MAHONEY, Circuit Judge:
This is an appeal by private plaintiffs and the Equal Employment Opportunity Commission (“EEOC”) in a consolidated class action brought pursuant to Title VII of the Civil Rights Act of 1964, 42 U.S.C. § 2000e et seq. (1982). Plaintiffs-appellants appeal from a final judgment of the United States District Court for the Southern District of New York, Dudley B. Bonsai, Judge, affirming and adopting the Final Report of an appointed Administrator Designee determining various class members’ eligibility for backpay and computing backpay awards. Plaintiffs-appellants challenge the district court’s refusal to disqualify the Administrator Designee, its dismissal of six backpay claims because of the claimants’ immigration status, the dismissal of another claim on the ground that the claimant failed to establish his application for union membership, and the calculation of back-pay awards. We affirm as to the disqualification issue, and reverse and remand as to the others.
Background
This appeal is the fourth in the long history of a Title VII class action commenced in 1971 and consolidated in 1972 with a Title VII action brought by the EEOC against the same parties. Familiarity with previous opinions is assumed. See Rios v. Enterprise Ass’n Steamfitters Lo[1170]*1170cal 638 of U.A., 501 F.2d 622 (2d Cir.1974) (affirming and modifying district court’s affirmative relief order); Rios v. Enterprise Ass’n Steamfitters Local Union #638 of U.A., 520 F.2d 352 (2d Cir.1975) (white applicants denied intervention as of right); EEOC v. Enterprise Ass’n Steamfitters Local No. 638 of U.A., 542 F.2d 579 (2d Cir.1976) (affirming in part and modifying in part district court’s backpay eligibility order, affirming award of attorney’s fees), cert. denied, 430 U.S. 911, 97 S.Ct. 1186, 51 L.Ed.2d 588 (1977). The case stems from the pattern and practice of Enterprise Association Steamfitters Local No. 638 of U.A. (the “Union”) of discriminating against black and Hispanic applicants for admission into its A Branch, consisting of union members who have the status of journeymen and work on construction projects. The current appeal concerns only the backpay stage of the litigation.
In the last appeal in this case, we affirmed Judge Bonsai’s backpay eligibility order, Rios v. Enterprise Ass’n Steamfitters Local 638 of U.A., 400 F.Supp. 988, 993 (S.D.N.Y.1975) (“Rios I”), with certain modifications. EEOC v. Enterprise Ass’n Steamfitters Local No. 638 of U.A., 542 F.2d 579 (2d Cir.1976), cert. denied, 430 U.S. 911, 97 S.Ct. 1186, 51 L.Ed.2d 588 (1977) (“Rios II”). The backpay eligibility criteria approved by this court were as follows:
1) the claimant must establish that he applied, either orally or in writing, for and was denied membership in the Union’s A Branch, or was otherwise discriminatorily denied work referrals by the Union, Rios II, 542 F.2d at 586-87;
2) the claimant must prove that he was discriminatorily denied admission after October 15, 1967, which discrimination, for backpay purposes, is deemed to commence on the date that the next non-class member was admitted following the rejection of the claimant and terminate on the date when the claimant was admitted to the A Branch, Rios II, 542 F.2d at 590-91, and Rios I, 400 F.Supp. at 993;
3) the claimant must establish that he resided within the geographical jurisdiction of Local 638, i.e., New York City, Nassau and Suffolk counties, and that he was qualified for admission, Rios II, 542 F.2d at 591, and Rios I, 400 F.Supp. at 993; and
4) the claimant must prove monetary damages (less any other employment income or public assistance) to be “computed on the basis of the average monthly wage paid to members who were admitted to the A Branch on or after October 15, [1967],” Rios I, 400 F.Supp. at 993, and Rios II, 542 F.2d at 590-92.
