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POOLER, Circuit Judge: This is a housing discrimination case relating to the community of Garden City in Long Island, New York. Defendants-Appellants the Incorporated Village of Garden City and the Garden City Board of Trustees (collectively “Garden City”) appeal from an April 22, 2014 final judgment following a bench trial in the United States District Court for the Eastern District of New York (Spatt, J.) finding Garden City liable for violations of the Fair Housing Act, Section 1981, Section 1983, and the Equal Protection Clause. We affirm this decision. Plaintiff-Appellee-Cross-Appellant MHANY Management, Inc. and Interve-nor-Plaintiff-Appellee-Cross-Appellant New York Communities for Change, Inc., (collectively, “Plaintiffs”), also cross-appeal from a February 15, 2012 grant of summary judgment by the same district court in favor of Defendants-Cross-Appellees County of Nassau, County of Nassau Planning Commission, and County of Nassau Office of Real Estate and Development (collectively “Nassau County”). We affirm this decision in part, vacate in part, and remand. BACKGROUND The following facts are drawn from the district court’s factual findings after the bench trial, which we accept unless clearly erroneous. Diesel Props S.r.l. v. Greystone Bus. Credit II LLC, 631 F.3d 42, 52 (2d Cir.2011). A. Nassau County and Garden City The Village of Garden City is a municipal corporation organized under the laws of the State of New York and located in Nassau County. As of the year 2000, individuals of Hispanic or African-American ethnicity comprised 20.3% of Nassau County’s population. However, these minority groups comprised a disproportionate share of the County’s low-income population. While constituting 14.8% of all households in Nassau County, African-Americans and Hispanics represented 53.1% of the County’s “very low” income, non-elderly renter households. In addition, African-Americans made up 88% of the County’s waiting list for Section 8 housing. Under the Section 8 program, the federal government provides funds to local housing .authorities, which then subsidize rental payments for qualifying low-income tenants in privately-owned buildings. See 42 U.S.C. § 1437f(o )(1)(A). Garden City’s African-American and Hispanic population in the year 2000 was 4.1%. However, excluding the 61% of the minority population representing students living in dormitories, Garden City’s minority population was only 2.6%. In addition, only 2.3% of the households in Garden City were headed by an African-American or Hispanic person. However, several of the communities surrounding Garden City are “majority-minority,” communities in which minorities make up a majority of the population. Although the lack of affordable housing has long been a problem for Nassau County, Garden City contains no affordable housing. Indeed, in the past, Garden City and its residents have resisted the introduction of affordable housing into the community. According to a Garden City official, in 1989, a developer proposed constructing 51 units of affordable housing at a site in Garden City. This project was never completed, apparently due to a village building moratorium, and a luxury development was ultimately approved for the site. In addition, in May 2006, Nassau County announced that it intended to sell a parcel of County land in Garden City known as the Ring Road Site, for the development of mixed-income affordable housing. But after Garden City residents expressed opposition to the construction of affordable housing in the community, the project was abandoned. Finally, Garden City has repeatedly declined to join the Nassau County Urban Consortium, a group of municipalities in Nassau County .that are eligible to receive federal- funding to support affordable-housing development. ' B. The Social Services Site In 2002, Nassau County faced a budget and infrastructure crisis. Under the leadership of then-County Executive Thomas Suozzi, the County undertook a Real Estate Consolidation Plan, which involved consolidating County operations in several facilities and selling excess government property in order to raise revenue to fund renovations of the County’s existing operations. One of the properties proposed for sale under the Real Estate Consolidation Plan was a parcel of land owned by Nassau County within the boundaries of Garden City. This parcel of land was part of Garden City’s Public or P-Zone. Garden City’s P-Zone encompasses numerous Nassau County Buildings, including the Nassau County Police Headquarters, the County Executive Building, and the Nassau County Supreme Court Building. The portion of the P-Zone site at issue in this case, referred to as the “Social Services Site,” is an approximately 25-acre site that housed the former Nassau County Social Services Building, the parking lots for the Nassau County Supreme Court, ,a garage, an ancillary building, and additional parking facilities. The Social Services Site consists of two segments: (1) 21.44 acres located on the eastern side of County Seat Drive, the site of the former Social Services building and parking facilities; and (2) ah additional 3.03 acres located on the western side of County Seat Drive, on which a County-owned building and a parking garage are located. Nassau County planned to sell the Social Services Site to a private developer, hoping to receive at least $30 million for the 'property. In order to facilitate this sale, Nassau County turned to Garden City, which controlled the Site’s zoning. C. Garden City’s Rezoning In June 2002, at the County’s request, Garden City began the process of rezoning the Social Services Site. This process was managed by the Garden City Board of Trustees, the elected body which governs Village affairs. In- response to the County’s request, the Board of Trustees created a sub-committee (the “P-Zone Committee”) charged with retaining a planner and reviewing zoning options for the Social Services' Site, as well as the remainder of the P-Zone properties in Garden City. This P-Zone Committee consisted of Village Trustees Peter Bee, Peter Negri, and Gerard Lundquist. Trustee Bee was the chairman of the P-Zone Committee. Garden City also retained the planning firm of Buckhurst Fish and Jacquemart (“BFJ”) to provide a recommendation with regard to the rezoning of the Social Services Site. Garden City had previously, worked with BFJ over several decades. Village officials trusted and respected BFJ’s work and generally adopted its recommendations. The P-Zone committee was supervised by Garden City Village Administrator Robert Schoelle, who served as. a liaison between the Committee and the Board of Trustees. The Village also hired attorney John Kiernan to advise it on the rezoning process. In the early part of this rezoning process, BFJ and Garden City emphasized that any proposal should rely on existing zoning mechanisms and respect the existing character of the Village.' In a September 13, 2002 fax outlining the general planning principles for redevelopment of the P-Zone properties, BFJ stressed that “[a]ny rezoning associated with the proposed development should be in accordance with the goals and parameters set forth in the zoning code [of Garden City].” App’x at 1063. This fax also emphasized that any proposed development should “be consistent with the existing character and surrounding neighborhoods of Garden City,” “not overburden roads, utilities, and schools,” and “not tend to depreciate the value of property in the village.” App’x at 1063. Similarly, in a November 15, 2002 memorandum.entitled “Potential Approach to ‘P’ Zone Changes,” and addressed to the P-Zone Committee, BFJ recommended that Garden City borrow from its existing zoning regulations in rezoning the P-Zone properties, rather than adopt a new form of zoning for.the property. On April 29, 2003, BFJ submitted its proposal to the P-Zone Committee, recommending a “CO-5(b) zone” for the Social Services Site. BFJ proposed applying “multi-family residential group” or “R-M” zoning controls to this property. R-M zoning would have allowed for the construction of up "to 311 residential apartment units on the Site, or 75 single-family homes. BFJ reiterated the proposed R-M zoning in a May 2003 report to the P-Zone Committee, stating that the rezoning would “be likely to generate a net tax benefit to the Village.” App’x at 1382. Throughout the rezoning process, the P-Zone Committee also kept Garden City’s four Property . Owners’ Associations (“POAs”)' apprised of the process.’ The POAs acted as liaisons between Garden City and the citizens living within their respective neighborhoods. The Social Services Site is located within the neighborhood of the Eastern Property Owners’ Association. On May 29, 2003, BFJ gave a PowerPoint presentation of its May 2003 report at a public forum. At the first forum, designed to solicit public input on the proposal, several residents expressed concern about the impact of 311 residential upits on traffic and schools, In response to these citizen concerns, BFJ analyzed these issues further. In July 2003, BFJ issued a revised version of its study, which reiterated the proposal for R-M zoning. BFJ emphasized again that its proposal “would be careful of not overwhelming the neighborhoods with any significant adverse environmental im-paets[,] particularly traffic, visual effects, or burdens on public facilities,” App’x at 1115. Responding to issues raised at the citizen forum, the July 2003 report states that “[t]here would be a smaller number of school children generated by the new development than with the development of single-family homes____With a community aimed at young couples and empty nes-ters[,] there could be as few as 0.2 to 0.3 public school children per unit.” ■ App’x at 1123-24. Upon review of the report, the P-Zone Committee adopted BFJ’s recommendation for R-M zoning for thé approval of the Board of Trustees. In September 2003, as required by state law, BFJ issued a draft Environmental Assessment Form (“EAF”) for the proposed rezoning. The EAF concluded that the proposed rezoning to R-M “will not have a significant impact on the environment.” App’x at 1146. The EAF further stated that the proposed multi-family development at the Sité would not “result in the generation of traffic significantly above present levels” and would have a minimal impact on schools. See App’x at 1155. In addition, the, EAF emphasized that “[i]n terms of potential aesthetic impacts, the proposed zoning controls were specifically designed to accommodate existing conditions, respect existing neighborhoods— particularly residential neighborhoods, maximize the use of existing zoning controls and minimize adverse visual impacts.” App’x at 1161. Michael Filippon, the Superintendent of the Garden City Buildings Department, concurred in these conclusions. On October 17, 2003, an ad was placed in the Garden City News entitled, “Tell Them What You Think About the County’s Plan for Garden City.” App’x at 1639. This notice stated: Where is the Benefit to Garden City? Are We Being Urbanized? ... The County is asking the Village to change our existing zoning — P (Public use) ZONE — to allow the County to sell the building and land ... now occupied by the Social Services Building, to private developers. Among the-proposed plans: Low-density (high-rise?) housing — up to 311 apartments____ These proposals will affect ALL. of Garden City. App’x at 1639. The Village -held a subsequent public forum on October 23, 2003, where BFJ gave another PowerPoint presentation summarizing the proposed rezoning. The record indicates that at this meeting, citizens again raised-questions'about traffic and an.increase' in schoolchildren. BFJ again reiterated that traffic would be reduced relative to existing use, and that multi-family housing would generate fewer schoolchildren than the development of single-family homes. In keeping with these conclusions, in November 2003, BFJ presented an additional report to the P-Zone Committee, again confirming its proposal for the R-M zoning control that allowed for a possible 311 apartment units on the Social Services Site. The November 2003 report set forth a draft text for the rezoning. In light of BFJ’s final report, on November 20, 2003, the Garden City Village Board of Trustees unanimously accepted the P-Zone Committee’s recommendation for the rezoning. In addition, oil December 4, 2003, the Board made a finding pursuant to New York State’s Environmental Quality Review Act that the zoning incorporated in what was now termed proposed Local Law 1-2004 would have “no impact on the environment.” App’x- at 1996. The proposed rezoning would, in keeping with Nassau County’s wishes, permit residential development on the Social Services Site in the new CO-5(b) . zone. In light of the R-M controls on the property, such development could include multi-family units, or less dense alternatives such as single-family homes. Having endorsed the proposed rezoning, the Board of Trustees moved Local Law 1-2004 to a public hearing. Starting in January 2004, three public hearings occurred in' the’ span of one month. At the first hearing, on January 8, 2004, residents voiced concerns that multifamily housing would" generate traffic, parking problems, and schoolchildren. In response, Filippon emphasized, “[y]ou have to remember that the existing use on that site now generates a certain amount of traffic, a fair amount of traffic. That use is going to be vacated. The two residential uses that are being proposed as one of the alternates, each of which on their face automatically generate far less traffic than the existing use. That is something to consider also.” App’x at 1435, In addition, although assured by Garden City officials that the rezoning, could result in single-family homes, one resident expressed concern that.Nassau County would ultimately only sell the property to a multifamily developer in order to maximize revenue. On January 20, 2004, the Eastern Property Owners’ Association held a meeting at which Trustee Bee discussed BFJ’s recommendation for the Social Services Site. A summary of - the meeting reports that “Trustee Bee addressed many questions from the floor” and, in doing so, expressed the opinion that “Garden City demographically has a need for multi-family housing.” App’x at 1665. Trustee Bee also reiterated that.because relatively few schoolchildren resided in existing multi-family housing in Garden City, BFJ and the Board had reasonably predicted that multi-family housing would have less of an impact on schools than single-family housing. Trustee Bee “indicated he would keep an open mind but he still felt the recommended zoning changes were appropriate.” App’x at 1665. In addition, Trustee. Bee'addressed citizen concerns about the possibility of affordable housing on the Site. In response to one question, Trustee