KEARSE, Circuit Judge:

Plaintiffs City of New York et al. appeal from a judgment entered in the United States District Court for the Eastern District of New York following a bench trial before Joseph M. McLaughlin, Judge, dismissing their action to compel defendants United States Department of Commerce ("DOC") et al. (collectively the "federal defendants") to make statistically-based adjustments to the 1990 United States census in order to rectify acknowledged undercounting of certain minority groups, including African-Americans, Hispanics, Asian-Pacific Islanders, and Native Americans. The district court, applying a standard of review set out in the Administrative Procedure Act, 5 U.S.C. § 706 (1988) ("APA"), see 713 F. Supp. 48, 54 (1989), dismissed the complaint on the ground that the decision of the Secretary of Commerce (the "Secretary") not to adjust the census figures was not arbitrary or capricious. See 822 F. Supp. 906 (1993). On appeal, plaintiffs contend that, because the constitutional right to equal apportionment of votes depends on having the most accurate census practicable, the district court should not have applied an arbitrary-and-capricious standard of review but should have reviewed the Secretary's decision de novo. In opposition, the federal defendants argue that the Secretary's decision not to make a statistical adjustment to the census was entirely immune from judicial review or, at the most, was reviewable only for reasonableness, and that the district court correctly found that the decision not to adjust was not unreasonable. The States of Wisconsin and Oklahoma, as intervenors-defendants-appellees, argue that the district court's decision should be affirmed on the ground that the Census Act, 13 U.S.C. § 131 et seq. (1988), prohibits any statistical adjustment of a census that is used for congressional apportionment.

For the reasons stated below, we conclude that the district court properly held that the Secretary's decision is reviewable and that the Census Act does not prohibit a statistical adjustment of the initial census enumeration; but we conclude that the court should not have reviewed the Secretary's decision under the APA's arbitrary-and-capricious standard of review. We vacate and remand for the court to determine whether the Secretary's decision not to make an adjustment in order to improve the overall count and reduce the disproportionate undercounting of minority groups was essential to the achievement of a legitimate governmental interest.

I. BACKGROUND

The background of this litigation focusing on the 1990 census has been painstakingly explored by the district court in several published opinions, see City of New York v. United States Department of Commerce, 713 F. Supp. 48 (E.D.N.Y. 1989) (" NYC v. DOC I"); City of New York v. United States Department of Commerce, 739 F. Supp. 761 (E.D.N.Y. 1990) (" NYC v. DOC II"); City of New York v. United States Department of Commerce, 822 F. Supp. 906 (E.D.N.Y. 1993) (" NYC v. DOC III"), familiarity with which is assumed. The following description is taken largely from NYC v. DOC III, which includes the district court's findings after trial.

A. The Constitutional Requirement of a Decennial Census

The Constitution of the United States requires a decennial census of the population. See Art. I, § 2, cl. 3 (an "actual Enumeration shall be made . . . within every . . . Term of ten Years"). The Constitution provides that members of the House of Representatives shall be apportioned among the states "according to their respective Numbers." Art. I, § 2, cl. 3; see also 14th Amend. § 2 ("Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State. . . ."). The apportionment of Representatives among the states also determines the allocation of votes to the states for the election of the President. See Art. II. § 1, cl. 2 ("Each State shall appoint . . . a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress. . . .").

In addition to these federal constitutional purposes, the census data are used by the states to draw boundaries for congressional and state legislative districts and are used by local governments to establish districts for other representative bodies such as county legislatures, city councils, and boards of supervisors. Census data are also used to allocate federal and state funding and services. For purposes other than apportionment, Congress has directed that, in addition to the decennial census, there be a mid-decade census. See 13 U.S.C. § 141(d).

The Constitution provides that the decennial census shall be conducted "in such Manner as [Congress] shall by Law direct." Art. I, § 2, cl. 3. The agency designated by Congress to conduct the census is the Bureau of the Census ("Bureau" or "Census Bureau"), an agency within DOC. See 13 U.S.C. § 2 (1988).

B. The Census Bureau's Planned Statistical Adjustment

Each decennial census has inevitably contained errors, resulting from, inter alia, the failures of millions of United States residents to return census forms or be counted by other means, leading to omissions, and the multiple counting of some residents and the listing of nonexistent persons, leading to overcounting. The census thus provides at best only an estimate of the nation's true population. Further, the census has been found to undercount members of ethnic and racial minority groups more severely than members of other demographic groups. This phenomenon, known as the "differential undercount," has skewed every census since at least 1940. The Census Bureau started measuring the differential undercount in that year.

In preparation for the 1980 census, the Bureau hoped that a combination of outreach efforts and attempts to focus energies on improving the count in areas such as inner cities, where the undercount was particularly great, would lead to a reduction of both the overall undercount and the differential undercount. When those efforts failed, the Bureau decided to create a program for the 1990 census that would address the problem though other techniques. By 1984, the Bureau had developed an internal research plan to aid it in deciding whether or not the 1990 census should be statistically adjusted in order to reduce the differential undercount. The Bureau created an Undercount Steering Committee and an Undercount Research Staff to consider the undercount problem and sought advice from outside experts and organizations such as the American Statistical Association and the National Academy of Science. The Bureau also consulted state and local governments, planned an extensive advertising campaign, designed a more ethnically inclusive census questionnaire, and developed an automated geographical control system to help assure accurate and timely maps and geographic files for the 1990 census.

Based on recommendations of the Undercount Steering Committee, the Undercount Research Staff, and other experts, the Bureau determined that the best tool for adjusting the census would be a "post-enumeration survey" ("PES"). Using a "dual system elimination," also known as "capture/recapture," the original enumeration would be followed by a second measurement, the PES, which would attempt to measure the rate at which people were omitted or erroneously enumerated by the census, in order to determine the net undercount rate. The net undercount rate would indicate the appropriate amount by which the census should be adjusted.

Although the Bureau had used a PES in a number of ways since 1950, it had never used dual system elimination to make a statistical adjustment to a decennial census. The Bureau worked throughout most of the 1980s to hone the PES into an effective tool for census adjustment. For example, an adjustment problem can occur when individuals who have different probabilities of being counted are placed in a single category. This problem was to be reduced by the use of "poststratification," a technique in which highly specific categories are created and all individuals with a similar likelihood of being counted are placed in a specific category. These categories, or "poststrata," were defined by age, sex, race, Hispanic origin, housing tenure, type of environment ( e.g., urban or rural), and geographic region. This categorization resulted in a total of 1,392 exhaustive and mutually-exclusive poststrata. In addition, anomalous results in the PES were to be addressed by statistical "smoothing," a procedure designed to minimize the effects of sampling error by reducing the difference between the results produced by PES sampling and the results that would be obtained if one were able to survey the entire population.

