
    Mario CUOMO, Edward I. Koch, Alan Chou, Rose L. Dawson, Samuel Lefkowitz, Michael Loizou, Edwin Martinez, Walter E. Marx, Brunilda Pacheco, Lemuel Stanislaus, the State of New York, the City of New York, Plaintiffs, v. Malcolm BALDRIGE, Secretary of Commerce, Thomas G. Keane, Director of Bureau of the Census, William F. Hill, Regional Director, New York Region, Bureau of the Census, Richard Bitzer, Acting Assistant Regional Director, New York Region, Bureau of the Census, Arthur G. Dukakis, Regional Director, Boston Region, Bureau of the Census, United States Department of Commerce, Bureau of the Census, Ronald Reagan, President of the United States, Edmund L. Henshaw, Jr., Clerk of the United States House of Representatives, Defendants.
    No. 80 Civ. 4550 (JES).
    United States District Court, S.D. New York.
    Dec. 8, 1987.
    
      Cravath, Swaine & Moore, New York City, for all plaintiffs except Mario L. Cuo-mo and the State of N.Y.; Robert S. Rif-kind, Alan R. Glickman, Robin C. Landis, Louis M. Solomon, Elizabeth S. Stong, Robert A. Wallner, of counsel.
    Robert Abrams, Atty. Gen. of the State of N.Y., New York City, for plaintiffs State of N.Y. and Mario L. Cuomo, Sanford Cohen, Rosemarie Rhodes, Lawrence S. Kahn, Dennis D. Parker, of counsel.
    Frederick A.O. Schwartz, Jr., Corp. Counsel of the City of New York, for plaintiffs City of New York and Edward I. Koch; Mary McCorry, of counsel.
    Rudolph W. Giuliani, U.S. Atty., S.D. N.Y., New York City, for defendants; Steven E. Obús, Jane E. Booth, Thomas D. Warren, Asst. U.S. Attys., of counsel.
   OPINION AND ORDER

SPRIZZO, District Judge.

In this action, plaintiffs seek a judgment declaring that New York City and New York State were disproportionately under-counted in the 1980 census and a Court order requiring the Bureau of the Census to statistically adjust the 1980 decennial census. Plaintiffs allege that such an adjustment will more accurately reflect the true population of the United States on a state-by-state and sub-state-by-sub-state basis than does the unadjusted census. See Plaintiffs’ Memorandum After Trial on Remand (“PI. Men.”) at 90-91. The plaintiffs include the State of New York and its Governor, New York City and its Mayor, and various individual residents of New York State and New York City. See Complaint at ¶114-15. Defendants include the Secretary of Commerce, the Director of the Bureau of the Census, and the New York Regional and Assistant Regional Directors of the Bureau of the Census. See id. at 111116-22. The defendants will be collectively referred to as the “Census Bureau” or the “Bureau.”

According to the plaintiffs, due to the demographic characteristics of New York City and State, both the City and State were disproportionately undercounted in the 1980 census as compared to the nation as a whole. Plaintiffs’ complaint alleges that this disproportionate undercount injures the plaintiffs in three different ways. First, plaintiffs argue that the disproportionate undercount has resulted in a loss to New York State of one or more congressional seats. See Complaint at 111150-56. Second, plaintiffs allege that because New York State uses the census figures for the purpose of redistricting representative districts for federal and state legislative bodies, the votes of the plaintiffs who reside in congressional, state senate, and state assembly districts which are disproportionately undercounted are diluted. See id. at ¶¶ 57-60. Third, the plaintiffs allege that as a result of the undercount, the City and State will lose federal funding. See id. at ¶¶ 61-63.

The plaintiffs contend that a statistical adjustment of the census will improve upon the accuracy of the census, thereby reducing the disproportionate undercount in the City and State. The Census Bureau, however, contends that although the census counts are imperfect, a statistical adjustment of the census will inject even greater inaccuracies into the population count, and that therefore, a statistical adjustment of the census is not technically feasible or warranted at this time.

Following extensive pre-trial proceedings, a bench trial was held to determine whether the City and/or State were disproportionately undercounted and, more importantly, whether a statistical adjustment would better reflect the true population of the United States on a state-by-state and/or sub-state-by-sub-state basis than the unadjusted census count. For the reasons set forth below, the Court finds as a matter of fact that the Census Bureau correctly determined that an adjustment of the census is not technically feasible or warranted and that no such adjustment should be made.

The following constitutes the Court’s findings of fact and conclusions of law in accordance with Fed.R.Civ.P. 52.

BACKGROUND

This action, commenced in the midst of the 1980 census, is one of more than fifty challenges to the 1980 census brought by various states and localities which flooded district courts across the country in 1980 and 1981. See Carey v. Klutznick, 653 F.2d 732, 735 n. 10 (2d Cir.1981), cert. denied, 455 U.S. 999, 102 S.Ct. 1630, 71 L.Ed.2d 866 (1982). In each of these actions, the plaintiffs claimed that their particular locality was or was going to be disproportionately undercounted in the 1980 census. Several of these other lawsuits have been consolidated in a multidis-trict proceeding in the District of Maryland and are currently pending. See In re 1980 Decennial Census Adjustment Litigation, 506 F.Supp. 648 (J.P.M.L.1981).

A. Prior History

A brief review of the lengthy history of the instant action is necessary.

In August of 1980, the plaintiffs, complaining primarily that the census was being mismanaged in New York City and New York State, sought a preliminary injunction in this Court before Judge Werker, enjoining the closing of census district offices until plaintiffs could review preliminary census figures. During the course of pre-trial discovery, in early September 1980, Judge Werker ordered the Census Bureau to produce the Master Address Registers (“MAR”) for New York City and every other municipality in the State. Upon the Census Bureau’s refusal to comply with that order on the grounds of privilege, Judge Werker entered a broad preclusion order, precluding the defendants from opposing most of plaintiffs’ principal allegations, including plaintiffs’ allegations of a disproportionate undercount and mismanagement. See Carey, supra, 653 F.2d at 738.

By October 10, 1980, intervening circumstances had mooted the plaintiffs’ request for a court order to keep the district offices open. The plaintiffs, therefore, abandoned that request and instead sought a preliminary injunction requiring that the Census Bureau: (1) match a 1.2 million name list of individuals from New York City’s Medicaid Eligibility File (“MEF”) to the census records, (2) receive and process “Were You Counted?” forms received from the City, and (3) determine how many people included in the MEF and “Were You Counted” forms had not been counted in the Census. Judge Werker granted this injunction. See Carey v. Klutznick, 508 F.Supp. 416, 417 (S.D.N.Y.1980) {“Carey I”).

On December 15,1980, a divided panel of the Second Circuit affirmed the grant of the preliminary injunction in a per curiam opinion. With respect to whether plaintiffs had demonstrated a sufficient likelihood of success on the merits, the Second Circuit determined that the plaintiffs had made a sufficient preliminary showing that the procedures employed by the Census Bureau were inadequate in New York to avoid what appeared to be an “inevitable” disproportionate undercount. According to the Court,

[a]ll of this may deprive New York State and New York City of the congressional representation and the federal funding to which they are entitled under the laws and Constitution of the United States. While mathematical exactness or precision is “hardly a workable constitutional requirement,” Reynolds v. Sims, 377 U.S. 533, 577, 84 S.Ct. 1362, 1389, 12 L.Ed.2d 506 (1964), the Supreme Court has held that Article I, section 2 of the Constitution means that “as nearly as is practicable one man’s vote in a congressional election is to be worth as much as another’s,” Wesberry v. Sanders, 376 U.S. 1, 7-8, 84 S.Ct. 526, 529-530, 11 L.Ed.2d 481 (1964).

Carey v. Klutznick, 637 F.2d 834, 839 (2d Cir.1980) {“Carey II”) (emphasis added).

Thereafter, at a trial on the merits, the main focus was on plaintiffs’ claims of mismanagement. See Carey v. Klutznick, 508 F.Supp. 420, 423-26, 429-31 (S.D.N.Y.1980) {“Carey III”). At the conclusion of that trial, the Court found that although the Census Bureau had developed careful plans and procedures to count the population of the United States, it had mismanaged the implementation of those procedures in New York. See id. at 430-31. The Court also found that there was a disproportionate undercount in both New York City and State. See id. Addressing the Bureau’s argument that it was unable to develop statistically defensible methods of adjustment, the Court stated that despite “the difficulties posed by the task ... [t]he task nevertheless must be accomplished.” Id. at 432. Based upon these findings, the Court restrained the defendants from certifying population totals to the President and ordered the Bureau to adjust the 1980 population figures for New York City and State “in a reasonable and scientific manner to compensate for the disproportionate undercount.” Id. at 433. The Supreme Court then stayed the district court’s restraining order. See Klutznick v. Carey, 449 U.S. 1068, 101 S.Ct. 799, 66 L.Ed.2d 614 (1980).