Bee stated that “[although economics would indicate that a developer would likely build high-end housing, the zoning language would also allow ‘affordable’ housing (as referred to by [the] resident' asking the question) at the [Social Services Site].” App’x at 1665. The meeting notes further indicate that a majority 15 of the residents “who asked questions or made comments” at the meeting 16 supported restricting the rezoning of the Site to single-family homes. App’x at 1665. According to these notes, “[Residents want[ed] to preserve the single-family character of the Village. One resident in particular requested the [Eastern Property Owners’ Association] Board take a firmer stand on the P-Zone issue and only support R-8 zoning, i.e. zoning for single-family housing. App’x at 1665. On February 5, 2004, the Village held a third public hearing on the proposed rezoning. The record indicates that this hearing was well attended and much more crowded than usual. App’x at 1209(‘‘Mind-ful of the number of people who are here this evening and the likelihood that this hearing will take some time.... ”). After an introduction by Trustee Bee, the meeting commenced with two presentations. First, Tom Yardley of BFJ emphasized that the proposed rézoning preserved- the possibility of single-family homes, and -that any multi-family housing would not result in high-rise apartments due to height and density restrictions. Second, Nassau County Executive Suozzi,- the author of the County’s Real Estate Consolidation Plan, emphasized the County’s need to sell the Social Services Site to a private developer, as well as-the benefits of developing multifamily housing on the property. During this discussion, a member of the audience interrupted Suozzi. Thomas Suozzi: Instead of putting commercial there or single family there, you do something right in between the two that creates a transition from the commercial area from one to' the other. I guarantee you that it will be much better than what is there now, which is a building that is falling apart with a lot of problems in the building, a lot of problems going on around the building on a regular basis and a huge sea of parking. This will make it a much more attractive area for the property. Multi-family housing will be. more likely to generate empty nesters and single people moving into the area as opposed to families that are going to create a burden on your school district to increase the burden on the school district. Unidentified Speaker: You say it’s supposed to be upscale. Thomas Suozzi: It’s going to be upscale. Single people and senior citizen empty nesters. If you sell your $2 million house in Garden City and you don’t want to take care of the lawn anymore, you can go into ... who lives in Wyndham for example? It’s a very upscale place. There’s a lot of retirees that live there. App’x at 1231. When Suozzi finished his presentation, the meeting was opened to questions from the public. The first question from the audience related to Trustee Bee’s .statements “last time,” referring to the January 20, 2004 meeting of the Eastern Property .Owners’ Association. Lauren Davies: I’m just. confused between what Mr. Suozzi said about the Social Services Building. You said you wanted it to be upscale, from what I understand from what Peter Bee said the last time is that they wanted it to be affordable housing.... Trustee Bee: Well, either I mis-spoke or you misheard, because I do not recollect using that phrase. If I did it was an inappropriate phrase. The idea was a place for Garden City’s seniors to . go when they did not wish to maintain the physical structure and cut the lawns and do all the various things. But not necessarily looking at a different style of life. In terms of economics. Thomas Suozzi: We’re absolutely not interested in building affordable housing there and there is a great need for affordable housing, but Garden City is not the location. We need to build housing there.... We would generate more revenues to the County by selling it to upscale housing in that location. That is what we think is in the character of Garden City and would be appropriate there. Unidentified Speaker: How do you have control over what the developer does Trustee Bee: Before the next speaker though, just to finish on that last remark, neither the County nor the Village is looking to create .... so-called affordable housing at that spot. Unidentified Speaker: Can you guarantee that, that it won’t be in that building? App’x at 1236-37. In response to these questions, Suozzi indicated that the County “would be willing to put deed restrictions on any property that we sold” so “that it can’t be anything but -upscale housing.” App’x at 1237. In response to further questioning, Suozzi stated “Don’t take my word for it, we’ll put whatever legal codifications that people want. This will not be affordable housing projects. That’s number one.” App’x at 1239. Gerard Fish-berg, Garden City’s counsel, further noted that the estimated sale prices for multifamily residential units “don’t suggest affordable housing.” App’x at 1242. Throughout the'remainder of the meeting, residents indicated their opposition to multi-family housing and their preference for single-family homes. App’x at 1242-43 (“I’m completely opposed to any multifamily dwellings -in that area. I’m only in support of the single family R-8 units.... ”). One resident. emphasized that .the, proposed multi-family development was not “in the flavor and character of what Garden City is now. Garden City started as a neighborhood of single family homes and it should remain as such.” App’x at 1243. Others stated, to applause from the audience, that “[wje’re not against residential, we’re against multi-lev-el residential. (Applause).” App’x at 1249; see also App’x at 1252(“Thomas Su-ozzi: You would probably like to see single family housing I presume. Unidentified Speaker: Single Family. (Applause).”); App’x at 1254 (“I don’t hear a compelling argument from anyone here tonight as to why we should have multi-dwelling homes. Can we take it put of the proposal?”). One resident expressed concern about the possibility of “four people or ten people in an apartment and nobody, is-going to know that.” App’x at 1275. In keeping with these statements, citizens repeatedly expressed concern about limiting the options of a developer. Gail Madigan: [W]hen you sell this property you can guarantee that it’s ... what control do you have when you sell it to a developer? Thomas Suozzi: Guarantee what? What would you like us to guarantee? Gail Madigan: Well, I would like to know what you . are going to be able to do with it. You can tell them ... Thomas Suozzi: The zoning controls ... what you can do. Gail Madigan: Yeah, but if you sell it to a developer that comes in and is going to make multi-family housing there. Thomas Suozzi: He wouldn’t do that if it was zoned for single family housing. If it’s zoned for single' family housing you can’t put [in] multi-family housing. App’x at 1253. Another citizen expressed concerns about the possibility of what any multi-family housing might eventually become. Anthony Agrippina: We left a community in Queens County that started off similar, single family homes, two family homes, town houses that became — six story units. It was originally' for the elderly, people who were looking to downsize. It started off that way. Right now you’ve got full families living in one bedroom