C. DOC's 1987 Decision, NYC v. DOC I, and the 1989 Stipulation

By May 1987, the Census Bureau had determined that an adjustment of the 1990 census using a postenumeration survey would be feasible and that the Bureau would undertake to conduct a full-fledged PES in order to be able to correct the census. High-ranking DOC officials, however, promptly decided against any adjustment in the 1990 census, though they instructed Bureau officials not to disclose that decision publicly. On October 30, 1987, DOC publicly announced its decision that the 1990 census would not be statistically adjusted.

The present action was commenced in 1988 by plaintiffs including the cities of New York, Los Angeles, and Chicago, the States of New York and California, Dade County, Florida, the National League of Cities, the League of United Latin American Citizens, the National Association for the Advancement of Colored People, and numerous individuals. The original plaintiffs were eventually joined by intervening plaintiffs that included more than a dozen other cities, the States of Texas, New Jersey, Florida, Arizona, New Mexico, and the Navajo Nation. Plaintiffs contended that the Secretary's announced decision not to adjust the 1990 census violated their rights under, inter alia, the Fifth Amendment. Complaining principally of an anticipated loss of representation and an anticipated deprivation of funds to be distributed under federal programs based on census figures, plaintiffs challenged the methodology to be used in the 1990 census and sought to enjoin the census unless it would be subject to adjustment.

The federal defendants moved to dismiss the complaint, contending that the Secretary's decision was unreviewable. The district court denied that motion, holding that plaintiffs had standing to challenge the census on constitutional grounds. NYC v. DOC I, 713 F. Supp. at 52. The court also ruled that it would review the Secretary's decision against adjustment under the arbitrary-and-capricious standard set out in the APA. Id. at 54.

In the wake of these decisions, the parties entered into a stipulation dated July 17, 1989 (the "1989 Stipulation"), pursuant to which plaintiffs would withdraw their motion to enjoin the census and DOC would reconsider, in accordance with specified ground-rules, its 1987 decision not to adjust the 1990 census. The principal premises of the 1989 Stipulation were that

the Secretary of Commerce is vested by law with supervisory authority over the Bureau of the Census and the conduct of the Decennial Census and does not by anything said herein intend to relinquish any authority or decision-making power thereby duly vested in him, including without limitation the decision whether or not to adjust the 1990 Decennial Census;

that

the Secretary of Commerce intends that the 1990 Decennial Census shall be conducted in conformity with all applicable statutory and constitutional requirements . . . and in a manner designed to achieve the most accurate population counts practicable;

and that

the parties hereto at this time believe that the Census, including a post-enumeration survey and other adjustment-related operations, can and will be conducted in a manner that will result in the most accurate counts practicable, and no party has any basis at this time to believe that the Census, including the PES and adjustment-related operations, cannot and will not be conducted in such a manner.

(1989 Stipulation "Whereas" clauses.)

The agreement called for the vacatur of the Secretary's 1987 decision against adjustment of the 1990 census (1989 Stipulation ¶ 2), and required the federal defendants to

undertake to conduct a [PES] of not fewer than 150,000 households . . . and such other procedures or tests as they deem appropriate, as part of the 1990 Decennial Census in a manner calculated to ensure the possibility of using the PES, not solely for evaluation purposes, but to produce corrected counts usable for congressional and legislative reapportionment, redistricting, and all other purposes for which the [Bureau] publishes data,

( id. ¶ 3). The Stipulation also required a de novo reconsideration by the then-new Secretary Robert Mosbacher, "undertaken with an open mind, without any prejudgment, and consistent with the procedures set forth" in the 1989 Stipulation, on "the question of whether or not to carry out a statistical adjustment of the 1990 Decennial Census." ( Id. ¶ 2.)

The 1989 Stipulation required that the Secretary's assessment of any proposed adjustment be in accordance with a set of published guidelines (the "Guidelines"), to be promptly developed by DOC, "articulating what defendants believe are the relevant technical and nontechnical statistical and policy grounds for decision on whether to adjust the 1990 Decennial Census population counts." (1989 Stipulation ¶ 4.) DOC was also required to appoint and fund a Special Advisory Panel of statistical and demographic experts ("Advisory Panel") to advise the federal defendants with respect to, inter alia,

the application and achievement of the [G]uidelines, . . . and plans and schedules for the implementation of the Census and the PES in a manner that will result in the most accurate final census data at the earliest practicable time.

(1989 Stipulation ¶ 7.) If the Secretary eventually decided against an adjustment to the census, his decision was to be accompanied by a "detailed statement of its grounds." ( Id. ¶ 5.) The 1989 Stipulation was approved by the district court in an order dated July 17, 1989 ("1989 Order").

D. The DOC Guidelines and NYC v. DOC II

Following the 1989 Stipulation, DOC appointed an eight-member Advisory Panel, which consisted of four persons selected from a list of seven candidates submitted by plaintiffs, and four members chosen by DOC without input from plaintiffs. DOC proposed and received comments on a set of guidelines, and in March 1990, it promulgated the following final Guidelines:

1. The Census shall be considered the most accurate count of the population of the United States, at the national, state, and local level, unless an adjusted count is shown to be more accurate. The criteria for accuracy shall follow accepted statistical practice and shall require the highest level of professional judgment from the [Bureau]. No statistical or inferential procedure may be used as a substitute for the Census. Such procedures may only be used as supplements to the Census.

2. The 1990 Census may be adjusted if the adjusted counts are consistent and complete across all jurisdictional levels: national, state, local, and census block. The resulting counts must be of sufficient quality and level of detail to be usable for Congressional reapportionment and legislative redistricting, and for all other purposes and at all levels for which census counts are published.

3. The 1990 Census may be adjusted if the estimates generated from the pre-specified procedures that will lead to an adjustment decision are shown to be more accurate than the census enumeration. In particular, these estimates must be shown to be robust to variations in reasonable alternatives to the production procedures, and to variations in the statistical models used to generate the adjusted figures.

4. The decision whether or not to adjust the 1990 Census should take into account the effects such a decision might have on future census efforts.

5. Any adjustment of the 1990 Census may not violate the United States Constitution or Federal statutes.

6. There will be a determination whether to adjust the 1990 Census when sufficient data are available, and when analysis of the data is complete enough to make such a determination. If sufficient data and analysis of the data are not available in time to publish adjusted counts by July 15, 1991, a determination will be made not to adjust the 1990 Census.

7. The decision whether or not to adjust the 1990 Census shall take into account the potential disruption of the process of the orderly transfer of political representation likely to be caused by either course of action.

8. The ability to articulate clearly the basis and implications of the decision whether or not to adjust shall be a factor in the decision. The general rationale for the decision will be clearly stated. The technical documentation behind the adjustment decision shall be in keeping with professional standards of the statistical community.

See NYC v. DOC II, 739 F. Supp. at 769 (emphasis omitted).