On appeal, the Second Circuit reversed the entire judgment, holding that the MAR was confidential and, therefore, not discoverable and that the district court abused its discretion by issuing the broad preclusion order. See Carey v. Klutznick, {“Carey IV”), 653 F.2d 732, 739 (2d Cir.1981), cert. denied, 455 U.S. 999, 102 S.Ct. 1630, 71 L.Ed.2d 866 (1982). The Court of Appeals remanded the action to the district court for a new trial in which the relevant facts could be fully and fairly developed. See id. at 736, 738.

In instructing the district court on remand, the Second Circuit noted that before the Court ordered any statistical adjustment of the census, all fifty states, and possibly subordinate governmental units, must be afforded the opportunity to be heard because an increase in the population count of even one state would adversely affect the interests of other states with respect to both membership in the House of Representatives and revenue sharing. See id. at 737. As the Court noted, “[i]f statistical adjustments are to be made, they should be made in all States where needed and in a uniformly fair manner.” Id. at 736-37 & n. 17.

Upon remand, the action was transferred from Judge Werker to this Court. Although the focus of the first trial had been on plaintiffs’ claims of mismanagement, after the Second Circuit’s reversal, the plaintiffs stated that they would no longer pursue these claims. See Pre-Trial Order at 21. Therefore, as noted above, the main issue to be tried after remand was whether it was technically feasible to improve upon the census counts by using a statistical adjustment.

The trial on remand, consisting almost exclusively of expert testimony by some of the leading experts in the fields of demographics and statistics, continued for twenty trial days. The direct testimony of most of the experts was taken by affidavit. Plaintiffs’ direct case consisted of the affidavits of six experts, supplemented by the entire record of the first trial plus 210 additional exhibits. Defendants submitted in support of their direct case the affidavits of seven Bureau experts and seven outside experts, as well as the live testimony of six witnesses and 130 additional exhibits. The trial transcript, including the parties’ direct, rebuttal, and surrebuttal cases, exceeds 2,800 pages.

B. The 1980 Census

The United States Constitution requires that a decennial census be taken. Article I, Section 2, Clause 3 of the Constitution states, “The actual Enumeration shall be made [every ten years] in such Manner as [the Congress] shall by Law direct.” By statute, Congress has delegated to the Secretary of Commerce the task of taking the decennial census “in such form and content as he may determine, including the use of sampling procedures and special surveys.” 13 U.S.C. § 141(a) (1982). The Bureau of the Census is the agency within the Department of Commerce entrusted with carrying out this responsibility. See 13 U.S.C. § 2 (1982).

The census results are used for many varied purposes. In particular, Congress uses the census figures to apportion the 435 members of the House of Representatives among the fifty states. The census figures are also used by Congress to determine the appropriate amount of monetary distributions which should be made to state and local governments pursuant to a number of federal funding programs. Moreover, New York State uses census figures for congressional and state legislative reapportionment.

Taking the census, which entails counting the well over two hundred million persons who reside in the United States, is an enormous task. The record in this case establishes that the Census Bureau ably met that task, developing and implementing procedures which were reasonably designed to count as nearly as practicable all those persons residing in the United States on Census Day, April 1, 1980.

The budget for the 1980 census exceeded one billion dollars. See Transcript of First Trial (“Tr. I”) at 1116. The methodology devised by the Census Bureau for taking the 1980 census was set forth in Judge Werker’s opinion after the first trial, and need not be repeated in detail herein. See Carey III, supra, 508 F.Supp. at 422-23. Briefly, the basic enumeration method used for the 1980 Census was a mail-out/mail-back procedure. See id. at 422; Affidavit of Peter Bounpane dated Jan. 23, 1984 (“Bounpane Aff.”) at ¶¶ 17, 23. The first step in this procedure was the compilation of an address list, followed by the mailing of questionnaires to each housing unit on the list. See Carey III, supra, 508 F.Supp. at 422; Bounpane Aff. at ¶ 24. Householders were asked to fill out the questionnaires and mail them back to the census district office on or before April 1, 1980.

The Bureau devised and implemented various procedures which were designed to correct address lists, to insure that questionnaires were filled out correctly, and to follow up on those questionnaires which were not mailed back to the Bureau. See Carey III, supra, 508 F.Supp. at 422-23. See generally Bounpane Aff. at ¶¶ 39-59; Transcript of Trial after Remand (“Tr.”) at 1658-1672. Moreover, the Census Bureau implemented additional procedures which were specifically designed to count “hard to enumerate” groups, such as minorities and transients. See Bounpane Aff. at 1154.

C. The Problem of Undercount

Despite the enormous cost of the census and the conscientious efforts of the Bureau, the 1980 census count was clearly not perfect. However, given the magnitude of the task, it is not at all surprising that many people were missed in the 1980 census. See Affidavit of Barbara Bailar (“Bailar Aff.”) at ¶ 11. Likewise, some people undoubtedly were counted who should not have been counted, either because they were counted twice or because the people counted never existed in the first place. See id.; see also Tr. at 461.

Nevertheless, it is undisputed that, as was the case in all previous decennial censuses, there was a net undercount in the nation as a whole in the 1980 census. See Tr. at 951. A net undercount in the census will occur if the difference between the total number of persons omitted exceeds the total number of erroneous enumerations. See Affidavit of Eugene P. Erick-sen, dated Oct. 21, 1983 (“Ericksen Aff.”) at II67. Although the extent of this under-count cannot be precisely known, the available evidence does tend to suggest that the undercount was less in 1980 than in previous censuses. See id. at 1464. The Court finds that this improvement in coverage is directly attributable to the increased efforts of the Bureau in the 1980 census.

It is also clear that blacks and hispanics have historically been disproportionately undercounted in the decennial censuses, and despite the efforts of the Census Bureau to reduce that undercount, that problem undoubtedly occurred in the 1980 census as well. See Affidavit of Jeffrey S. Passel (“Passel Aff.”) at 1131; Tr. at 1442. As plaintiffs’ experts testified, a complex combination of social, economic, and cultural characteristics which tends to be associated with those minorities makes those groups harder to count than the rest of the population. See Ericksen Aff. at 1169; Affidavit of Charles B. Keely (“Keely Aff”) at 1T1Í15-16. These characteristics include poverty, poor education and language abilities, irregular living arrangements, residence in high crime areas, and fear or distrust of government.

The plaintiffs contend that because New York City has a large concentration of hard-to-count blacks, hispanics and illegal aliens, it follows that New York City was disproportionately undercounted in the 1980 census. See PI. Mem. at 41. The defendants do not dispute that there probably was an undercount in the City. See Bailar Aff. at ¶ 51. Moreover, in light of the heavy concentration of hard-to-count groups in the City, most experts suspect that the City probably was disproportionately undercounted as compared to the un-dercount in the nation as a whole. See, e.g., Tr. at 450, 673, 690, 933, 1041-42, 1110-11, 2181a. However, given the difficulties in quantifying the magnitude of the undercount both in the City and in the nation, it is difficult to statistically test whether this apparently logical suspicion is in fact true. See Tr. at 449, 556, 673, 933-34, 1041-42, lili; Bailar Aff. at 1151.

The evidence with respect to whether New York State was disproportionately un-dercounted is even less clear. Indeed, the statistical adjustment techniques suggested by the plaintiffs, which, as discussed infra, are themselves inaccurate, yield inconclusive and inconsistent results on the issue of whether there was any substantial disproportionate undercount in the State. See, e.g., Tr. at 2208-10. In short, given the problems in attempting to measure the undercount, the Court agrees with those experts who concluded that it is unknown whether there was in fact a disproportionate undercount in the State as compared to the national average. See id. at 1042, 1113.

D. Statistical Adjustment of the Census

No contention is made here that the Bureau can simply arbitrarily adjust the census upwards in areas with large concentrations of hard-to-count groups. Indeed, no one disputes that the Bureau must at least have some method of reasonably approximating the extent of the disproportionate undercount before any adjustment can be made. It is also undisputed that it is essential to any such adjustment that a technically feasible adjustment methodology exist which gives a truer picture of the United States population on a state-by-state basis for apportionment purposes, and a sub-state-by-sub-state basis for federal funding purposes, than the census itself. If it does not, then no adjustment can or should be made because, as the Second Circuit noted, both congressional seats and revenue sharing funds are fixed quantities, and an increase in the population in one state or sub-state area will adversely affect the shares of other localities. See Carey IV, supra, 653 F.2d at 736-37; Declaration of Leon Gilford (“Gilford Dec.”) at MI 6, 7; Affidavit of Richard P. Nathan (“Nathan Aff.”) at ¶¶ 5, 8. Thus, rectifying one state's alleged deprivation will be achieved at the expense of depriving another state of a benefit to which it may properly be entitled.