townhouses, two bedroom co-ops, the school is overburdened and overcrowded. App’x at 1259-60. In response, another resident emphasized that the only way to control such consequences was to restrict the zoning. App’x at 1260 (“The only guarantee is the zoning. This Board,is the only set of people who are here who can guarantee or do that. Mr. Suozzi is not going .to be the County Executive forever. We don’t know what the predecessors [sic] will do.”). As at the previous ineetings, residents also expressed concern about traffic and schools. County and Village officials reiterated that a transition to residential use, including multi-family housing, would generate far less traffic than the existing use of the Social Services Site. Thomas Suozzi: One thing that would happen is that you would have 1,000 less employees that work in that building, that would no longer be working there anymore. Sheila DiMasso: But, we would also have more traffic because of more people owning cars and leaving there in and out. As opposed to ... [applause] Thomas Suozzi:. You may want to clap for that, but that’s irrational. (Applause) App’x at 1238-39. ■ In addition, Suozzi and Garden City officials tried to explain to citizens their view that the proposed multifamily housing would actually generate fewer schoolchildren than development of single-family homes. David Piciulo: If you have 311 units you will have more children potentially in there than 956 single family homes. David Piciulo: If you have 311 units you will have more children potentially in there than 956 single family homes. Thomas Suozzi: That’s not accurate. Based upon statistics, people spend their whole lives looking at this stuff. That’s not true. So you may feel that way, but it’s not accurate. David Piciulo: Those are statistics having to do with a national study. If you drive down into the neighborhood, the average home here has two kids. They’re in the system for 15 years and you are going to have children in the system ... let me just make a point. Gerard Fishberg: Not to argue with you, again, I don’t think anybody has prejudged this. How many apartments are there in Wyndham? Michael Filippon: 312. Gerard Fishberg: How many school children are there in 312 apartments? Tom Yardley: Less than twenty. Gerard Fishberg: Less than twenty children in 312 apartments. App’x at 1255. BFJ’s Fish later testified that those residents who claimed to prefer single-family homes because of school impacts were “simply wrong.” App’x at 277. In response to these questions Suozzi made clear that before any development project was approved at the Site, the developer would have to satisfy state environmental guidelines, including addressing concerns regarding traffic and impact on public services, such as schools. He further emphasized that these conclusions would be subject to public comment. In March 2004, in the weeks after this meeting, a flyer began circulating around Garden City. The flyer stated, in relevant part: WILL GARDEN CITY PROPERTY VALUES. DECREASE IF OVER 300 APARTMENTS ARE BUILT AT THE SITE OF SOCIAL SERVICES? ... The Garden City Village Trustees are close to voting on how to zone this property. They might choose to zone it for multi-family housing (If Senator Balbo-ni’s current bill passes in June, as many as 30 of those apartments would be considered “affordable housing”. According to this bill, “Affordable workforce housing means housing for individuals or families at or below 80% of the median income for the Nassau Suffolk primary metropolitan statistical area as defined by the Federal Department of housing and urban development.” ... NOT JUST GARDEN CITY INCOMES! ... ISN’T OUR SCHOOL DISTRICT CROWDED ENOUGH NOW? The trustees are saying that there will be fewer additional students to the Garden City school, district- if there are 340 apartments or townhouses built at the “P ZONE[”j as opposed to 90 single family homes.' HOW CAN THEY BE SURE OF THAT? ISN’T IT TRUE THAT MANY FAMILIES MOVE TO GARDEN CITY TO ASSURE THEIR CHILDREN OF A QUALITY EDUCATION? WHAT WILL BRING MORE STUDENTS, OVER 300 FAMILIES OR 90 FAMILIES? App’x at 1632. ■ The reference to “Senator Balboni’s current bill” in the flyer related to legislation pending at the time which would impose affordable-housing requirements on developers on Long Island. The flyer reached Garden City Village Administrator Schoelle, who faxed it to Fish and at least one member of the Board of Trustees. The flyer also came to the attention of Trustee Lundquist. At a Board meeting held on March 18, 2004, residents again raised concerns about the possibility of affordable housing at the Social Services Site. Schoelle’s notes from that meeting indicate that residents expressed concern that the Balboni Bill might apply “retroactive[ly].” App’x at 363. One resident urged decision-makers to “play it safe” with respect to the Balbo-ni Bill and “vote for single family homes;” App’x at 362. The following month, Trustee Negri told residents at a Central Property Owners’ Association meeting that he and other Village officials met with state representatives to discuss the Balboni Bill. He noted that the bill called for 10% of all new housing developments to include affordable housing, and that a family of four making $67,000 would qualify. Negri indicated that he did not think the bill would pass. In response to public pressure, BFJ and Garden City began modifying the rezoning proposal. In materials produced in April 2004, BFJ changed the proposal, reducing the number of multi-family units potentially available at the Social Services Site to 215. However, by a memorandum to the Board dated May 4, 2004, BFJ scrapped the proposed R-M zoning entirely. Instead, BFJ proposed rezoning the vast majority of the Social Services Site “Residential-Townhouse” (“R-T”), an entirely new zoning classification. App’x at 1360. The May 2004 proposal only preserved RM zoning on the 3.03 acres of the Social Services Site west of County Seat Drive, and only by special permit. Thus, the development of multi-family housing would be restricted to less than 15% of the Social Services Site, and only by permit. BFJ’s proposed description of the R-T zone defined “townhouse” as a “single-family dwelling unit.” App’x at 1361, Whereas the previous proposed rezoning took more than a year to come before the Board, the shift to R-T zoning moved rapidly through the Village’s government. BFJ issued a final EAF for R-T rezoning in May 2004. Even though BFJ officials testified that a switch from R-M zoning to R-T zoning was a significant change, no draft EAF was ever issued for the R-T rezoning. In addition, the shift from the P-Zone to R-T zoning was proposed by the Board as Local Law No. 2-2004 and moved to a public hearing on May 20, 2004. The Trustees further stated at this meeting that they hoped to have a final vote on the rezoning as soon as June 3, 2004, and that the bill had already been referred to the Nassau County Planning Commission. Explaining the switch, Fish offered the following rationale: This was, this was a conscious decision, and I think those of you who might have been at the last two ... workshops, this was discussed in quite a bit of detail, that there was, there was a concern that if the whole 25 acres were developed for multi family it would generate too much traffic and it didn’t serve, it didn’t serve as a true transition.... So, that, the proposal has been modified where previously multi