In April 1990, plaintiffs challenged the Guidelines, contending that, in violation of the 1989 Order, they were impermissibly vague and were biased against any adjustment to the 1990 census. Plaintiffs also requested a declaratory judgment that a statistical adjustment to the census would not violate the Constitution or any federal statute. Defendants opposed, contending that any decision by the Secretary on whether or not to adjust the census presented a nonjusticiable political question, and that, in any event, since the Secretary could still elect to adjust the census, plaintiffs' requests were premature.

The district court rejected defendants' contention that these motions presented nonjusticiable issues, and it granted plaintiffs' request for a declaration that statistical adjustment would not of itself violate either the Constitution or the laws of the United States, see NYC v. DOC II, 739 F. Supp. at 767. As to the attack on the Guidelines, the court ruled that, while they were vague and while some of them "lend themselves easily to abuse," id. at 770, the Guidelines satisfied defendants' obligations under the 1989 Stipulation and were not unduly biased against adjustment, see id.

E. The Implementation and Results of the 1990 Census

In eventually conducting the 1990 census, the Census Bureau used a four-step process for the initial enumeration. It followed with a PES as required by the 1989 Stipulation.

1. The Initial Enumeration

As a first step in the enumeration, the Bureau compiled a list indicating every household in the nation to which the Bureau would send questionnaires. Since the Bureau would rely on the mail return of those questionnaires to count most of the population, an accurate and comprehensive list was vital. In constructing the list, the Bureau relied primarily on commercial mailing lists, supplemented by extensive field research and collaboration with the United States Postal Service. Numerous quality controls were instituted to improve the accuracy of the list.

Step two was the "mail out/mail back" phase, in which census questionnaires were mailed to each housing unit, and members of each household were asked to complete and return the questionnaires to the local census office on or before April 1, 1990 ("Census Day"). The Bureau's efforts to encourage participation in this phase included a general advertising campaign; campaigns specifically directed at African-Americans, Hispanics, Asian-Pacific Islanders, and Native Americans; publication of specialized foreign-language brochures; maintenance of a set of toll-free telephone numbers providing answers in any of eight languages for persons having questions regarding the questionnaire, including one number from which callers could request questionnaires written in Spanish. The Bureau employed different outreach methods in areas where it was believed that the normal procedure would be particularly ineffective.

The return rate of questionnaires in phase two was only 63 percent. Step three was a follow-up phase. The Bureau sent second mailings to households that had failed to return forms; in census districts with particularly low return rates, it remailed forms to all residents.

In the fourth phase, the Bureau engaged in a further, largely in-person, "nonresponse follow-up" with respect to households that still had not returned questionnaires. Each nonresponding unit was assigned a census enumerator who was to make as many as six attempts to contact a household member to obtain the information necessary to complete a census form. If these efforts proved unproductive, the enumerator would try to obtain basic information on the missing housing unit from a neighbor, building manager, or other reliable source. Once 95 percent of a district's operations were completed, enumerators made one final attempt to visit each remaining nonresponding household to obtain as complete an interview as possible. Then the Bureau implemented "Coverage-Improvement Programs," which included (1) a 100-percent recheck of vacant or uninhabitable units, (2) a "Were you counted?" advertising campaign to reach people who thought they might have been missed by the census, (3) a parolee and probationer check to set the names and Census Day addresses of those people and add them to the census if they had not already been counted, (4) a housing coverage check, in which the Bureau recanvassed select blocks, and (5) a local government review program, which provided local governments with an opportunity to challenge census counts for their areas. The Bureau's follow-up efforts in phase four added 5.4 million people, bringing the total count to 249,632,692.

2. The PES

The Bureau also implemented the PES. In preparation, the Bureau had selected approximately 5,000 blocks to achieve what it deemed an appropriate sample size for each of the 1,392 poststrata previously developed; in February 1990, Bureau employees had visited each sample block and listed all the housing units they found, identifying approximately 170,000 households.

After the Census Day enumeration, Bureau interviewers returned to each address in the sample blocks to obtain information regarding the residency status of those households on Census Day, and discovered that those blocks contained approximately 400,000 people. The Bureau then compared the data obtained in these visits against the information collected in the original enumeration of the sample blocks. From this comparison, the Bureau estimated rates of omission and rates of erroneous overcounting, and calculated a net rate for each poststratum. The Bureau used these results to develop an "adjustment factor" for each poststratum, i.e., a number which, when multiplied by the population count as indicated by the actual enumeration, would reflect the variations found in the PES. The 1,392 poststrata resulted in 1,392 corresponding adjustment factors.

After the use of statistical "smoothing," the Bureau applied the smoothed adjustment factors to produce adjusted counts down to the block level; these counts were then aggregated to provide population estimates for cities, counties, states, and the nation. The Bureau then implemented quality-control checks, including more than twenty formal research projects which analyzed potential sources of error within the PES. The results of these studies were then combined in a "total error model," which summarized the overall quality of the PES data.

3. The Results Shown by the Combined Enumeration and PES

In the end, estimates drawn from the PES revealed that the enumeration resulted in a national undercount of 2.1 percent, or approximately 5.3 million persons out of a total population of approximately 255 million. As was expected, the undercount was greater for members of racial and ethnic minorities. Hispanics were undercounted by 5.2 percent, Native Americans by 5.0 percent, African-Americans by 4.8 percent, and Asian-Pacific Islanders by 3.1 percent. The PES-calculated undercount for non-African-Americans was 1.7 percent, and for non-Hispanic Whites, 1.2 percent. The impact of the differential undercount was naturally more severe in those areas in which racial and ethnic minorities were more concentrated. If the adjusted count indicated by the PES were adopted, Arizona and California would each gain a seat in the House of Representatives; Wisconsin and Pennsylvania would each lose one seat.

F. The Secretary's 1991 Decision Not To Adjust

The Secretary decided not to adjust the 1990 census. The population count reported to the President was thus 249,632,692 rather than 254,902,609 as indicated by the enumeration supplemented by the PES.

The Secretary's decision was issued on July 15, 1991, in a 178-page document entitled "Decision of the Secretary of Commerce on Whether a Statistical Adjustment of the 1990 Census of Population and Housing Should be Made for Coverage Deficiencies Resulting in an Overcount or Undercount of the Population" ("Secretary's 1991 Decision" or "Decision"). Stating that "Blacks appear to have been undercounted in the 1990 census by 4.8%, Hispanics by 5.2%, Asian-Pacific Islanders by 3.1%, and American Indians by 5.0%, while non-Blacks appear to have been undercounted by 1.7%," the Secretary acknowledged that the enumeration "was lower than average among certain segments of our population," but stated that "[i]f we change the counts by a computerized, statistical process, we abandon a two hundred year tradition of how we actually count people." (Secretary's Decision at 1-1.)