Over the past thirty years, the Census Bureau has conducted, and continues to conduct, extensive studies in an attempt to measure the net undercount and to develop statistical methodologies for adjusting the census. See Tr. at 828-30, 840-41, 1131, 2169a-70a; Bailar Aff. at ¶ 15. For the 1980 Census, the Bureau experimented primarily with two possible adjustment methodologies, demographic analysis and the Post Enumeration Program (“PEP”). It is, however, the Bureau’s contention that neither of these methodologies is sufficiently reliable for the purpose of adjusting the census counts. Therefore, on December 11, 1980, after carefully studying the problem of statistical adjustments to the census, and after reviewing comments and reports from various advisory committees and other members of the demographic and statistical professions, the Census Bureau announced that it would not adjust the 1980 census because “[a]t present, the Bureau has no sound statistical basis for estimating the true undercount or introducing adjustments.” See 45 Fed.Reg. 82,872 (Dec. 16, 1980); see also Tr. at 1403; Affidavit of Vincent P. Barabba (“Barabba Aff.”) at MI 43-44. This decision was published by the Bureau in the Federal Register along with a lengthy position paper supporting its position. See 45 Fed.Reg. 82,872-85 (Dec. 16, 1980).

Vincent P. Barabba, the former Director of the Bureau who made the decision not to adjust, explained at trial that the Bureau had optimistically hoped that demographic analysis could provide a reliable estimate of the undercount at the national level and that the PEP might provide estimates of that undercount for subnational geographic units, but by late 1980 it became clear that this would not be the case. See Tr. at 1570-71, 1579, 1603-06. As described in more detail below, due to a large influx of illegal aliens into this country after 1970, demographic analysis could not provide the reliable estimate of the national undercount that was previously anticipated. See Bar-abba Aff. at ¶ 46. Likewise, problems in the implementation of the PEP rendered the results of that program unreliable. See Tr. at 1258, 1497-98; Bailar Aff. at ¶ 32. Moreover, the difficulty of developing a technically feasible method of adjusting the 1980 census was further compounded because the available demographic evidence tended to indicate that the net under-count in the United States was considerably smaller in 1980 than in previous censuses, see Tr. at 1464, rendering it even more difficult to precisely measure the extent of that undercount and its distribution across subnational geographic units. See Barab-ba Aff. at ¶ 46; 45 Fed.Reg. 82,874 (Dec.' 16, 1980); see also Tr. at 1401-04, 1603-06; Bailar Aff. at ¶¶ 29-30.

The plaintiffs contend, however, that either demographic analysis or the PEP can and must be used to adjust the 1980 census and that the use of either methodology would improve upon the accuracy of the census. Both of these methodologies are discussed in more detail below.

1. Demographic Analysis

Demographic analysis involves developing estimates of the population of demographic groups, such as age, sex and race groups, primarily by using birth, death, and legal immigration statistics. See Passel Aff. at 11115-7. By totalling up these estimates, the Bureau then derives a demographic estimate of the total national population. In past decennial censuses, many experts believed that the demographic estimate of the national population was more reliable than the census count itself and that by comparing that estimate with the actual census count, the Bureau would be able to reliably estimate the national net undercount in the census.

However, when employed to estimate an undercount (and it is generally agreed among the experts that there was a net undercount in the 1980 census) this method is useful only if the count as shown by demographic analysis exceeds the population as shown in the census itself. When there is a large number of people that cannot be accounted for by demographic analysis, the converse may occur: the census estimate may be larger than that shown by demographic analysis. The large influx of illegal aliens after 1970 resulted in precisely this converse situation. See Tr. at 482, 1010, 1109-10; Passel Aff. at ¶¶ 26, 33, 41; cf Tr. at 285-86. Since illegal aliens are not accounted for in either the birth or legal immigration statistics upon which the demographic estimate depends, they were not included in the demographic population estimate. Under these circumstances, an estimate based upon demographics will not accurately measure un-dercount because that estimate may not only be less than the true population, but may even be less than the figures shown by the census.

A comparison of the results of the 1980 demographic analysis with the results of that analysis for prior census years illustrates the unreliability of demographic analysis as a means of measuring the national undercount for 1980. The demographic analysis for the 1960 and 1970 censuses, as expected, indicated that there was a national undercount in those censuses. The 1980 demographic analysis, however, indicated that there was a net overcount of approximately 0.4%; that is, the census count exceeded the demographic population estimate. However, while some experts believe that the 1980 census was an improvement on earlier censuses, see Tr. at 1464, no one suggests or contends that there was in fact an overcount in 1980 as demographic analysis would suggest. Rather, as explained by defendants’ experts, the most plausible explanation for the 1980 results is that a substantial number of illegal aliens were in fact counted in the 1980 Census, but not included in the demographic estimate. See Tr. at 1407; Passel Aff. at 1110.

More importantly, even assuming ar-guendo that demographic analysis could reliably measure the undercount at the national level, this would not indicate that the Bureau should use demographic analysis to adjust the census because that analysis clearly cannot provide reliable estimates of the population for subnational geographic units. See Passel Aff. at 11II43-44; Declaration of James Trussell (“Trussell Dec.”) at 114; Declaration of Ansley J. Coale (“Coale Dec.”) at II 5; Bailar Aff. at 1145; Tr. 286, 834-35. The only means by which the plaintiffs have suggested that demographic analysis could be used to adjust the census on a state-by-state and sub-state-by-sub-state basis is the so-called “synthetic method.” This method simply allocates the nationally estimated under-count rates for age, race, and sex groups to subnational areas based on the demographically defined groups of persons counted in the census in each area. Thus, the synthetic method simply ignores geographical variations and assumes that a person is as likely to be missed in the census whether he lives in Alabama or in Alaska. Cf. Trussell Dec. at ¶ 16; Tr. at 554-55, 834-35. However, as defendants’ experts persuasively explained, this assumption that the undercount rates for the various age, race, and sex groups are constant from one subnational area to another has no basis in fact whatsoever. See Trussell Dec. at ¶ 16; see also Passel Aff. at 1153a; Tr. at 554-58, 2148a-49a. It is not surprising, therefore, that the American Statistical Association’s Technical Panel on Census Undercount supports the Census Bureau’s view that the synthetic method is simply inadequate as a means of adjusting the census. See Affidavit of Michael A. Stoto (“Stoto Aff.”) at 1134; see also Bailar Aff. at H 45; Tr. at 1076-77.

2. The Post Enumeration Program (“PEP”)

The Post Enumeration Program, or “PEP,” is an experimental program which was designed by the Bureau to evaluate the results of the 1980 census. Although the development and implementation of the PEP is quite detailed, see generally Affidavit of Charles D. Cowan (“Cowan Aff.”) at ¶119-54, for the purposes of this action, only a relatively brief overview of the mechanics of the PEP, the problems with the program, and the results of the PEP is necessary.

The PEP was comprised of two separate studies of the census: the “P sample,” which attempts to measure census under-count, and the “E sample,” which attempts to measure census overcount. See Cowan Aff. at If 20. In grossly oversimplified terms, the PEP estimate of the total population is arrived at by adding the census count and the P sample estimate of the undercount, and then subtracting the E sample estimate of the overcount. See Affidavit of Kirk M. Wolter (“Wolter Aff.”) at 1Í 9(c); Ericksen Aff. at II97.

In the P sample, the Bureau compared the census to a list of approximately 80,000 households which was obtained from the monthly Current Population Survey (“CPS”) to determine how many individuals enumerated in the CPS were also enumerated in the census. See Ericksen Aff. at ¶ 98. This procedure is referred to as “matching,” and each individual included in the CPS is assigned a “match status.” If an individual enumerated in the CPS is also included in the census, it is a “match”; if the individual is not included in the census, it is a “non-match” or a “miss.”

The P sample provides an estimate of the total undercount in the census by employing the number of misses in a mathematical formula known as the dual system estimator. See Tr. at 121,5. Of course, the accuracy of that estimate will depend on the accuracy with which the matching procedure is performed. For example, if an individual enumerated in the CPS is erroneously labeled a miss, the PEP estimated undercount will be overstated.

In implementing the P sample, the Bureau executed two separate match studies. The Bureau matched the census to the April, 1980 CPS and also matched the census to the August, 1980 CPS. See Cowan Aff. at 111121-23.

The E sample, which seeks to measure overcount in the census, is derived from a random sample of names and addresses taken from the census. The samples are then field checked to determine the rate of erroneous enumerations or “curbstoned cases” (the inclusion in the census of fictitious persons or persons who should not have been included in the census) and multiple enumerations (the inclusion in the census of an individual more than once). See id. at ¶¶ 30-31.

The evidence at trial established that the PEP was plagued by various errors caused by inadequacies in the PEP methodology. This type of error is referred to as “bias.” See generally Tr. at 704-05, 1256-57. A significant source of bias in the PEP arises because the process of matching people from the CPS to the census in the P sample is an extraordinarily difficult and inexact task. See Stoto Aff. at 1118; Cowan Aff. at 111115-16. Because of inaccurate, irregular, and incomplete information in both the CPS and the census, the Bureau undoubtedly and inevitably made many errors in determining the match status of individuals enumerated in the CPS, thereby distorting the P sample’s undercount estimate. Moreover, the evidence at trial established that most of this matching error occurred because the Bureau erroneously determined many cases to be misses when they were in fact matches. See Tr. at 823-26,1514; see also Wolter Aff. at ¶ 9(b). This error, therefore, resulted in the PEP overstating the undercount. The extent of this error and the degree to which it varies from one geographic area to another is unknown. See Wolter Aff. at ¶ 9(b); Cow-an Aff. at 1158.