family would have been allowed in all 25 acres, as of right, the proposal’s been modified so that it’s no longer allowed at all as-of-right, you’d have to get a special permit for it, through the Trustees, and it is a condition of the permit is that it can only be to the west of County Seat Drive. So, in essence, what the Trustees have done, is they have reduced the multi family to less than 15 percent of [the] site. App’x at 1471. At this meeting, a member of the Garden City community thanked the Board of Trustees for responding to the concerns of residents: [M]y husband works twelve hour, fourteen hour days so that we can live here. We didn’t inherit any money from anyone. We weren’t given anything. We didn’t expect anything from anyone. We worked very hard to live in Garden City because [of] what it is. And I feel like very slowly it’s creeping away by the building that is going on.... [A]nd I just think to all of you, just keep, be strong, like, just keep Garden City what it is. That is why people want to come here. You know, it’s just a beautiful, beautiful town, people would like to live here, but I just think, just think of the people who live here, why you yourselves moved here. You don’t move here to live near apartments. You don’t move here so that when you turn your corner there’s another high-rise. App’x at 1487-88. Toward the close of this meeting, a member of former Plaintiff ACORN spoke about the need for affordable housing in Nassau County and asked that Garden City consider building affordable housing. [W]hat we’re saying with respect to the people that live in Garden City, you know, everybody wants to see their community, you know, keep its values So, we’re asking other communities ... to share and build affordable housing in their community. I mean, I don’t know how we’re going to, you know, I guess the county executive [has] to figure out, give respect to each community. It’s not just, just not good for affordable housing to be built in s[o]me communities because it impacts on us and our school districts. It’s not turning out the best education system we could if we move into the other areas. We’d be able to get, we’d all benefit from it. App’x at 1499. ACORN members subsequently attended the Nassau County Planning Commission the following week and again expressed opposition to R-T zoning. At the same time, former Plaintiff MHANY, then known as New York Acorn Housing Company (“NYAHC”), sent a letter to the Nassau County Planning Commission strongly opposing R-T zoning and warning that the new zone would “ensure that developers cannot create affordable multi-family housing.” App’x at 1871. On June 3, 2004, the Garden City Board of Trustees unanimously adopted Local Law No. 2-2004 and the Social Services Site was rezoned R-T. The following month, Nassau County issued a Request for Proposals (“RFP”) concerning the Social Services Site under the R-T zoning designation. The RFP stated that the County would not. consider bids of less than $30 million. Plaintiffs were unable to submit a bid meeting the specifications of the RFP. Is-mene Speliotis, Executive Director of NYAHC/MHANY, analyzed the R-T zoning and concluded that it was not financially feasible to build affordable housing under R-T zoning restrictions at any acquisition price. Testifying at trial, Suozzi concurred with' this assessment. Recognizing the futility of an affordable-housing bid under R-T zoning, NYAHC contacted the County to work on a proposal that would include multi-family affordable housing, and “urge[d] the Planning Commission to delay, any action on [its] proposal while its legal and policy implications are considered more carefully.” App’x at 1871. NYAHC and New York ACORN met with Suozzi and other County officials to discuss the possibility of including affordable housing on the Social Services Site, But the County did not reissue the RFP. Failing in these negotiations, on September 10, 2004, NYAHC submitted a non-conforming “protest” proposal to the County for development of the Social Services Site. The County ultimately awarded the contract to develop the Social Services Site to Fairhaven Properties, Inc. (“Fairhaven”), a developer of single-family homes, for $56.5 million, the highest bid. Fairhaven proposed the development of 87 single-family detached homes, and did not include any townhouses. After the contract was awarded to Fair-haven, NYAHC prepared four proposals, or “pro formas,” for development at- the Social Services Site under the R-M zoning designation, with the percentage of affordable and/or Section 8 housing units of the 311 total rental units ranging from 15% to 25%. Plaintiffs’ expert Nancy McArdle evaluated each proposal in conjunction with the racial/ethnic distribution of the available pool of renters and determined that, had NYAHC been able to build housing under any of the.- four proposals in accordance with the rejected -R-M zoning designation, the pool of renters likely to occupy all units, including market-rate, affordable, and Section 8 units, would have likely been between 18% and 32% minority, with minority households numbering between 56 and 101. Under the proposal predicting 18% minority population, NYAHC would have been able to bid $56.1 million for- the Social Services Site. McArdle further analyzed the likely racial composition of the pool of homeowners who could afford to purchase single-family units potentially developed by Fairhaven. She determined that between three and six minority households could afford such a purchase. Thus, while the NYAHC proposals would likely increase racial diversity in Garden City, McArdle testified, the Fairhaven proposal would likely leave the racial composition of Garden City “unchanged.” '' D. Procedural History On May 12, 2005, ACORN, NYAHC, and several individual Plaintiffs filed suit against Garden City arid Nassau County. Plaintiffs asserted claims under the Fair Housing Act (“FHA”), 42 U.S.C. § 3601 et seq., as well as 42 U.S.C. § 1981, 42 U.S.C. § 1983, and Title VI of the Civil Rights Act of 1964, 42 U.S.C. § 2000d et seq. Plaintiffs principally argued that Garden City’s shift from R-M to R-T zoning was racially discriminatory, and that Nassau County failed to prevent, this discrimination. Plaintiffs also argued that the abandonment of R-M zoning in favor of R-T zoning had a disparate impact on minority groups, and thus violated the disparate-impact component of the- Fair Housing Act. Finally, Plaintiffs argued that Nassau County’s actions and policies -in steering affordable housing to certain-communities violated its obligations under Title VI of the Civil Rights Act not to discriminate in the administration, of federal funding, and under Section 808 of the Fair Housing Act to affirmatively further fair housing. On July 21, 2006, the district court (Bianco, /.), denied Garden City and' Nassau County’s motions to dismiss in their entirety. The district court rejected Defendants’ arguments that Plaintiffs-lacked standing and concluded that they had adequately alleged discrimination on the basis of race. Accordingly, the district court directed the parties to discovery. ACORN disbanded in early 2010. At the same time, NYAHC changed its name to MHANY. In addition, NYCC, an organization with the same goals' and mission, and many of the same members as ACORN, moved to intervene in this litigation. On June 15, 2010, the district court (Spatt, J.) granted NYCC permission to intervene as