Though acknowledging that the PES-indicated adjustment would appear to make the aggregate national count more accurate, reflecting more accurately both the total population of the country and certain racial and ethnic subpopulations of the country ( id. at 2-1), the Secretary was concerned that with respect to places having populations of less than 100,000 there was no direct evidence that the adjusted counts would be more accurate. He stated that while at the state and local levels the statistical analyses had not been completed, "the total error model" suggested that "the adjusted figures tend to be too high." The Secretary acknowledged, however, that the adjusted figures were "generally closer in numeric terms to the true population than the census counts which tend to be too low." ( Id. at 2-1.) The Secretary also recognized that up to 2/3 of the population "lives in jurisdictions where the adjusted counts appear more accurate," and that only "one third of the population lives in areas where the census appears more accurate." ( Id. at 1-5.) He concluded, however, that "[t]he loss function analysis and hypothesis tests that have been prepared by the Census Bureau to date, although of uncertain reliability, do support the superior accuracy of the census counts versus the adjusted figures when we consider distributive accuracy — or fairness — and use reasonable estimates of the error variance of the alternative" PES-based adjustment. ( Id. at 2-2.) The Secretary defined "distributive accuracy" as "getting most nearly correct the proportions of people in different areas." ( Id. at 2-1.) He declined to use the adjustments unless not only numerical accuracy but also distributive accuracy would be increased.

In sum, though conceding that the adjustments would likely bring greater accuracy in the count at the national level, the Secretary expressed the principal concerns (1) that adjustment might not improve distribution of Representatives among the states; (2) that about half of his advisors believed accuracy at the state and local levels would not be improved; and (3) that uncertainty as to the methods of adjustment and assumptions behind them might engender dispute about the accuracy of the census and create the danger that an adjustment might "be made on the basis of research conclusions that may well be reversed in the next several months" (Secretary's 1991 Decision at 1-8). In addition, he expressed the concern that the adjustment process might be subject to manipulation, since the effects of different adjustment methods could be ascertainable in advance; he stated, however, that he was confident that there had been no such manipulation with respect to the 1990 PES.

The Secretary also noted the divergence of views among his advisors. The Advisory Panel split evenly, with the four members selected from plaintiffs' list recommending adjustment, and the four members chosen solely by DOC recommending against it. The Undercount Steering Committee voted seven to two in favor of adjustment, and both the Under-Secretary of Commerce for Economic Affairs and the Administrator of the Economics and Statistics Administration voted against adjustment. The Director of the Census Bureau, while recognizing that "adjustment is an issue about which reasonable men and women and the best statisticians and demographers can disagree" (Administrative Record, Defendants' Exhibit 1, at 1118), recommended in favor of adjustment.

G. The Trial and NYC v. DOC III

Plaintiffs attacked the Secretary's 1991 Decision as a self-serving, post-hoc compilation of documents assembled for the purpose of strengthening DOC's position, and contended that the Secretary's decision was tainted by partisan political influence and violated the Constitution, the APA, and the 1989 Stipulation. After yet another unsuccessful motion by defendants to dismiss the action on nonjusticiability grounds, and after a consolidation of the case with two others presenting identical issues, City of Atlanta v. Mosbacher, 92-CV-1566, and Florida House of Representatives v. Franklin, 92-CV-2037, a 13-day bench trial was held. The evidence consisted chiefly of the testimony of experts in demographics and statistics, hundreds of exhibits, and numerous deposition transcripts.

Following the trial, the district court entered its findings of fact and conclusions of law. Though it confirmed its earlier ruling that it had the authority to review the Secretary's decision not to adjust the census, because "`Article I, § 2 requires the census to be as accurate as practicable,'" NYC v. DOC III, 822 F. Supp. at 919 (quoting NYC v. DOC II, 739 F. Supp. at 767), and though the court found substantial merit in plaintiffs' contentions that the PES-indicated adjustment in the 1990 census was warranted, it rejected plaintiffs' claims and dismissed the complaint on the basis of the standard of review to be applied. See NYC v. DOC III, 822 F. Supp. 906.

The court found that "for most purposes the PES resulted in a more accurate — or to be statistically fashionable, a less inaccurate — count than the original census." NYC v. DOC III, 822 F. Supp. at 916. Plaintiffs contended that the Secretary's finding of greater distributive accuracy in the loss function analysis was flawed because it was based solely on the larger number of states where greater distributive accuracy was produced by the unadjusted count, without regard for the fact that adjustment produced greater distributive accuracy for the larger percentage of the nation's population; plaintiffs also challenged the rationality of "the Secretary's rejection of numerous loss function analyses performed by the Bureau supporting the superior accuracy of the adjusted counts, and his putative concern with the technical aspects of the PES." The court found that these challenges constituted "a compelling attack on the Decision." NYC v. DOC III, 822 F. Supp. at 923 (italics omitted).

However, adhering to its NYC v. DOC I ruling that the Secretary's refusal to adjust the census was to be reviewed under the APA's arbitrary-and-capricious standard, the district court concluded that it could not overturn the Secretary's decision. The court stated that

[t]he conclusion that the Secretary must provide the most accurate census practicable . . . does not lead inexorably to the conclusion that a decision against adjustment is therefore unconstitutional. In deciding whether the Secretary's decision was arbitrary and capricious in light of the requirement that the decision provide the most accurate census practicable, the Court must turn to the Secretary's consideration of the [G]uidelines, which help to illuminate the meaning of both "accuracy" and "practicability."

NYC v. DOC III, 822 F. Supp. at 920. The court reviewed the Secretary's evaluation of the PES-indicated adjustments against each of the eight Guidelines, and found that none of the Guidelines was applied in an arbitrary or capricious manner. For example, the court found that, in applying Guideline One, the Secretary's "decision to focus on distributive, rather than numeric, accuracy was consonant with the constitutional goal of assuring the most accurate census practicable, given the census's function as a standard by which to distribute political representation and economic benefits." Id. at 924. The district court also found that the Secretary's skepticism concerning the methodology of adjustment was not an inappropriate consideration. See id.

The court concluded that

[p]laintiffs have made a powerful case that discretion would have been more wisely employed in favor of adjustment. Indeed, were this Court called upon to decide this issue de novo, I would probably have ordered the adjustment. However, it is not within my province to make such determinations. The question is whether the Secretary's decision not to adjust is so beyond the pale of reason as to be arbitrary or capricious. That far I cannot go.

Id. at 928-29 (footnote omitted). The court added that "[w]hile plaintiffs' counsel has illustrated that adjustment is statistically feasible, and would improve the quality of the counts for most purposes while ameliorating the profoundly disturbing problem of differential undercount, the Court cannot, on the record before it, supplant the Secretary's decision." NYC v. DOC III, 822 F. Supp. at 931.

This appeal followed.

II. DISCUSSION

On appeal, plaintiffs challenge the district court's use of the arbitrary-and-capricious standard of review and contend that the court should have reviewed the Secretary's Decision de novo. While we agree with the district court's rejection of the de novo standard, we disagree with its use of the arbitrary-and-capricious standard. For the reasons below, we conclude that, given the concededly greater accuracy of the adjusted count, the Secretary's decision was not entitled to be upheld without a showing by the Secretary that the refusal to adjust the census was essential to the achievement of a legitimate governmental objective.