Even more troubling was the Bureau’s inability to make any reasonable determination as to the match status of a substantial number of individuals enumerated in the CPS due to the inexact information in the census and the CPS. See Cowan Aff. at 1158; Affidavit of Kenneth W. Wachter (“Wachter Aff.”) at 1115. It is undisputed that the Bureau could not, consistent with sound statistical principles, simply ignore these “unresolved” cases. Therefore, the Bureau resorted to “imputing” a match status to these unresolved cases, experimenting primarily with two different imputation procedures. See Bailar Aff. at 1180. However, as the evidence at trial established, there is no consensus among experts with respect to which imputation procedure is preferable, and further research, therefore, is needed in this area. See Tr. at 622-24. Indeed, the evidence establishes that both imputation procedures are based on factual assumptions which are currently unsupported and unverified. It follows that the unresolved cases and the use of the varying imputation assumptions referred to above injected a great deal of error into the PEP estimates. See Stoto Aff. at ¶ 18-19; Bailar Aff. at 1182; Tr. at 2763, 2777-78.

Just as with the P sample, the E sample was also subject to bias. Due to insufficient data, the Bureau was unable to determine whether an erroneous enumeration in the census had been made in a substantial number of cases. See Wolter Aff. at ¶ 9; Bailar Aff. at 1132. The Bureau experimented with different procedures to follow up on cases which were difficult to resolve and, as in the P sample, the Bureau used different imputation procedures for cases which could not be resolved even after follow-up. Unfortunately, there is no reliable way to know which follow-up procedure and which imputation method will best lead to accurate estimates of the E sample over-count.

Apart from the biases in the P and E samples caused by inaccurate or insufficient data, another significant bias in the PEP is “correlation bias.” Correlation bias occurs because the census and the CPS are not independent samples of the population; i.e., the probability of a person being included in the census is not independent of the probability of that person being included in the CPS. See Bailar Aff. at 1190; Cowan Aff. at 1112; Tr. at 2816. Thus, for example, certain hard-to-count people such as illegal aliens will likely be missed in both the CPS and the census. Given that some people are likely to have been missed in both the CPS and the census, this type of bias in the PEP tends to underestimate the undercount, although again, the extent of this bias and how it affects various geographic locations is unknown. See Trussell Dec. at 111114-15; Cowan Aff. at 111112, 14; Stoto Aff. at ¶ 25; Tr. at 675, 1050-53, 1221-24, 2156-57, 2760.

There was also testimony at trial about a second kind of correlation bias which arose from a behavioral response to the census and the CPS. This type of bias, which is referred to as “negative correlation bias,” results because in some instances, the inclusion of a person in the CPS might reduce the probability of that person’s inclusion in the census. See Tr. at 928-29, 1220-25, 2816-17. Thus, for example, follow-up by the Bureau revealed that some persons responding to the April CPS did not thereafter respond to census questionnaires based on the erroneous belief that the CPS was itself the census and that therefore, there was no need to respond to a second questionnaire. See id. at 2816-17. Of course, it may also be true that some people responded to the census and therefore did not respond to the CPS.

Defendants’ experts testified that negative correlation bias would lead to overestimation of the undercount, see id. at 1220-21, 2816-17, but both the existence of this bias and the reasons offered by defendants’ experts in support of its impact were disputed by plaintiffs’ experts, see, e.g., id. at 2353-56. In any event, whether this bias affected the PEP and the extent of its effect on various locations is unknown. See id. at 929, 1224.

In addition to the biases discussed above, the PEP also suffered from some amount of “sampling error.” Simply stated, sampling error occurs because the PEP uses a sample of the population, i.e., a particular CPS, to determine how many people in that sample were missed in a portion of the census and then from that number provides an estimate of how many people were missed from the total population in the census. Therefore, even if the match had been performed flawlessly, the miss rate in the sample could still be expected to vary by some random amount from the true miss rate in the entire population because sampling error will inevitably occur.

The results of the PEP confirmed that the PEP’s value as an adjustment tool was severely impaired by both bias and sampling error. The Bureau produced twelve series of PEP estimates of the undercount, each series of estimates differing only with respect to which procedures and assumptions were used in the PEP. Thus, the 12 series of estimates differed depending upon: (1) whether the April or August CPS was used in the P sample; (2) which followup procedures were used in the E sample; and (3) which imputation method was used for the unresolved cases in the P and E samples. As numerous experts at trial testified, and as is plainly evident from a review of the PEP results, the alteration of even one of these procedures resulted in dramatically different PEP estimates, producing inconsistent and irreconcilable results. See, e.g., Tr. at 1465; Bailar Aff. at 1178; Stoto Aff. at 1ÍH 19-21; PX 613. Indeed, the choice of PEP procedures virtually determined the results of the PEP estimates. For example, holding everything else constant, by simply varying the imputation procedure used, the PEP estimates first a 2.30% undercount in New York State (PEP series 2-9) and then a .64% overcount in the State (PEP series 14-9).

Moreover, as defendants' experts persuasively explained, no one series of PEP estimates can be reliably shown to be superior to the others, or indeed, to the census itself, because there is insufficient knowledge with respect to which PEP procedures are better suited for measuring census un-deramnt. See Tr. at 748, 882; Bailar Aff. at ¶ 78; Wolter Aff. at 1f 16; Stoto Aff. at ¶¶ 19-21. While two of plaintiffs’ experts expressed a preference for the “series 2-9” PEP estimates based upon the hypothesis that the PEP procedures employed in arriving at those estimates were superior to the procedures used for the other PEP estimates, the plaintiffs’ experts offered nothing more than unsupported assumptions in support of that position. On the other hand, the defendants’ experts offered equally plausible assumptions which favored different PEP procedures, producing dramatically different PEP estimates. Since there is no reliable empirical or scientific evidence supporting either set of assumptions, the Court agrees with the Bureau’s contention that it cannot accurately choose which PEP estimates are superior and, indeed, cannot reliably determine that the use of any PEP estimate to adjust the census will result in a count closer to the true population than the census itself. See Bailar Aff. at 1188; Tr. at 882.

In preferring the series 2-9 estimates, the Court notes that the plaintiffs’ expert witnesses relied heavily on the circumstance that the series 2-9 estimate of the national black undercount was closest to the national black undercount measured by demographic analysis. See Tr. at 372-73, 424. However, as defendants’ experts testified, there was no substantial agreement between demographic analysis and any of the PEP series of estimates, including series 2-9, for age and sex groups. See, e.g., Tr. at 708-09, 825-26, 878-82, 2499-2514, 2819-20. This lack of correlation between the PEP estimates and the results of demographic analysis with respect to age and sex tends to refute the plaintiffs’ claim that the PEP can accurately measure under-count and supports the view espoused by defendants’ experts that the correlation between the series 2-9 estimates and demographic analysis with respect to the national black undercount is a mere coincidence. See id. at 878-80. In short, as one of defendants’ experts concluded after analyzing both the results of the PEP and demographic analysis:

The PEP does not happen to be measuring undercount very well at all; ... whatever it’s measuring, it’s not measuring undercount. It may be measuring difficulties in matching or inability to reconcile the PEP and the census but it does not appear to be capturing the same phenomenon that demographic analysis is. That is, they do not both appear to be measuring uhdercount, and ... if indeed demographic analysis is measuring un-dercount, then the PEP is measuring something else.

Id. at 2506.

In their rebuttal case, the plaintiffs argued that the application of regression analysis to the undercount estimates derived from the PEP would enable the Bureau to use the PEP to accurately adjust the 1980 census. However, both plaintiffs’ and defendants’ experts agreed that regression analysis will not in any way alleviate the bias in the PEP, see Tr. at 260, 420, 2611-15, 2626-36, 2693, 2697-700, 2746, and plaintiffs apparently do not contend otherwise, see Plaintiffs’ Reply Memorandum After Trial on Remand at 31-34. In short, while regression analysis may remove some of the random sampling error in the PEP, regression analysis will not reduce the substantial errors in the PEP caused by erroneous matches, the untested assumptions made with respect to the unresolved cases, and correlation bias. See Tr. at 2611-15, 2746-47. Moreover, the overwhelming weight of the evidence supports the conclusion of defendants’ experts that the principal difficulties with the PEP stem from these biases rather than from sampling error. See id. at 742-43, 1205, 1268, 2810-11; Bailar Aff. at 111132, 39-46; Wol-ter Aff. at ¶¶ 8-9.

Indeed, as some experts testified, the application of regression analysis to the PEP is analogous to calibrating a rifle — the calibration may enable one to shoot closer to a particular target but tells nothing about whether one is shooting at the correct target in the first place. See Tr. at 2629-31. In short, while regression analysis may reduce the random error in the PEP, because of bias in the PEP it is unclear whether the PEP is even measuring undercount at all, and regression analysis does not make it any more likely that that is what the PEP is in fact measuring. See id. at 2703. As one expert testified, “the regression measuring adjustment of PEP does not give you anything more than PEP itself gives you.” Id. at 2615.