ACORN’s practical successor. SJA 135. By Memorandum and Order dated February 15,2012, the district court (Spatt, J.) (1) granted the County’s motion for summary judgment and dismissed all claims against the County, and (2) denied Garden City’s motion for summary judgment. The district court concluded Nassau County was not causally responsible for the alleged discriminatory conduct of Garden City. The district court also rejected Plaintiffs’ challenge to the- County’s policies i-e-garding the siting of affordable housing under Section 808 of the Fair Housing Act, concluding that Plaintiffs lacked a private cause of action to. enforce this provision. The district court did not address Plaintiffs’ parallel claim under Title VI of the Civil Rights-Act, assuming that this claim was premised on the alleged discrimination regarding the Social Services Site, In resolving the summary judgment motions, the district court rejected Defendants’ arguments that events at the Social Services Site had rendered this case moot. Despite Nassau County’s sale contract, the transaction with Pairhaven had never closed, apparently due to the pendency of this litigation. On January 1, 2010, Suozzi was succeeded as County. Executive by Edward P. Mangano. In its summary judgment filing, the County, informed the district court that rather than proceed with plans for private development, Man-gano had decided instead to construct a new Nassau County Family Court building at the Social Services Site. Defendants thus argued that, because the County government was no longer selling the Site to a private developer, and because Plaintiffs only sought injunctive relief, the case had been rendered moot. The district court rejected this argument, concluding first that it was still possible to grant Site-specific relief to Plaintiffs, and second that even if the Site was not sold, the court could still grant other effectual relief. On June 17, 2013, the district court commenced a bench trial that spanned eleven days. In a December 6, 2014 post-trial decision, the district court concluded that Plaintiffs had established, by a preponderance of the evidence,- liability on the part of the Garden City Defendants for the shift from R-M to R-T zoning under (1) the FHA, 42 U.S.C. § 3601 et seq., based on a theory of disparate treatment and disparate impact; (2) 42 U.S.C. § 1981; (3) 42 U.S.C. § 1983; and (4) the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution. The district court reiterated the conclusions of previous opinions that Plaintiffs had standing, and also rejected a renewed mootness argument from Garden City. The district court subsequently issued an order concerning appropriate remedies in light of Plaintiffs’ violations. In a final judgment issued April 22, 2014, the district court granted Plaintiffs the following relief against Garden City: (1) a prohibitory non-discrimination injunction, (2) fair housing training for Garden City officials, (3) a directive to Garden City to pass a Fair Housing Resolution, (4) appointment of .a third-party Fair Housing Compliance Officer by Garden City, and (5) expenditure of reasonable sums to fund the relief required by the judgment. The district court also ordered that if Nassau County decided to sell the Social Services Site within one year of the date of judgment, then Garden City must begin the process of rezoning the Social Services Site from R-T to R-M controls. If Nassau County did not make such an announcement, Garden City would be required to (1) join the Nassau County , Urban Consortium, a group of Nassau County municipalities eligible for HUD affordable-housing funds; and '(2) require that 10% of newly constructed residential development of 5 units or more be reserved for affordable housing. Garden City then filed the present appeal. Plaintiffs cross-appealed, challenging the district court’s grant of summary judgment to Nassau County. JA 1Q4&-4&. According to Defendants, Nassau County recently entered into a contract with MPCC Corp. to build the courthouse. On June 9, 2014, MPCC Corp. commenced interior demolition and asbestos abatement. Although construction has begun, the project is not scheduled to be completed until 2018. DISCUSSION Section 804(a) of the Fair Housing Act, also known as Title VIII of the Civil Rights Act .of 1968, makes it unlawful “,[t]o refuse to' sell or rent ... or otherwise make unavailable or deny, a dwelling to any person because of race, color, ... or national origin.” 42 U.S.C. § 3604(a). “The phrase ‘otherwise make unavailable’ has been interpreted to reach a wide variety of discriminatory housing practices, including discriminatory zoning restrictions,” LeBlanc-Sternberg v. Fletcher, 67 F.3d 412, 424 (2d Cir.1995), and its “results-oriented language counsels in favor of recognizing disparate-impact liability,” Tex. Dep’t of Hous. & Cmty. Affairs v. Inclusive Communities Project, Inc., — U.S. —, 135 S.Ct. 2507, 2518, 192 L.Ed.2d 514 (2015). For this reason Sections 804(a) and 805(a) of the FELA provide for both discriminatory intent and disparate-impact liability. I. Standing In analyzing Plaintiffs’ standing here, we look to the requirements of Article III. Standing under the Fair Housing Act is as broad as Article III permits. See Havens Realty Corp. v. Coleman, 455 U.S. 363, 372, 102 S.Ct. 1114, 71 L.Ed.2d 214 (1982); Fair Hous. in Huntington Comm. Inc. v. Town of Huntington, 316 F.3d 357, 362 (2d Cir.2003) (“Standing under the FELA, whether suit is brought under section 810 or section 812 of the Act, is coextensive with Article III standing.”). Similarly, the parties do not argue, nor do we discern, any standing concerns that would prevent Plaintiffs from bringing claims under Sections 1981 and 1983. To establish Article III standing, “a plaintiff must show (1) it has suffered an ‘injury in fact’ that is (a) concrete and particularized and (b) actual or imminent, not conjectural or hypothetical; (2) the injury is fairly traceable to the challenged action of the defendant; and (3) it is likely, as opposed to merely speculative, that the injury will be redressed by a favorable decision.” Friends of the Earth, Inc. v. Laidlaw Envtl. Servs., 528 U.S. 167, 180-181, 120 S.Ct. 693, 145 L.Ed.2d 610 (2000). We evaluate Plaintiffs’ standing “as of the outset of the litigation.” Cook v. Colgate Univ., 992 F.2d 17, 19 (2d Cir.1993). In challenging standing, Garden City focuses on the latter two prongs- of the standing analysis, arguing that Plaintiffs’ alleged injury — denial of the opportunity to build affordable housing at the Social Services Site — is not “fairly traceable” to Garden City’s rejection of R-M zoning, nor redressable by a favorable decision. Garden City contends, in essence, that there is no guarantee Plaintiffs’ bid would have been accepted by Nassau County even under R-M zoning, and no certainty that the project would be built if a court ordered a return to R-M zoning. Garden City notes that, of Plaintiffs’ four pro forma bids under R-M zoning, the highest was $56,1 million for a project containing 85% market-rate apartments and 15% affordable housing. This bid was, in relative terms, slightly less than the $56.5 million Fairhaven bid for the development of single-family homes which Nassau County ultimately accepted under R-T zoning. Based primarily on this difference, Garden City speculates that even if the property remained zoned as R-M, Plaintiffs would have nevertheless been out-bid by a