A. Statutory Authorization for Statistical Adjustment

Preliminarily, we reject the contention of intervenors-defendants-appellees, relying on 13 U.S.C. § 195, that any statistical adjustment of the census is barred by the Census Act (the "Act"). As presently formulated, § 195 of the Act provides as follows:

Except for the determination of population for purposes of apportionment of Representatives in Congress among the several States, the Secretary shall, if he considers it feasible, authorize the use of the statistical method knowing as "sampling" in carrying out the provisions of this title.

13 U.S.C. § 195 (1988) (emphasis added). Since any reapportionment of Representatives hinges on the number of persons "as ascertained under the . . . decennial census," 2 U.S.C. § 2a(a) (1988), § 195 might appear to preclude the use of sampling in connection with the decennial census, as contrasted with a mid-decade census. However, § 195 must be read in conjunction with § 141 of the Act and in light of the Act's legislative history.

Section 141, as presently formulated, reads as follows:

The Secretary shall, in the year 1980 and every 10 years thereafter, take a decennial census of population as of the first day of April of such year, . . . in such form and content as he may determine, including the use of sampling procedures and special surveys.

13 U.S.C. § 141(a) (1988) (emphasis added). Thus, § 141(a) plainly provides for the use of sampling and surveys in connection with the decennial census.

Section 141's provision for sampling was added in 1976. See Pub.L. 94-521, 90 Stat. 2459 ("1976 Act"). Previously, that section had made no provision whatever for sampling or special surveys; and while § 195 had mentioned such methods, it did not appear to urge their use. The prior version of § 195 read as follows:

Except for the determination of population for apportionment purposes, the Secretary may, where he deems it appropriate, authorize the use of the statistical method known as "sampling" in carrying out the provisions of this title.

13 U.S.C. § 195 (1970) (emphasis added). In the 1976 Act, the present version of § 195, quoted at the beginning of this section, was adopted in order to strengthen the call for use of sampling. Thus, whereas the pre-1976 version of § 195 provided that statistical sampling "may" be used where "appropriate," the present version provides that such methods "shall" be used where "feasible." The legislative history indicated that, by "if . . . feasible" Congress meant "whenever possible":

Section 10 amends section 195 of title 13, U.S.C. to require that the Secretary of Commerce authorize the use of sampling procedures in carrying out the provisions of this title whenever he deems it feasible, except in the apportionment of the U.S. House of Representatives. This differs from present language which grants the Secretary discretion to use sampling when it is considered appropriate. This section as amended strengthens congressional intent that, whenever possible, sampling shall be used.

Report of the Senate Post Office and Civil Service Committee 94-1256 ("S.Rep.") at 6, reprinted in 1976 U.S.Code Cong. Admin. News ("USCCAN") at 5468 (emphasis added). The Senate Report further explained that the 1976 Act inserted the authorizing language in § 141 in order "to encourage the use of sampling and surveys in the taking of the decennial census." S.Rep. at 4, reprinted in 1976 USCCAN 5466; see also Conf.Rep. No. 94-1719, at 13, reprinted in 1976 USCCAN at 5481 (Senate and House of Representatives proposals same with respect to amendment of § 141). In addressing the 1976 Act as a whole, the Senate Report stated that one of "[t]he purposes of this legislation [was] . . . to direct the Secretary of Commerce to use sampling and special surveys in lieu of total enumeration in the collection of statistical data whenever feasible. . . ." S.Rep. at 1, reprinted in 1976 USCCAN at 5463-64 (emphasis added).

Reading §§ 141 and 195 together in light of their legislative history, we conclude that Congress intended the Secretary (a) to conduct an actual enumeration as part of the decennial census, and (b) in lieu of a "total" enumeration, S.Rep. at 1, reprinted in 1976 USCCAN at 5464, to use sampling and special surveys "whenever possible," id. at 6, reprinted in 1976 USCCAN at 5468. Accordingly, we conclude that a statistical adjustment to the initial enumeration is not barred by the Census Act and indeed was meant to be encouraged.

We turn, therefore, to the question of what standard should have been used by the district court in this case in reviewing the Secretary's decision not to adjust the census.

B. The Standard of Review

In reasoning that the district court should have applied a standard of review more stringent than the arbitrary-and-capricious test, we begin with a review of Supreme Court decisions in cases involving apportionment and the right to vote, most of which focused on the drawing of voting districts by states. In Baker v. Carr, 369 U.S. 186, 82 S.Ct. 691, 7 L.Ed.2d 663 (1962), presented with equal protection challenges to the apportionment of seats for the Tennessee state legislature, the Court rejected the defendants' contentions (a) that apportionment presented a nonjusticiable political issue, and (b) that the plaintiffs had no standing to seek judicial review. Id. at 209, 82 S.Ct. at 706. The Court observed that "[a] citizen's right to a vote free of arbitrary impairment by state action has been judicially recognized as a right secured by the Constitution, when such impairment resulted from dilution by a false tally . . . ." Id. at 208, 82 S.Ct. at 705 (citing United States v. Classic, 313 U.S. 299, 61 S.Ct. 1031, 85 L.Ed. 1368 (1941) (emphasis ours)).

In Wesberry v. Sanders, 376 U.S. 1, 84 S.Ct. 526, 11 L.Ed.2d 481 (1964) (" Wesberry"), the Court, reviewing the drawing of congressional districts in Georgia, confirmed that "[t]he right to vote is too important in our free society to be stripped of judicial protection by" an interpretation of Article I that would shield from judicial review state congressional apportionment systems that debase a citizen's right to vote. Id. at 7, 84 S.Ct. at 529. Noting that "[t]he history of the Constitution, particularly that part of it relating to the adoption of Art. I, § 2, reveals that those who framed the Constitution meant that, no matter what the mechanics of an election, whether statewide or by districts, it was population which was to be the basis of the House of Representatives," 376 U.S. at 8-9, 84 S.Ct. at 530, the Wesberry Court held that,

construed in its historical context, the command of Art. I, § 2, that Representatives be chosen "by the People of the several States" means that as nearly as is practicable one man's vote in a congressional election is to be worth as much as another's . . . . To say that a vote is worth more in one district than in another would not only run counter to our fundamental ideas of democratic government, it would cast aside the principle of a House of Representatives elected "by the People," a principle tenaciously fought for and established at the Constitutional Convention.

376 U.S. at 7-8, 84 S.Ct. at 530 (footnotes omitted) (emphasis added). The Court concluded that

[w]hile it may not be possible to draw congressional districts with mathematical precision, that is no excuse for ignoring our Constitution's plain objective of making equal representation for equal numbers of people the fundamental goal for the House of Representatives. That is the high standard of justice and common sense which the Founders set for us.