DISCUSSION

Notwithstanding the complexity of the facts set forth above, this action presents one issue to be resolved by the Court: whether the plaintiffs have sustained their burden of proving that a statistical adjustment of the 1980 census will result in a more accurate picture of the proportional distribution of the population of the United States on a state-by-state and sub-state-by-sub-state basis than the unadjusted census. The Court finds as a matter of fact that the plaintiffs have not sustained that burden, and that the action must therefore be dismissed.

At the outset, the Court rejects plaintiffs’ argument that the question of an adjustment is merely one of remedy and that to succeed in this action, they need only prove a disproportionate undercount in New York City and State. See PI. Mem. at 47. This argument is flatly inconsistent with the Second Circuit’s statement that the plaintiffs are not entitled to a perfect population count, but only to one which “as nearly as is practicable” reflects the true population of the United States. See Carey II, supra, 687 F.2d at 839. That statement necessarily assumes that the plaintiffs must not only prove that there was a disproportionate undercount, but also that there is a practicable method that would more accurately reflect the population of the United States. The only method suggested by the plaintiffs in this action is a statistical adjustment. The plaintiffs must, therefore, prove the feasibility of that method.

The Court also notes at the outset that the parties disagree as to what standard of review the Court should use to determine whether plaintiffs have sustained their burden of proof. The defendants argue that the Court should only review whether the Census Bureau’s decision not to adjust the census was “arbitrary” or “capricious,” pursuant to the Administrative Procedure Act (“APA”), 5 U.S.C. § 706(2)(A) (1982). See Defendants’ Post-Trial Memorandum (“Def.Mem.”) at 62. The plaintiffs, on the other hand, argue that the APA’s arbitrary and capricious standard of review is not applicable because plaintiffs “challenge the Bureau’s conduct as a direct violation of their constitutional rights.” See Pl.Mem. at 83. Plaintiffs contend that because they allege that their constitutional rights have been violated, the Court must determine the issue of the feasibility of an adjustment on a de novo basis, without any deference to the Bureau’s expertise. See id. at 88.

The Court agrees with the defendant that an arbitrary and capricious standard of review is appropriate. Accord City of Philadelphia v. Klutznick, 503 F.Supp. 663, 676 (E.D.Pa.1980). As set forth by the court in City of Philadelphia, strong policy considerations dictate a narrow standard of review in this action. Indeed, the extensive testimony at trial overwhelmingly demonstrates that the determination as to whether the use of the currently available adjustment techniques will provide a more or less reliable estimate of the population than the unadjusted census is an extraordinarily technical one, about which reasonable statisticians and demographers can and do disagree. Certainly the Bureau, which has the necessary experience, expertise, and resources to collect and analyze the complex statistical data, is better equipped than the courts to decide whether, in view of this dispute among the experts, the census should be adjusted. See id.

In addition, since Congress entrusted to the Secretary of Commerce the discretion to conduct the census “in such form and content as he may determine,” see 13 U.S.C. § 141(a), it would be wholly inappropriate for this Court to substitute its own judgment with respect to the feasibility of an adjustment for that of the Bureau unless, at a minimum, the plaintiffs proved that the Bureau’s determination was unreasonable. Thus, in light of the policy considerations discussed above and the grant of discretion found in the statute, the Court concludes that the arbitrary and capricious standard is appropriate notwithstanding plaintiffs’ allegation that their constitutional rights have been violated. See Borough of Bethel Park v. Stans, 449 F.2d 575, 579 (3d Cir.1971); City of Willacoochee v. Baldridge, 556 F.Supp. 551, 555 (S.D.Ga.1983); City of Philadelphia, supra, 503 F.Supp. at 675-77; Quon v. Stans, 309 F.Supp. 604, 607 (N.D.Cal.1970); West End Neighborhood Corp. v. Stans, 312 F.Supp. 1066, 1068 (D.D.C.1970); cf. Baltimore Gas & Elec. v. Natural Resources Defense Council, 462 U.S. 87, 103, 103 S.Ct. 2246, 2255, 76 L.Ed.2d 437 (1983); Railroad Commission of Texas v. Rowan & Nichols Oil Co., 310 U.S. 573, 581-82, 60 S.Ct. 1021, 1024, 84 L.Ed. 1368 (1939) (where, as here, agency is making determinations within its area of special expertise at frontiers of science, particular deference to agency’s factual determinations is appropriate). But cf. Young v. Klutznick, 497 F.Supp. 1318 (E.D.Mich.1980) (rejecting arbitrary and capricious standard but agreeing court must accord “great deference” to Bureau’s actions), rev’d on other grounds, 652 F.2d 617 (6th Cir.1981), cert. denied, 455 U.S. 939, 102 S.Ct. 1430, 71 L.Ed.2d 650 (1982).

The record in this case overwhelmingly demonstrates that plaintiff has failed to prove that the Bureau’s decision not to adjust was unreasonable or arbitrary and capricious. In addition to the Bureau’s own employees, the defendants presented at trial the testimony of some of the world’s most distinguished demographers and statisticians who supported the Bureau’s position that an adjustment of the census is not technically feasible. See Trussed Dec. at Till 4-20; Stoto Aff. at ¶¶ 17-37; Affidavit of Jacob S. Siegel (“Sie-gel Aff.”) at Iff 4-21; Coale Dec. at ¶¶14-8; Wachter Aff. at HU 4-28; Affidavit of Nathan Keyfitz (“Keyfitz Aff.”) at ¶¶ 10 — 18; Bailar Aff. at 1HI48-56. Although the plaintiffs presented expert testimony from equally preeminent statisticians and demographers arguing in favor of adjustment, this disagreement among the experts is not even a sufficient basis upon which the Court can or should conclude that an adjustment of the census will increase the accuracy of the census, and is therefore hardly a basis upon which to conclude that the Bureau acted unreasonably in refusing to adjust. The Bureau has and should have substantial discretion to accept one body of expert opinion over another, especially in light of the concession by plaintiffs’ own experts that reasonable experts could disagree with their conclusion that an adjustment was feasible. See Tr. I at 447-49, 1009; Tr. at 204.

Moreover, even if the Court accepts plaintiffs’ argument that a de novo review is appropriate, the plaintiffs must still prove by a preponderance of the evidence that an adjustment of the census will more accurately reflect the true population than the unadjusted census itself. The plaintiffs have failed to discharge that burden. Indeed, after carefully considering all of the evidence, the Court finds as a matter of fact that the arguments advocated by defendants’ experts are more persuasive and credible than those advanced by plaintiffs' experts.

Specifically, as described above, the inability of demographic analysis to account for illegal aliens and especially its inability to measure the population at subnational levels renders that method wholly unsuitable for adjustment purposes. In addition, the weight of the evidence supports the factual finding that the PEP, even when further refined by regression analysis, cannot at the present time be reliably used to adjust the census. The substantial number of unresolved cases and other sources of non-sampling error in the PEP, described above, amply support a finding that the plaintiffs have not shown by a preponderance of the evidence that the use of the PEP will result in an increase in the overall accuracy of the census. See Tr. at 1258. Instead, the evidence establishes that further research is needed to resolve the problems in the PEP before it can be used as an adjustment tool.

The Court cannot accept plaintiffs’ argument that an adjustment is feasible merely because the Bureau has in the past expressed optimism at the prospects of developing methodologies which could be used to adjust the 1980 census. While it is true that the Bureau worked diligently in the hopes of developing an accurate adjustment methodology for the 1980 census, this is not in any way inconsistent with the Bureau’s subsequent conclusion that those hopes and expectations were not in fact realized. See Tr. at 1401-03, 1497-98, 1500, 1570-71, 1579, 1602-06; Barabba Aff. at TÍTI45-46. Indeed, it would not be consistent with sound public policy to discourage the Census Bureau, or any agency for that matter, from optimistically pursuing new methods of improving its performance by holding it bound by its expectations ¿ven where, as here, those methods subsequently prove to be unsuccessful.

Similarly meritless is the plaintiffs’ argument that merely because the Bureau used limited adjustment techniques in the 1970 decennial census, see, e.g., Ericksen Aff. at 1186, the Bureau should now be foreclosed from arguing that the adjustments suggested by the plaintiffs for the 1980 census are technically unfeasible. In the first place, none of those adjustments in 1970 were even remotely similar to the types of wholesale adjustments presently suggested by the plaintiffs. See Tr. at 495-96, 499-500, 1167-68, 1180-82. More importantly, the Bureau is certainly free to change its mind on the viability of statistical adjustments for producing accurate census counts. See id. at 497. Indeed, as the credible evidence at trial established, the Bureau has had second thoughts about the wisdom of the adjustments made in 1970 and did not wish to repeat those mistakes in 1980. See id. at 498, 1250-51,1440-41.

