., and apparently lacks formal training in that area.
     
      
      . Specifically, in terms of net numbers, plaintiffs showed that eight fewer white students were admitted to the Murphy School under the New Plan’s 50% walk zone preference as compared to a 100% walk zone preference; three fewer at the Mozart School; and two fewer at the Lyon School.
     
      
      . We also note that plaintiffs’ extensive reliance on Wessmann is misplaced. Without belaboring the point, the admissions plan in Wessmann subjected a certain number of seats to strict numerical racial guidelines. Here, in contrast, the New Plan is facially race-neutral with no mention of race, racial classifications, set-asides, or quotas.
     
      
      . In their brief to this court, plaintiffs' request for prospective injunctive relief was limited to a prohibitory injunction against the future use of the Old Plan. However, the district court ruling on this issue addressed one of the broader prohibitory injunctions plaintiffs sought during litigation-namely, an injunction proscribing the future use of race in the student assignment system in any way. BCF IV, 260 F.Supp.2d at 333. Because of our disposition of this issue on appeal, the discrepancy between these two requests is immaterial.
     
      
      . These seven plaintiffs were Nicholas Anderson, Kayleigh Barry-Meltzer, Michael Gattozzi, Kathleen McCoy, John O'Toole, Andrew Sharaffa, and Thomas Stoddard. The three remaining plaintiffs — John Feeney, Jamie Lee Higgins, and Sean Stoddard — failed to attest that they intended to reapply for placement.
     
      
      . For the 2000-01 school year, John Feeney applied in the third application round for a kindergarten seat, ranking five schools in order of his preference. The first two had been filled in earlier rounds. He was not assigned to his third and fourth choice schools because under the racial guidelines then in force, no more seats were available for white students. As a result, the remaining available seats were assigned to black students with worse random numbers. BCF III, 183 F.Supp.2d at 388-89.
      Similarly, for the 1996 school year, Kathleen McCoy applied for assignment to four schools. She was unsuccessful in gaming assignment to her first and second choice schools. At her third choice school, Condon, she was denied a seat solely because of the operation of the racial guidelines; black students with worse random numbers than hers received assignments to Condon instead. Id. at 389.
     