Id. at 18, 84 S.Ct. at 535.

The principles set out in Wesberry were further explained in Reynolds v. Sims, 377 U.S. 533, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964), which struck down an Alabama scheme that had resulted in state legislative districts of widely disparate size. The Court noted that

[t]he right to vote freely for the candidate of one's choice is of the essence of a democratic society, and any restrictions on that right strike at the heart of representative government. And the right of suffrage can be denied by a debasement or dilution of the weight of a citizen's vote just as effectively as by wholly prohibiting the free exercise of the franchise.

Id. at 555, 84 S.Ct. at 1378 (emphasis added). The Reynolds v. Sims Court discussed Wesberry as follows:

We determined [in Wesberry] that the constitutional test for the validity of congressional districting schemes was one of substantial equality of population among the various districts established by a state legislature for the election of members of the Federal House of Representatives.

In that case we decided that an apportionment of congressional seats which "contracts the value of some votes and expands that of others" is unconstitutional, since "the Federal Constitution intends that when qualified voters elect members of Congress each vote be given as much weight as any other vote. . . ." We concluded that the constitutional prescription for election of members of the House of Representatives "by the People," construed in its historical context, "means that as nearly as is practicable one man's vote in a congressional election is to be worth as much as another's." We further stated:

"It would defeat the principle solemnly embodied in the Great Compromise — equal representation in the House for equal numbers of people — for us to hold that, within the States, legislatures may draw the lines of congressional districts in such a way as to give some voters a greater voice in choosing a Congressman than others."

We found further, in Wesberry, that "our Constitution's plain objective" was that "of making equal representation for equal numbers of people the fundamental goal. . . ." We concluded by stating:

"No right is more precious in a free country than that of having a voice in the election of those who make the laws under which, as good citizens, we must live. Other rights, even the most basic, are illusory if the right to vote is undermined. Our constitution leaves no room for classification of people in a way that unnecessarily abridges this right."

Reynolds v. Sims, 377 U.S. at 559-60, 84 S.Ct. at 1380 (emphasis added).

In Kirkpatrick v. Preisler, 394 U.S. 526, 89 S.Ct. 1225, 22 L.Ed.2d 519 (1969), which involved a drawing of congressional districts in Missouri which resulted in a 1.06 to 1 ratio of the largest district to the smallest, the Court elucidated the Wesberry/Reynolds v. Sims as-nearly-as-practicable standard. The Court

reject[ed] Missouri's argument that there is a fixed numerical or percentage population variance small enough to be considered de minimis and to satisfy without question the "as nearly as practicable" standard. The whole thrust of the "as nearly as practicable" approach is inconsistent with adoption of fixed numerical standards which excuse population variances without regard to the circumstances of each particular case. The extent to which equality may practicably be achieved may differ from State to State and from district to district. Since "equal representation for equal numbers of people [is] the fundamental goal for the House of Representatives," Wesberry v. Sanders, supra, 376 U.S. at 18, 84 S.Ct. at 535, the "as nearly as practicable" standard requires that the State make a good-faith effort to achieve precise mathematical equality. See Reynolds v. Sims, 377 U.S. 533, 577, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964). Unless population variances among congressional districts are shown to have resulted despite such effort, the state must justify each variance, no matter how small.

. . . .

Equal representation for equal numbers of people is a principle designed to prevent debasement of voting power and diminution of access to elected representatives. Toleration of even small deviations detracts from these purposes. Therefore, the command of Art. I, § 2, that States create congressional districts which provide equal representation for equal numbers of people permits only the limited population variances which are unavoidable despite a good-faith effort to achieve absolute equality, or for which justification is shown.

Clearly, the population variances among the Missouri congressional districts were not unavoidable. Indeed it is not seriously contended that the Missouri Legislature came as close to equality as it might have come. . . . [I]t is simply inconceivable that population disparities of the magnitude found in the Missouri plan were unavoidable.

Kirkpatrick v. Preisler, 394 U.S. at 530-32, 89 S.Ct. at 1229.

In Karcher v. Daggett, 462 U.S. 725, 103 S.Ct. 2653, 77 L.Ed.2d 133 (1983), the Court confirmed the strictness of this standard when it upheld the invalidation of a New Jersey congressional districting plan where the population of the largest district was less than 1% greater than the population of the smallest. Quoting the Wesberry/Reynolds v. Sims "as nearly as practicable" language, 462 U.S. at 730, 103 S.Ct. at 2658, the Court held that deviations could not be sanctioned where, though small, they "were not the result of a good-faith effort to achieve population equality," id. at 727, 103 S.Ct. at 2656.

In sum, the Supreme Court has long held that the right to vote is too important to be deprived of judicial protection; that that right is impaired not only by total disenfranchisement but also by dilution, because the Constitution calls for one person's vote to be worth as much as another's as nearly as is practicable; that dilution may result from creating voting districts of different sizes or from "a false tally"; and that, in apportioning legislative seats through districting, a state must make a good-faith effort to achieve the goal of "one-person, one-vote."

The root of the guarantee of "one-person, one-vote" is the Constitution's guarantee to all persons of the equal protection of the law. See, e.g., New York City Board of Estimate v. Morris, 489 U.S. 688, 699, 109 S.Ct. 1433, 1441, 103 L.Ed.2d 717 (1989) (" Reynolds v. Sims line of cases" reflects an "equal protection approach"); id. at 692, 109 S.Ct. at 1437-38 ("equal protection guarantee of `one-person, one-vote'"); Hadley v. Junior College District, 397 U.S. 50, 56, 90 S.Ct. 791, 795, 25 L.Ed.2d 45 (1970) ("as a general rule, whenever a state or local government decides to select persons by popular election to perform governmental functions, the Equal Protection Clause of the Fourteenth Amendment requires that each qualified voter must be given an equal opportunity to participate in that election, and when members of an elected body are chosen from separate districts, each district must be established on a basis that will insure, as far as is practicable, that equal numbers of voters can vote for proportionately equal numbers of officials"); Baker v. Carr, 369 U.S. at 209-10, 82 S.Ct. at 706. The equal protection requirement appears explicitly in the Fourteenth Amendment, which applies to the states, and is a component of the Due Process Clause of the Fifth Amendment, which applies to the federal government. See, e.g., United States Department of Agriculture v. Moreno, 413 U.S. 528, 93 S.Ct. 2821, 37 L.Ed.2d 782 (1973); id. at 533 n. 5, 93 S.Ct. at 2825 n. 5 ("`[w]hile the Fifth Amendment contains no equal protection clause, it does forbid discrimination that is "so unjustifiable as to be violative of due process"'" (quoting Schneider v. Rusk, 377 U.S. 163, 168, 84 S.Ct. 1187, 1190, 12 L.Ed.2d 218 (1964))); Shapiro v. Thompson, 394 U.S. 618, 641-42, 89 S.Ct. 1322, 1335, 22 L.Ed.2d 600 (1969); Bolling v. Sharpe, 347 U.S. 497, 74 S.Ct. 693, 98 L.Ed. 884 (1954). Because the right to equal apportionment is rooted in the right to equal protection, a court faced with a challenge to the constitutionality of an apportionment system is not called upon to "enter upon policy determinations for which judicially manageable standards are lacking. Judicial standards under the Equal Protection Clause are well developed and familiar," and applicable. Baker v. Carr, 369 U.S. at 226, 82 S.Ct. at 715.