The plaintiffs also argue that Congress had at one time determined that a statistical adjustment of the census was feasible and that, therefore, the Court should likewise make that factual finding. See Pl.Mem. at 56-57. The Court rejects this argument. In support of their position, the plaintiffs rely solely on a 1976 amendment to the General Revenue Sharing statute which provided that the “Secretary of the Treasury shall request the Secretary of Commerce to adjust the population information ... os soon as practicable to include a reasonable estimate of the number of resident individuals not counted in the 1980 census or revisions of the census.” See 31 U.S.C. § 6713(b), repealed by Pub.L. 99-272 § 14001(a)(1), 100 Stat. 327 (Apr. 7,1986) (emphasis added). The Court notes that subsequent to plaintiffs’ memorandum, this statute was repealed. In any event, nothing in that statute suggested that Congress had determined that an adjustment was presently feasible or practicable, and, indeed, the plain language of the statute suggests otherwise. In short, a congressional directive to adjust the census “as soon as practicable” is not the same as, and, indeed is inconsistent with, a directive to adjust the census now, a task which the evidence at trial establishes is not feasible.

Since the Court finds as a matter of fact that a statistical adjustment of the 1980 census is not feasible, plaintiffs’ request that the Court order such an adjustment is denied. Moreover, in light of that factual finding, the Court denies plaintiffs’ request for a judgment declaring that New York City and New York State were disproportionately undercounted. Since plaintiffs have failed to discharge their burden of proving that the census can or should be adjusted, a declaratory judgment stating that there was a disproportionate under-count could not affect any legally cognizable rights of the plaintiffs or afford them any remedy, and would therefore, constitute an advisory opinion which the Court is not constitutionally empowered to give. See Maryland Casualty Co. v. Rosen, 445 F.2d 1012, 1014 (2d Cir.1971).

CONCLUSION

For the reasons set forth above, the complaint is dismissed with prejudice. The Clerk of the Court shall enter judgment accordingly.

It is SO ORDERED. 
      
      . Specifically, the Court found that the plaintiffs had established a prima facie case of disproportionate undercount. However, because of the preclusion order, the defendants were unable to introduce any evidence to rebut plaintiffs' case. See Carey III, supra, 508 F.Supp. at 432.
     
      
      . Had the plaintiffs satisfied their burden of establishing that a statistical adjustment of the census was feasible, the Court anticipated a second phase of the trial, in accordance with the Second Circuit’s instructions, wherein other states would be given an opportunity to be heard on that and all issues.
     
      
      . The parties agreed that the Court could consider all evidence presented at the trial before Judge Werker, and the Court has carefully reviewed that trial record.
     
      
      . The Census Bureau used the mail-out/mail-back procedure for areas of the country containing 95% of the population. See Affidavit of Peter Bounpane, dated Jan. 23, 1984 ("Boun-pane Aff.") at ¶ 23. In certain sparsely populated areas of the country, however, adequate address lists could not be devised. In these areas, unaddressed questionnaires were delivered by mail carriers to householders, who were instructed to fill them out and hold them for enumerator pickup. See id at ¶ 23.
      The Bureau also hired a special set of enumerators to canvass a variety of places where people may reside other than housing units, such as nursing homes, prisons, dormitories, and even railway stations. See id. at ¶ 64.
     
      
      . These procedures were purposely designed to have "layers of redundancy,” /.&, multiple follow-ups and rechecking of data to insure that the census captured as much of the population of the United States as possible. See Bounpane Aff. at ¶¶ 15» 54, 108. For example, to deal with housing units which failed to return a questionnaire, the Census Bureau hired a large work force to personally visit and enumerate each such housing unit. See Tr. at 1664-65. Enumerators were instructed to make up to four visits to a housing unit if necessary to complete a questionnaire. See Bounpane Aff. at ¶ 52. Additionally, every unit designated as vacant by the follow-up enumerator was rechecked by a second independent enumerator to verify the occupancy status of that housing unit. See id. at ¶ 66; Tr. at 1666.
     
      
      . For example, the Bureau instituted a so-called "Nonhousehold Sources Check" which was performed in certain areas of large minority populations. This check consisted of comparing the census records with lists of names and addresses from outside sources such as drivers’ license lists. Census employees then attempted to contact each person on the independent list who was not listed in the census to see if that person should have been enumerated in the census. See Bounpane Aff. at ¶ 67.
     
      
      .Following the first trial, the District Court concluded that although the Bureau’s methodology was reasonable, the Bureau’s implementation of that methodology in New York City and State "was on the whole unreasonable and at times irrational.” See Carey III, supra, 508 F.Supp. at 430. However, this conclusion was impacted by the improper preclusion order which prevented the defendants from presenting their case. Moreover, as noted above, the plaintiffs abandoned their claim of mismanagement at the second trial. In any event, the Court now concludes, based upon a more complete presentation of the facts and taking into account the magnitude of the Census Bureau's task and the time and budgetary constraints on the Bureau, that the Bureau did a reasonably competent job in conducting the census in New York and, indeed, went to great lengths to insure that as many people as practicable were counted. See, e.g., Tr. at 1647-48, 1672, 1680-87, 1693-99, 1723, 1742-43, 1748-49, 1773-74, 1831-44, 1855-57, 1879-80, 1893, 1900-01, 1931-32.
     
      
      . Although the national black/non-black under-count differential has not been eliminated, the available demographic evidence tends to indicate that both the absolute undercount rate for blacks and the black/non-black differential were reduced in the 1980 census as compared to previous censuses. See Tr. at 834, 1094; Affidavit of Jeffrey S. Passel ("Passel Aff.”) at ¶¶ 31-32.
     
      
      . For example, persons living in poverty will be less likely to be included on commercial mailing lists used to develop the address lists; enumerators may be unwilling to enter areas with a high incidence of violent crimes resulting in "curbstoning," or fabrication of a census count by the enumerator, rather than actual door-to-door enumeration; and persons with less education may answer the questionnaires incorrectly-
     
      
      . While blacks comprise approximately 11.7% of the population nationally, they comprise 25.2% of the population counted in New York City. See Plaintiffs' Exhibit ("PX”) 633 at 19, 237. Likewise, hispanics account for approximately 19.9% of the City’s population, and 6.4% of the national population. See id. at 19, 21, 287.
     
      
      . Because pages numbered 2140-2206 appear in both the February 7 and February 21 trial transcripts, the parties have agreed that citations to the February 21 transcript will be followed by the letter , "a.” The Court will adhere to that convention in this opinion.
     
      
      . There are more than 39,000 sub-state revenue sharing areas, referred to as SMSAs. See Tr. at 1378.
     
      
      . Although the Census Bureau had previously maintained that it was unconstitutional to statistically adjust the census count for apportionment purposes, a position which has since been rejected by several courts, see, e.g., City of Philadelphia v. Klutznick, 503 F.Supp. 663, 678-79 (E.D.Pa.1980); Young v. Klutznick, 497 F.Supp. 1318, 1332-35 (E.D.Mich.1980), rev'd on other grounds, 652 F.2d 617 (6th Cir.1981), the Census Bureau has, at least, always worked toward achieving a feasible way of statistically adjusting the census counts for federal funding purposes.
     
      
      .The results of the PEP program were not even available to the Bureau until 1982, and, therefore, the Bureau obviously could not have used the PEP to adjust the census in 1980. In any event, as early as 1980 it became clear that there were grave problems with the PEP which rendered that adjustment methodology unreliable. The results of the PEP in 1982, as described below, simply confirmed the Bureau’s belief that the PEP was unreliable.
     
      
      . The foundation of these estimates is the assumption that the population of the country at a given point in time is equal to the population at some earlier time plus all births and immigrations during that time interval and less all deaths and emigrations during that same time. See Passel Aff. at ¶¶5-7.
     
      
      . Aside from the illegal alien problem, there is another significant limitation on the reliability of demographic analysis to give an accurate picture of the national population. The demographic data for persons who were between the ages of 45 and 64 in 1980 is incomplete, rendering the estimates for that population group highly suspect. See Tr. at 475, 1128. This data is incomplete because comprehensive birth registration did not exist in this country until 1933, resulting in inadequate birth records for persons over the age of 45 in 1980, see Passel Aff. at ¶-14. Furthermore, Medicare records, an alternative data source, do not include persons under the age of 65. See Tr. at 471.
     
      
      .In addition to showing a national overcount, the demographic analysis for the 1980 census indicated that there was an undercount for blacks of 4.8%, but an overcount for non-blacks of 1.1%, i.e., the census count for non-blacks exceeded the demographic estimate for non-blacks, see PX 616, Table 1 at 6. Thus, demographic analysis showed a black/non-black differential undercount of 5.9% for 1980. The plaintiffs deduce from these results that the 1980 census failed to reduce the black/non-black differential undercount rate in the 1980 census over the 6.1% differential measured in the 1970 census.
      However, the plaintiffs’ argument ignores the fact that the great majority of illegal aliens entering the United States after 1970 are believed to be non-black, and, therefore, the demographic estimate for non-blacks, which will not include that illegal alien population, is probably grossly understated. See Passel Aff. at ¶ 32. Thus, although the census count for non-blacks exceeds the demographic estimate for non-blacks, it is likely that this did not occur because non-blacks were overcounted, but rather because the demographic estimate missed many non-black illegal aliens. As defendants’ experts persuasively explained, it is more likely that both non-blacks and blacks were undercounted in the census and that in view of the large numbers of non-counted, non-black illegal aliens, the black/non-black differential under-count is likely to be less than the 5.9% indicated by demographic analysis. See id. Unfortunately, there is no reliable estimate of the illegal alien population or the racial makeup of that group. See Tr. at 482, 1010, 1109-10; Passel Aff. at ¶ 26. It is, therefore, impossible to attempt to correct the demographic estimate of the population even at the national level so that the undercount can be measured using this method.
     