market-rate developer, due to Nassau County’s hopes of maximizing the sale value of the Site. Garden City’s standing argument requires both improper speculation and unnecessary certainty. As an initial matter, Garden City’s argument depends on a level of certainty that we do not typically require in housing discrimination cases. A housing plaintiff need not show with absolute certainty that a project will succeed in order to establish standing. See Fair Hous. in Huntington Comm. Inc., 316 F.3d at 363(“[A]bsent defendants’ challenged conduct, there is a ‘substantial probability’ that housing with greater minority occupancy would have been built....”). Because of the uncertainties inherent in the housing ■ market, we have permitted housing discrimination plaintiffs to proceed based on “a realistic opportunity to proceed with construction.” Huntington Branch, N.A.A.C.P. v. Town of Huntington, 689 F.2d 391, 394 (2d Cir.1982) For example, in Huntington Branch, this Court emphasized that “[indeterminacy of financing alone ... is not enough to dismiss [a housing discrimination action at the motion to dismiss stage].” 689 F.2d at 394. Indeed, the Court noted that “the multitude of factors affecting ultimate financing capability are too variable to permit certainty in prediction.” Id. Of course, “those who have absolutely no realistic financing capability have no standing, because, as to them, invalidation of an offending ordinance would afford only moral satisfaction rather than a realistic opportunity to proceed with- construction.” > Id. (internal citation omitted). However, in the case of the plaintiffs, who-had proposed a specific project, the Court' concluded that “[invalidation of the challenged ordinance ... would tangibly improve the chances of construction of [the project].” Id. at 395; see also Scott v. Greenville Cty., 716 F.2d 1409, 1416 (4th Cir.1983) (noting “[t]he uncertainty surrounding carrying any large-scale housing development to fruition”). Moreover, in Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977), the Supreme Court found that the defendants’ “challenged action[s]” stood as an “absolute barrier” to the construction project proposed by the plaintiff. Id. at 261, 97 S.Ct. 555. If plaintiff “secure[d] the injunctive relief it [sought], that barrier [would] be removed.” Id. The injunction sought by the plaintiff “would not, of course, guarantee that [the proposed housing development] w[ould] be built.” Id. The Court recognized that the plaintiff “would still have to secure financing, qualify for federal subsidies, and carry through with construction,” Id. (footnote omitted). But the Court concluded that such contingencies associated with housing development did not eliminate standing, because “all housing developments are subject to some extent to similar'uncertainties.” Id. The Court found that the plaintiffs proposed project was sufficiently “detailed and specific” that no undue speculation was required to establish standing. Id. In challenging standing here, Garden City esséntially demands the sort of certainty rejected in Arlington Heights and Huntington Branch. Pointing to the slight difference between Plaintiffs’ bid and the Fairhaven bid, the only other market-rate bid in the record, Garden City contends that Plaintiffs cannot guarantee that they would have outbid a market-rate developer. But Garden City neglects to mention that, in addressing this exact same standing argument, the district court concluded, as a factual matter, that Plaintiffs’ bid and the Fairhaven bid were “directly competitive.” Special App’x at 140. Given the relatively small difference in bids — a matter, of only 0.7% — this finding was not clearly erroneous. See Rajamin v. Deutsche Bank Nat’l Tr. Co., 757 F.3d 79, 84-85 (2d Cir.2014) (noting that while we review a district court’s legal conclusion as to standing de novo, we review the factual findings underlying this determination only for clear error). Garden City also argues this case is distinguishable from Huntington Branch and Arlington Heights because in those cases, the plaintiffs had secured conditional contracts or options on the relevant properties. But “the plaintiff who challenges a zoning ordinance, or zoning practice[ ] [need not] have a present contractual interest in a particular project” to have standing. Warth v. Seldin, 422 U.S. 490, 508 n. 18, 95 S.Ct. 2197, 45 L.Ed.2d 343 (1975). Given the uncertainties associated with financing in the housing market, the fact that Plaintiffs’ bid was directly competitive with the only market-rate bid in the record provides us reason to believe thát “[i]nvalidation of the’ challenged ordinance ... Would tangibly improve the chances of construction of [the project].” Huntington Branch, 689 F.2d at 395. Although overturning the shift to R-T zoning would not guarantee Plaintiffs’ success, given their' ability to bid neck-and-neek with a market-rate bidder, the district court appropriately concluded that they enjoyed a “realistic opportunity to proceed with construction.” Id. at 394. To demand more “would be to close our eyes to the uncertainties which shroud human affairs.” Id. “Redressability is not a demand for mathematical certainty.” Toll Bros., Inc. v. Township of Readington, 555 F.3d 131, 143 (3d Cir.2009). Despite the district court’s conclusion that Plaintiffs’ bidding was competitive with the only market-rate bid in the record, Garden City argues that other hypothetical bids under R-M zoning from for-profit developers might have been higher than the Fairhaven bid. Yet Garden City’s argument on this point is founded in pure speculation. Garden City theorizes that because luxury apartments would provide more units than single-family homes, this would likely increase the return to the developer, and thus raise the bid price the project could support. But no such market-rate bids for apartments exist in the record. Moreover, our review of the record does not reveal a clear answer to Garden City’s surmise. Compare App’x at 1286 (BFJ zoning study suggesting. that apartments, although each lower. priced than single-family houses, would yield a greater total market value in light of the greater number of units), with App’x at 1104 (suggesting differing estimates for whether single-family homes or multi-family development would yield a . higher land value). Moreover, the mere fact that Plaintiffs’ bid includes an affordable-housing element does not necessarily mean that a hypothetical market-rate apartment developer would outbid them. As Plaintiffs note, an affordable-housing developer, unlike a market-rate developer, need not consider profit in making its bid proposal. Moreover] affordable-housing developers have access to sources of funds a market-rate developer does not, including tax credits and others government programs encouraging affordable housing. II. Mootness Next, both Nassau County and Garden City argue that, even if Plaintiffs had standing at the outset of this litigation, this case is now moot. In light of the County’s plans to construct a courthouse on the Social Services Site, they contend any injury to Plaintiffs regarding inability to construct affordable housing on the Site is no longer caused by purported discriminatory zoning. Rather, the superseding source of this injury is the decision to build a courthouse. Defendants, and Garden City in particular, rely on the principle that mootness is “standing set in a time frame: The requisite