Under the familiar judicial standards, a claim of denial of equal protection subjects the challenged governmental act to a degree of scrutiny that depends in part on the nature of the affected right and in part on the nature of the classification. At one end of the spectrum, a program that (a) is social or economic in nature, and (b) is not alleged to discriminate on the basis of inherently suspect classifications or to implicate "fundamental" personal rights, will not be held to violate equal protection principles if it has any rational relationship to a legitimate governmental purpose. See, e.g., Schweiker v. Wilson, 450 U.S. 221, 230, 101 S.Ct. 1074, 1080, 67 L.Ed.2d 186 (1981); City of New Orleans v. Dukes, 427 U.S. 297, 303, 96 S.Ct. 2513, 2516-17, 49 L.Ed.2d 511 (1976) (per curiam). At the other end of the spectrum, a scheme that either (a) impinges on the exercise of a fundamental personal right, or (b) disadvantages a "suspect" class, such as a racial or ethnic group, has traditionally been subject to strict scrutiny to determine whether the scheme is "precisely tailored to serve a compelling governmental interest." Plyler v. Doe, 457 U.S. 202, 217, 102 S.Ct. 2382, 2395, 72 L.Ed.2d 786 (1982); see, e.g., Kramer v. Union Free School District No. 15, 395 U.S. 621, 627-30, 89 S.Ct. 1886, 1889-91, 23 L.Ed.2d 583 (1969) (right to vote in school district election); Shapiro v. Thompson, 394 U.S. 618, 638, 89 S.Ct. 1322, 1333, 22 L.Ed.2d 600 (1969) (right to travel); Skinner v. Oklahoma ex rel. Williamson, 316 U.S. 535, 541, 62 S.Ct. 1110, 1113, 86 L.Ed. 1655 (1942) (right to procreate). In general, if a law alleged to infringe a certain right directly would require a heightened degree of scrutiny, heightened scrutiny should also be given when the law is alleged to infringe that right discriminatorily. See Police Department v. Mosley, 408 U.S. 92, 96, 101-102, 92 S.Ct. 2286, 2293-94, 33 L.Ed.2d 212 (1972); Eisenbud v. Suffolk County, 841 F.2d 42, 45-46 (2d Cir. 1988).

In the present case both the nature of the right and the nature of the affected classes are factors that traditionally require that the government's action be given heightened scrutiny: the right to have one's vote counted equally is fundamental and constitutionally protected, and the unadjusted census undercount disproportionately disadvantages certain identifiable minority groups. Inaccuracies in the decennial census affect both the distribution of Representatives among states and the distribution of Representatives within most states, since states use the census figures in drawing district lines. Though the differential undercount has been noted, see, e.g., Karcher v. Daggett, 462 U.S. at 737 n. 9, 103 S.Ct. at 2662 n. 9 ("the rate of undercount in the census for black population on a nationwide basis is significantly higher than the rate of undercount for white population"), that disparate effect has been tolerated in the past only because the census figures were considered to be "the `best population data available,'" see id. at 738, 103 S.Ct. at 2662 (quoting Kirkpatrick v. Preisler, 394 U.S. at 528, 89 S.Ct. at 1227). Here, however, the district court implicitly found that the census did not achieve equality of voting power as nearly as practicable. It found that the PES-indicated statistical adjustment was feasible; that for most purposes and for most of the population that adjustment would result in a more accurate count than the original census; and that the adjustment would lessen the disproportionate undercounting of minorities. Equal protection analysis requires that heightened scrutiny be given to the Secretary's decision to adhere to an acknowledged undercount that concededly impacts minority groups more severely than nonminority groups. Governmental action that disproportionately denies representation on the basis of race or ethnicity cannot be upheld solely on the basis that the action was "not so far beyond the pale of reason as to be arbitrary or capricious," NYC v. DOC III, 822 F. Supp. at 929.

There are, of course, differences between the present case and the Wesberry/Reynolds v. Sims line of cases because the present case focuses not on action by a state within its boundaries but rather on federal action that is nationwide in scope. One difference is the result of institutional factors. When the defendant is a state entity, the Supremacy Clause of the Constitution, Art. VI, cl. 2, is applicable, and federal law prevails. When the defendant is the federal government, the Supremacy Clause does not come into play, and a court must give effect to the principle of separation of powers. See, e.g., Department of Commerce v. Montana, ___ U.S. ___, ___, 112 S.Ct. 1415, 1426, 118 L.Ed.2d 87 (1992) (" DOC v. Montana"). In our view, the latter factor means that, except with respect to questions of law, a court generally should not review decisions of the Executive Branch under a de novo standard.

A second difference between cases involving state actors and those involving federal actors is the result of constraints that are in part geographical. While it may be possible for a state to achieve equality of population in its congressional election districts, efforts toward such a goal nationwide are constrained by three constitutional requirements: (1) that each state be allotted at least one Representative, (2) that the number of Representatives not exceed one for every 30,000 persons, and (3) that congressional election districts not cross state boundaries. Given these constraints, the goal of precise equality in voting power is "illusory for the Nation as a whole." DOC v. Montana, ___ U.S. at ___, 112 S.Ct. at 1429. That the goal of precise equality cannot be achieved nationwide on account of those constraints, however, does not relieve the federal government of the obligation to make a good-faith effort to achieve voting-power equality "as nearly as is practicable." See id. at ___-___, 112 S.Ct. at 1426-29 (relying on Wesberry/Reynolds v. Sims line of cases and applying good-faith test in challenge to federal apportionment legislation); Franklin v. Massachusetts, ___ U.S. ___, ___, 112 S.Ct. 2767, 2777, 120 L.Ed.2d 636 (1992) (reviewing merits of census claim to "determin[e] whether the Secretary's [judgment in allocating overseas military personnel among states] is consistent with the constitutional language and the constitutional goal of equal representation" (citing DOC v. Montana)). We conclude that the federal government, no less than the states, is required to make a good-faith effort to achieve the Constitution's plain objective of equal representation for equal numbers of people. The impossibility of achieving precise mathematical equality is no excuse for not making this mandated good-faith effort.