      
      . Demographic analysis cannot provide estimates of the population at the subnational level because there is no reliable data on interstate migration.
     
      
      . It should also be noted that the Bureau’s studies, which have not been rebutted by the plaintiffs, establish that application of the synthetic method to adjust the 1980 census would result in a reduction in the population count of New York State to such an extent that New York would lose a congressional seat. See Affidavit of Kirk M. Wolter (“Wolter Aff.”) at ¶ 18; Declaration of Leon Gilford ("Gilford Dec.”) at ¶ 3; Affidavit of Jacob S. Siegel (“Siegel Aff.”) at ¶ 16.
     
      
      . The CPS is a monthly survey of households conducted by the Census Bureau principally to derive periodic labor statistics. See Affidavit of Charles D. Cowan ("Cowan Aff.”) at ¶ 22.
     
      
      . The E sample also attempted to measure and correct for geocoding errors, i.e., errors in the census which place a housing unit in the wrong enumeration district. See Cowan Aff. at ¶¶27-29. If geocoding errors are not accounted for, the estimate of the undercount in the P sample will be inflated. This is because when a searcher checks to see whether an individual included in the CPS was also included in the census, he searches through address registers which are organized by enumeration district. If there is a geocoding error in the census, the searcher will not find the CPS respondent in the census, not because the respondent was not included in the census, but rather because the searcher was looking in the wrong address register. See Tr. at 610.
     
      
      .Most matching studies are used to estimate animal or fish populations rather than human populations. When measuring a deer population, for example, the process is much simpler. The deer in the first sample are simply tagged in some way, such as by notching the ear, and then released. When the second sample is matched to the first, it is a simple task to look for the tagged deer in the second sample. Obviously, such a straightforward tagging system is impracticable for human populations, rendering it considerably more difficult to match one sam-pie of a human population with another. See generally Cowan Aff. at 1fH 15-19; Tr. at 552.
     
      
      . In order to understand the two imputation procedures used by the Bureau, it is helpful to first understand how the matching procedure was carried out. In implementing the match, Bureau employees searched through the census address registers for individuals enumerated in the CPS. If the person was found in the census, it was determined to be a match. Those cases not initially determined to be matches, however, were not automatically labeled misses, but instead were then sent for a more detailed followup review to determine their match status. See Tr. at 618, 850. Out of this follow-up group, the Bureau determined that some cases were matched to the census and that some were unmatched. However, even after the follow-up, the Bureau was unable to determine the match status of many individuals and these cases remained unresolved. See Tr. at 868, 1479.
      The Bureau used two procedures to impute a match status to these unresolved cases. The first imputation procedure used by the Bureau linked unresolved cases only to those demographically similar cases that had been assigned a match status after follow-up. See Affidavit of Eugene P. Ericksen, dated Oct. 21, 1983 ("Erick-sen Aff.”) at ¶ 193-20; Affidavit of Kenneth W. Wachter ("Wachter Aff.”) at ¶ 16. The second procedure assigned a match status to the unresolved cases by ascribing to those cases the characteristics of the entire CPS sample, and not just those cases resolved after follow-up. Due to the large number of unresolved cases and various other problems in the matching process, the Bureau had to impute a match status to 8.4% of the people enumerated in the April CPS and 9.7% of those enumerated in the August CPS. See Wolter Aff. at ¶ 9.
     
      
      . The Bureau initially developed 29 series of estimates. However, several of these estimates were discarded because the assumptions underlying them were obviously extreme. For example, some estimates were based on an imputation procedure whereby all unresolved cases were simply assigned a match status, whereas in other estimates all unresolveds were assigned a miss status. These extreme cases were eliminated by the Bureau from serious consideration, leaving 12 sets of estimates. See Affidavit of Barbara Bailar ("Bailar Aff.”) at ¶ 81.
      Each series of estimates provides varying estimates of the census undercount for the United States as a whole, each of the SO states, 23 SMSAs, and 16 large central cities including New York City. See Ericksen Aff. at ¶¶[ 96-112.
     
      
      . The undercount estimates for many other states and revenue sharing areas revealed even greater inconsistencies. For example, by varying the imputation procedure, Nevada goes from a 4.76% undercount (PEP series 5-8) to .27% overcount (PEP series 14-8), Florida goes from a 4.18% undercount (PEP series 5-8) to a 1.03% overcount (PEP series 14-8); and Houston goes from a 4.09% undercount (PEP 2-9) to a 2.75% overcount (PEP 14-9). See PX 613.
      The differentials are even larger when one begins to vary between the April and August CPS, and between different follow-up procedures for the E sample. For example, the 12 PEP estimates for the District of Columbia go from a 7.06% undercount to a .84% overcount; Nevada goes from a 6.83% undercount to a .27% over-count; and New York State ranges from an undercount of 2.30% to an overcount of 1.14%. See Stoto Aff. at ¶ 20.
     
      
      . PEP series 2-9 employs the following procedures. First, PEP 2-9 uses the April CPS instead of the August CPS. Plaintiffs’ witnesses favored the April CPS primarily because substantially more people had moved in the period between Census Day and August, rendering those people harder to match to the census address registers than the April CPS respondents. See Wolter Aff. at If 919(a); Tr. at 177. However, because the April CPS was conducted so near to Census Day, the April estimates were arguably affected by negative correlation bias to a greater extent than the August estimates. See Wolter Aff. at ¶ 9(d); Tr. at 650, 927-29, 1221-23. The very nature of this dispute as to which assumptions are more valid tends to support defendants’ claim that one set of assumptions is not more intrinsically reliable than the other. See Tr. at 893-94, Wolter Aff. at ¶ 9(d).
      Second, PEP estimate 2-9 uses a follow-up procedure for the E sample which does not use any information provided to the Bureau by local post office officials, i.e., information from mail carriers with respect to whether someone was living in a particular household. The plaintiffs’ experts favored discarding all of the local post office information primarily because they assumed that some information provided by the post office might be inaccurate. See Tr. at 153; cf. Ericksen Aff. at ¶ 108. However, this assumption is highly questionable since quite clearly some information provided by the post office is accurate, and, therefore, a procedure which considers the post office information may indeed increase overall accuracy. See Cowan Aff. at ¶72; Tr. at 643-44, 678.
      Third, PEP 2-9 uses the imputation procedure in the P sample in which the unresolved cases are assigned the characteristics of only those persons resolved after follow-up. As noted in note 23, supra, the Bureau also experimented with an imputation procedure in which the unresolveds are assigned the characteristics of the entire CPS sample. It is undisputed that the use of the former procedure, favored by plaintiffs’ experts, resulted in the PEP estimating a much higher undercount rate than the latter procedure because there is a much greater percentage of non-matches in the follow-up group than in the entire CPS sample. See Wachter Aff. at ¶¶ 15-18. Plaintiffs' experts favored the former imputation procedure based on the assumption that the unresolved cases are probably people who are hard to count and, therefore, most likely missed in the census. See Tr. at 2346-47, 2368-69. Since these experts believe that the unresolveds were most likely missed in the census, they believe that it is more appropriate to impute to them the characteristics of the follow-up group, which has a higher miss rate than the entire CPS sample. However, these assumptions are not only empirically untested, but also reflect what these experts believed to be true in the first place and were ostensibly trying to prove by using the PEP. Such a circular approach is not only unpersuasive, but in itself constitutes strong proof that a PEP method which is so susceptible to manipulation based upon the assumptions used hardly constitutes the kind of scientific statistical proof that should be used to adjust the census count. See Tr. at 1511.
      Moreover, the defendants’ experts offered equally plausible arguments that the unresolved cases may have a higher rate of misses than the entire CPS sample not because the individual was missed in the census, but rather because inaccurate data in the CPS makes it impossible to find those persons in the census. See Tr. at 2761-63.
     