personal interest that must exist at the commencement of the litigation (standing) must continue throughout its existence (mootness).” Arizonans for Official English v. Arizona, 520 U.S. 43, 68 n. 22, 117 S.Ct. 1055, 137 L.Ed.2d 170 (1997) (quoting U.S. Parole Comm’n v. Geraghty, 445 U.S. 388, 397, 100 S.Ct. 1202, 63 L.Ed.2d 479 (1980)); see also Henry P. Monaghan, Constitutional Adjudication: The Who and When, 82 Yale L.J. 1363, 1384 (1973) (providing the source of this formulation). This'principle, however, is “not comprehensive,” Laidlaw, 528 U.S. at 190, 120 S.Ct. 693, and it fails to capture exceptions to' mootness, particularly voluntary cessation cases and cases capable of repetition but evading review, id. These exceptions underline the different aims of the standing and mootness doctrines. The burden of establishing standing falls on the plaintiff, as it “functions to ensure, among other things, that the scarce resources of the federal courts are devoted to those disputes in which the parties have a concrete stake.” Id. at 191, 120 S.Ct. 693. By contrast, the burden of showing mootness logically falls on a defendant because, “by the time mootness is an issue, -the case has been brought and litigated, often (as here) for years. To abandon the case at an advanced stage may prove more wasteful than frugal.” Id. at 191-92, 120 S.Ct. 693. In our view, this case is appropriately analyzed under the voluntary cessation doctrine. Under this principle, “a defendant’s voluntary cessation of a challenged practice does not deprive a federal court of its power to determine the legality of the práctice.” City of Mesquite v. Aladdin’s Castle, Inc., 455 U.S. 283, 289, 102 S.Ct. 1070, 71 L.Ed.2d 152 (1982); see also Laidlaw, 528 U.S. at 189, 120 S.Ct. 693 (stating the voluntary cessation doctrine applies in cases “mooted by the defendant’s voluntary conduct”). “The voluntary cessation of allegedly illegal activities will usually render a case moot if the defendant can demonstrate that (1) there is no reasonable expectation that the alleged violation will recur and (2) interim relief or events have completely and irrevocably eradicated the effects of the alleged violation.” Granite State Outdorr Advert., Inc. v. Town of Orange, 303 F.3d 450, 451 (2d Cir.2002) (internal quotation marks omitted). At bottom, the “rule traces to the principle that a party should not be able to evade judicial review, or to defeat a judgment, by temporarily altering questionable behavior.” City News & Novelty, Inc. v. City of Waukesha, 531 U.S. 278, 284 n. 1, 121 S.Ct. 743, 148 L.Ed.2d 757 (2001). “[A] defendant claiming that its voluntary compliance moots a case bears the formidable burden of showing that it is absolutely clear the allegedly wrongful behavior could not reasonably be expected to recur.” Laidlaw, 528 U.S. at 190, 120 S.Ct. 693 (emphasis added). This is both a stringent, City of Mesquite, 455 U.S. at 289 n. 10, 102 S.Ct. 1070, and a formidable burden, Laidlaw, 528 U.S. at 190, 120 S.Ct. 693. In this case, we are deeply skeptical that Defendants have met their “formidable burden” of showing that it is “absolutely clear” that the Social Services Site will never be used for housing. We are unpersuaded that the County has committed to this course permanently. Although vte recognize that when “the defendant is a government entity, some deference must be accorded to a legislative body’s representations that certain conduct has been discontinued,” Lamar Advert. of Penn, LLC v. Town of Orchard Park, 356 F.3d 365, 376 (2d Cir.2004) (internal quotation njiarks and alterations omitted), some deference does not equal unquestioned acceptance. Indeed, in City of Mesquite, the Supreme Court reached the merits despite the fact that the offending language in the challenged ordinance had been removed during the pendency of the appeal. 455 U.S. at 289, 102 S.Ct. 1070. In finding the case not moot, the Court noted that “the city’s repeal of the objectionable language would not preclude it from reenacting precisely the same provision if the District Court’s judgment were vacated.” Id. Here, suspicious timing and circumstances pervade the County’s decision to build a courthouse. Although the County has authorized funding for the courthouse and has contracted with a construction management corporation, Plaintiffs argue compellingly that various actions with respect to the courthouse project appear to track the development of this litigation. For example, the County announced its decision to build a courthouse on the Social Services Site only on the eve of summary judgment motions. The County claims that plans for the courthouse were in place as early as 2010. App’x at 118 (noting that schematic designs for the building were issued in 2010). Despite counsel’s “continuing duty to inform the Court of any development which may conceivably affect [the] outcome” of litigation, Fusari v. Steinberg, 419 U.S. 379, 391, 95 S.Ct. 533, 42 L.Ed.2d 521 (1975) (Burger, C.J., concurring), the County failed to notify the district court of the proposal until 2011, when it moved for summary judgment, App’x at 119 (affidavit submitted February 2011). The Supreme Court has viewed mootness claims skeptically when they are not timely raised. See City of Erie v. Pap’s A.M., 529 U.S. 277, 288, 120 S.Ct. 1382, 146 L.Ed.2d 265 (2000) (“[0]ur appraisal of Pap’s affidavit is influenced by Pap’s failure, despite its obligation to the Court, to mention a word about the potential mootness issue in its brief in opposition to the petition for writ of certiorari____”). Bolstering our skepticism of Defendants’ mootness claim, Plaintiffs assert, and Defendants do not contest, that the project was dormant for years after Nassau County was dismissed at the summary judgment stage, and the threat of liability against the County diminished. Although Defendants note construction fences were recently put up around the Site, Plaintiffs observe, again without contradiction, that these fences went up approximately around the time the parties filed the respective notices of appeal in this case, and the threat of liability against Nassau County again reemerged. Cf. Lillbask ex rel. Mauclaire v. Conn. Dep’t of Educ., 397 F.3d 77, 89 (2d Cir.2005) (finding the voluntary cessation doctrine applicable where “there [was] no reason to doubt the sincerity of defendants’ representation to the court” that the challenged conduct had ceased). Nor are we persuaded by Defendants’ contentions that the injuries of two workers during construction on the Site, along with asbestos abatement and interior demolition, render the County’s decision to build a courthouse irreversible. Defendants argue that two workers have been injured during construction. Asbestos abatement and interior demolition, at least on the basis of the record before us, would appear to be actions necessary before any action could be taken on the Site. In fact, the article cited in Garden City’s brief makes- no mention of a courthouse, noting only that the workers were injured performing asbestos abatement on the: Social Services Site. The County asserts that the courthouse project is in response to an emergency need for a new courthouse. But the County’s own filings' indicate the County has been aware of the alleged urgent need for a new courthouse since at least 2004. “[An] emphasi[s] that the change had been under consideration long before the federal lawsuit ... of course cuts two wa