C. Burdens of Proof

Although for most types of equal protection claims, a plaintiff must show that the government's discrimination was intentional, see, e.g., Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 265-66, 97 S.Ct. 555, 563-64, 50 L.Ed.2d 450 (1977) (housing); Washington v. Davis, 426 U.S. 229, 239-45, 96 S.Ct. 2040, 2047-50, 48 L.Ed.2d 597 (1976) (employment), the Supreme Court has not imposed such a requirement in any of the cases involving apportionment. As the Seventh Circuit noted in Tucker v. United States Department of Commerce, 958 F.2d 1411 (7th Cir.), cert. denied, ___ U.S. ___, 113 S.Ct. 407, 121 L.Ed.2d 332 (1992), cases such as Reynolds v. Sims

do not place on plaintiffs any burden of proving that a malapportionment represents a deliberate effort to dilute some group's voting power. It is enough that the state's electoral districts are malapportioned. We assume that those cases survive the later ones, such as Washington v. Davis, supra, that require proof of intentional discrimination. The purpose of that requirement is to prevent the concept of equal protection from being used to invalidate governmental policies that just happen to bear more heavily against a vulnerable group, whereas the reapportionment cases vindicate a right that the Supreme Court has found to be implicit in the Constitution to an apportionment mechanism that will, so far as possible give each person's vote the same weight in an election. A state's failure to create the required mechanism is an intentional denial of the right to an equally weighted vote.

958 F.2d at 1414 (emphasis in original). Rather, the Supreme Court has held that the burden of a plaintiff asserting an apportionment claim is simply to show that the governmental entity failed to make a good-faith effort to achieve equal districts as nearly as practicable. Thus, in Karcher v. Daggett, the Court stated the principal issue as

whether the population differences among districts could have been reduced or eliminated altogether by a good-faith effort to draw districts of equal population. Parties challenging apportionment legislation must bear the burden of proof on this issue, and if they fail to show that the differences could have been avoided the apportionment scheme must be upheld. If, however, the plaintiffs can establish that the population differences were not the result of a good-faith effort to achieve equality, the State must bear the burden of proving that each significant variance between districts was necessary to achieve some legitimate goal.

462 U.S. at 730-31, 103 S.Ct. at 2658. Once the plaintiff shows that a scheme was not the product of a good-faith effort to achieve equality, "the burden shift[s] to the [governmental entity] to prove that the population deviations in its plan were necessary to achieve some legitimate state objective." Id. at 740, 103 S.Ct. at 2663 (emphasis added); see also Kirkpatrick v. Preisler, 394 U.S. at 532, 89 S.Ct. at 1229-30 (state did not carry its burden of showing that disparity was "unavoidable"); Reynolds v. Sims, 377 U.S. at 560, 84 S.Ct. at 1381 (Constitution prohibits "`unnecessary'" abridgement of right to vote (quoting Wesberry, 376 U.S. at 18, 84 S.Ct. at 535)).

In those cases in which a plaintiff is required to show that discrimination was intentional, the requisite intent may be inferred from such factors as "the totality of the relevant facts, including the fact, if it is true, that the law bears more heavily on one race than another," Washington v. Davis, 426 U.S. at 242, 96 S.Ct. at 2049, or from the historical background of the decision, see, e.g., Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. at 267-68, 97 S.Ct. at 564-65, or from the foreseeability of discriminatory effects, see, e.g., Columbus Board of Education v. Penick, 443 U.S. 449, 465, 99 S.Ct. 2941, 2950, 61 L.Ed.2d 666 (1979). The government's "[a]dherence to a particular policy or practice, `with full knowledge of the predictable effects of such adherence upon racial imbalance,'" is a factor that may be taken into account in determining whether acts were undertaken with discriminatory intent. Id. The same types of evidence may support an inference that the discrimination resulted from the lack of a good-faith effort to achieve equality as nearly as practicable.

In the present case, the findings of the district court, set out principally in Part I.G. above, plainly show that plaintiffs carried their burden of proving that the Secretary's refusal to adjust the census in accordance with the PES did not reflect an effort to achieve equality as nearly as practicable. Those findings are supported by, inter alia, the Secretary's acknowledgement that the PES-indicated adjustments would likely not only make the census more accurate nationally, but would also reduce the disparate impact of the census' inaccuracies on minority groups, and that he gave other factors priority over achievement of greater accuracy. For example, he stated that he valued "distributive accuracy" over numerical accuracy; and in stating that an adjustment would not be made because it would not result in greater distributive accuracy, the Secretary revealed that he would decline to make the generally improving adjustment that would lessen the disproportionate undercounting of minorities if it would result in a distribution of Representatives that would be different from the present distribution, although just as accurate. The Secretary also stated that he felt that eliminating the possibility of manipulation of statistical surveys in the future was more important than using the admittedly unmanipulated 1990 PES to achieve a more accurate overall count; and that he believed that the use of statistics (notwithstanding Congress's expressed intent to encourage such use) was undesirable because it might reduce state cooperation in the actual enumeration phase of future censuses. He adopted presumptions against any adjustment to the census, stating that greater accuracy at the national level would not lead him to make an adjustment unless it were "convincingly" shown to be not just as accurate, but "more accurate" at every other level as well. ( See, e.g., Secretary's Decision at 2-5.)

The inference that the Secretary did not make the required good-faith effort is also supported by the fact that the differential undercount in the 1990 enumeration was plainly foreseeable and foreseen. In the 1940 census and in every census since, members of ethnic and racial minority groups had been undercounted more severely than members of other demographic groups; and the Census Bureau had noted those disproportionate undercounts. Though the Bureau set out to design a program to lessen that effect for the 1990 census, the Secretary initially decided in 1987 that no adjustment would be made; and after the proceedings in this case led to the withdrawal of that decision, the Secretary again decided in 1991 that no adjustment would be made, notwithstanding his acknowledgements that it was generally agreed that at the national level the adjustments would result in greater accuracy, that half of his advisors apparently believed that the adjustments would not reduce accuracy even at regional or local levels, and that a PES-adjusted count appeared to be more accurate in areas encompassing up to two-thirds of the national population.

In sum, we conclude that plaintiffs amply showed that the Secretary did not make the required effort to achieve numerical accuracy as nearly as practicable, and that the burden thus shifted to the Secretary to justify his decision not to adjust the census in a way that the court found would for most purposes be more accurate and would lessen the disproportionate counting of minorities. The Secretary's decision not to make that adjustment is subject to scrutiny not under an arbitrary-and-capricious standard of review but rather under the more traditional standard applicable to an equal protection claim that a fundamental right has been denied on the basis of race or ethnicity. While precise equality is a goal that at the national level may be illusory, there must be a good-faith effort to approach that goal as nearly as is practicable, and the substantive question becomes what choice should be made among imperfect alternatives. When the official answer is that it is preferable to undercount minorities, that answer must be supported by an official showing that that result (a) furthers a governmental objective that is legitimate, and (b) is essential for the achievement of that objective.

CONCLUSION

We have considered all of defendants' arguments in support of the judgment dismissing the complaint and have found them to be without merit. The judgment is vacated, and the matter is remanded for further proceedings not inconsistent with this opinion.