      
      . The Court rejects plaintiffs' argument that the Court is somehow bound by Judge Werker’s prior determination that an adjustment was technically feasible. See Plaintiffs' Memorandum After Trial on Remand ("Pl.Mem.”) at 52-56. Judge Werker’s opinion was reversed in toto and remanded to the district court for "a full and fair development of the facts," see Carey IV, supra, 653 F.2d at 738, 746. The Court will not ignore that instruction. Moreover, quite aside from the clarity of that direction, nothing in the Second Circuit’s opinion or mandate explicitly or implicitly forecloses a retrial of the adjustment issue, and the Court therefore undoubtedly has discretion to conduct a trial on that issue. Cf. United States v. Cirami, 563 F.2d 26, 33 (2d Cir.1977); Beltran v. Myers, 701 F.2d 91, 93 (9th Cir.), cert. denied, 462 U.S. 1134, 103 S.Ct. 3115, 77 L.Ed.2d 1369 (1983); IB J. Moore, Moore’s Federal Practice ¶ 0.404[10] at 172-73 (2d ed. 1984).
      This is especially true since the Bureau's ongoing research with respect to the reliability of the PEP continued after the first trial, and as a result, a good deal of relevant evidence with respect to the PEP became available only after the first trial. It would clearly be an improvident exercise of discretion for this Court not to consider that new evidence on a retrial in a case as important as this one.
      The cases cited by the plaintiffs in support of their argument that the Court is foreclosed from redetermining the adjustment issue are both factually and legally inapposite. Indeed, those cases generally involved situations where the Court of Appeals specifically limited the issues to be retried by the district court on remand. See, e.g., Pritchard v. Liggett & Myers Tobacco Co., 370 F.2d 95, 95-6 (3d Cir.1966), cert. denied, 386 U.S. 1009, 87 S.Ct. 1350, 18 L.Ed.2d 436 (1967). That is clearly not the case here.
     
      
      . In an apparent attempt to justify their conclusion that the question of adjustment is simply a question of remedy, the plaintiffs in their memorandum argue that the census was not as accurate as is practicable because "the Bureau clearly could have done a much better job conducting the New York headcount.” See Pl.Mem. at 48. However, as noted previously, the plaintiffs have abandoned any claim of mismanagement and, in any event, the Court finds as a matter of fact that taking into account the enormous difficulties involved in counting the United States population, the Bureau did a commendable job in attempting to count as nearly as practicable the population in New York. See supra, note 7.
      Moreover, the Court notes that even if the question of adjustment is merely one of a remedy, it would obviously be plaintiffs’ burden to prove the feasibility of such a remedy before the Court could or should order the Bureau to adjust. Indeed, throughout the trial, the plaintiffs repeatedly conceded that the only issue in this case was whether an adjustment of the census would make the census more accurate and the plaintiffs conceded that it was their burden to prove that. See, e.g., Tr. at 22.
     
      
      . The Court rejects plaintiffs’ argument that the Court should not defer to the Bureau’s determination because the Bureau’s decision not to adjust allegedly “rested on non-technical, political grounds.” Pl.Mem. at 82. That claim is simply not supported by the evidence. The Court finds as a matter of fact that while nontechnical considerations played a minor role in the Bureau’s decision not to adjust, the Bureau’s decision was primarily based on its determination that it was not feasible to develop and implement an adjustment methodology which would be more accurate than the census itself, see Tr. at 1482, 1485-86, 1570, 1579, 1582, 1592-96, 1602-03; cf. 45 Fed.Reg. 82,877-78 (Dec. 16, 1980), a determination supported and confirmed by the evidence at trial.
     
      
      . It should be noted that the extensive record in this action, which illustrates that both conducting the census and determining whether to adjust the census involve complex and difficult questions which the Bureau has substantial expertise in resolving, amply demonstrates the wisdom of the congressional grant of that discretion to the Secretary.
     
      
      . The Court notes that the Second Circuit has not specifically decided whether de novo review is required in a case such as this. Although the Second Circuit indicated in Carey II that where constitutional rights are asserted, review of the Bureau’s decision is not precluded by the APA, defendants correctly observe that the Second Circuit relied on case authority applying a limited standard of review. See Carey II, supra, 637 F.2d at 838-39 (citing City of Camden v. Plotkin, 466 F.Supp. 44, 52-53 (D.N.J.1978); United States v. Little, 321 F.Supp. 388, 391 (D.Del.1971)).
      The Court also notes that the plaintiffs’ claimed violations of their constitutional rights are highly questionable in any event. The plaintiffs claim two distinct constitutional injuries. First, that unless the census is adjusted, New York State will lose one or more congressional seats; and second, that because the State chooses to use census figures for the purposes of redistricting its representative districts, the votes of the plaintiffs who reside in districts which are disproportionately undercounted will be diluted. See Complaint at ¶¶ 50-60.
      Regardless of which standard of review is employed, the plaintiffs have failed to prove their claim that New York State was deprived of any congressional seats by virtue of an alleged disproportionate undercount. Using any of the adjustment methods proposed by plaintiffs, the evidence unequivocally establishes that New York would not gain any seats, and, indeed, under the synthetic method and several PEP series of estimates, would in fact lose congressional seats. See Gilford Dec. at ¶¶ 3(b), 13; Wolter Aff. at ¶ 18 & Ex. C, Figures 19-34. The simple answer to plaintiffs’ second claim is that New York State does not have to utilize the census figures in apportioning its legislative districts, and, therefore, for the reasons set forth by the Sixth Circuit in Young v. Klutznick, 652 F.2d 617, 624-25 (6th Cir.1981), cert. denied, 455 U.S. 939, 102 S.Ct. 1430, 71 L.Ed.2d 650 (1982), plaintiffs may lack standing to raise that claim. Cf. Borough of Bethel Park v. Stans, 449 F.2d 575, 582-83 n. 4 (3d Cir.1971); FAIR v. Klutznick, 486 F.Supp. 564, 570 n. 11 (D.D.C.1980). But cf. Travis v. King, 552 F.Supp. 554, 571 (D.Haw.1982) (states required to use census statistics in apportioning legislative districts). However, in affirming Judge Werker’s preliminary injunction order, the Second Circuit held that the individual plaintiffs had standing to bring this action because they "have alleged concrete harm in the form of dilution of their votes." See Carey II, supra, 637 F.2d at 838. It is not entirely clear whether the Second Circuit was referring to plaintiffs’ claim with respect to the loss of congressional representation by the State or to the claim relating to intrastate redistricting. Given this ambiguity, the Court does not feel free to dismiss the latter claim because of a lack of standing. However, the Court does note that at least New York State, which itself chooses to use the unadjusted census figures, certainly lacks standing to complain about the Bureau’s decision not to adjust since it can easily avoid the consequences of that decision by apportioning its districts on a different basis.
     
      
      . While the parties have not disputed that a technically feasible adjustment methodology must create a more accurate picture on average than the census on a state-by-state and sub-state-by-sub-state basis, plaintiffs’ and defendants’ experts have differing views on what “on average" means. In other words, if the PEP improves the census count in some areas but makes it less accurate in others, is this an “on average” improvement? This dispute, however, is not relevant to a resolution of this action. As defendants’ experts correctly noted, due to the problems in the PEP, it is impossible to know in which geographic areas the PEP is more accurate than the census and in which areas the PEP may be even less accurate. See Tr. at 1416-17; Wolter Aff. at ¶| 23. Since it is impossible to make even this threshold determination, plaintiffs have failed to demonstrate that the use of the PEP will result in an “on average” improvement of the census, regardless of how one defines the term “on average.”
     
      
      . Moreover, as defendants’ experts persuasively explained, it would be especially inappropriate to use either demographic analysis or the PEP to adjust the census in light of the fact that the undercount for the 1980 census was probably relatively small, possibly approaching zero. See Tr. at 1257. Indeed, as noted above, the census count exceeded the demographic estimate of the population, probably because of the inability of the demographic method to account for illegal aliens. See id. at 1257,1464, 1603-06. Given the suspected small undercount in the census, using adjustment techniques such as the PEP or the synthetic method, which are plagued with errors, is likely to inject an even greater inaccuracy into the census than the relatively small undercount those techniques are seeking to correct. See id. at 1257-58, 1603-06; Bailar Aff. at ¶¶ 29-30.
     
      
      .The Court also rejects plaintiffs’ argument that the Court should find as a matter of fact that a statistical adjustment of the census will improve upon the accuracy of the census merely because the Bureau uses statistical techniques to produce post-census estimates of the population for years subsequent to the census year. See Pl.Mem. at 58-60. Obviously, unless the Bureau is to conduct a new census each year, which neither the Constitution nor the Congress requires, the Bureau has no choice but to use statistical techniques to estimate the population change in years subsequent to the census. The mere fact that those post-census estimates are preferable to outdated census figures, however, in no way supports the conclusion that a statistical adjustment of the census will produce a more accurate count than the census itself for the census year in which a current census count is available. See Tr. at 1162-63, 1345-48, 1451-56.
     
      
      . At oral argument, the plaintiffs requested that the Court at a minimum make the factual finding that New York City and State were disproportionately undercounted in the 1980 census. Moreover, in their reply memorandum, plaintiffs request that the Court judicially declare that the unadjusted census figures are “seriously flawed” on the theory that the public is "entitled to a ‘red-herring1 legend or ‘caution’ sign placed on the unadjusted counts.” See Plaintiffs’ Reply Memorandum After Trial on Remand at 13. However, in the context of this case, since a factual finding of a disproportionate undercount in and of itself affects no legally cognizable rights of the plaintiffs and can lead to no legal relief, that factual finding would be nothing more than a fact finding in a vacuum, which this Court declines to make. In addition, plaintiffs’ attempt to have this Court place a caution sign on the census figures, while possibly of some informational value to the public at large, far exceeds the limits of the Court's judicial power.
     