On remand, the district court implemented the backpay order in two phases, and followed the suggestion of this court, see Rios II, 542 F.2d at 588, that the backpay matters be referred to a special master pursuant to 28 U.S.C. § 636 (1982 and Supp. IV 1986) and/or Fed.R.Civ.P. 53. Vincent McDonnell, a partner in Shea & Gould, was initially appointed as Administrator. He resigned in 1979 because of the press of other duties. At his recommendation, an associate in the same firm, Marshall E. Lippman, was appointed his successor, with the title “Administrator Desig-nee.” Prior to that appointment, a copy of Mr. Lippman’s resume was circulated to the parties, none of whom objected to his appointment.
Phase I of the backpay proceedings, which commenced in 1979, dealt with the eligibility of individual claimants for back-pay awards. In 1983, the Administrator Designee recommended that the claims of six individuals — Edward St. Hill, Claude S. Polidore, Fitzroy Callender, Vibert Caesar, Eric Campbell and Eric Forbes — be dismissed because those claimants were undocumented aliens at the time they were denied admission to the A Branch. It is undisputed that resident alien status was never a requirement for union membership and that each of the six claimants had actually been admitted to the union as a result of the affirmative relief ordered by the district court. Administrator Designee Lippman recommended the dismissal of another claimant, Isidro Diaz, on the ground that his oral request for employment, made [1171]*1171to a union clerk at a union office, did not constitute an oral application for membership in the union. The district court adopted the Administrator’s report as to Phase I “in all respects” in 1984.
At this juncture, the EEOC and the private plaintiffs moved for Mr. Lippman’s disqualification on the ground of conflict of interest. The EEOC claimed that it had only recently discovered that Mr. Lippman was representing another union, the Newspaper and Mail Deliverer’s Union, that was a defendant in an unrelated Title VII case brought by the EEOC. Mr. Lippman had been counsel for that union since 1978, although the resume that he had previously circulated to the parties made no reference to this representation. Judge Bonsai held a hearing concerning this matter and denied the motion for disqualification. He denied a similar motion upon renewal in 1986.
Accordingly, Phase II of the proceedings, to determine individual backpay awards, was also conducted by the Administrator Designee. In order to determine the date for commencement of backpay for each claimant, the Administrator chose a specific “triggering person,” i.e., a specific non-class member admitted to the union at some time after the claimant was denied admission. Generally, under this so-called “one-for-one” approach, where more than one claimant was denied admission before the triggering person was admitted, the triggering person could only trigger back-pay for a single claimant.
In order to determine the average monthly wage upon which the backpay award was to be based, see Rios I, 400 F.Supp. at 993, the Administrator chose to use the earnings of those same specific triggering persons, rather than a random representative group of union members admitted after October 15,1967, for a data base. Four of twenty-seven triggering persons had zero income from steamfitting during the entire backpay period, and several others had years of zero earnings from steamfitting. There were no findings concerning whether these zero income year included in the data base were the result of voluntary or involuntary unemployment at steamfitting. In 1986, the district court approved the Administrator’s method of backpay calculation and the awards based thereon. 651 F.Supp. 109.
On appeal, the EEOC and the private claimants assert numerous errors pertaining to both Phase I and Phase II of the backpay proceedings. With respect to Phase I, appellants assert error in the dismissal of backpay claims solely on the ground of the claimants’ immigration status and the dismissal of Isidro Diaz’s claim on the ground that he failed to establish that he made an oral application for union membership. With respect to Phase II, appellants assert error in the use of the “one-for-one” method and in the inclusion of a substantial number of zero income years in the average wage data base. Appellants also challenge the district court’s denial of their motion to disqualify the Administrator Designee.
We affirm the district court’s decision to deny the disqualification motion. We reverse and remand as to the immigration status issue, the Diaz dismissal, and the two backpay calculation issues.
Discussion
A. Immigration Status.
The original order defining eligibility for backpay required residence in a county within the jurisdiction of Local 638, i.e., New York City (comprising New York, Bronx, Richmond, Kings and Queens counties), Nassau and Suffolk counties. Rios I, 400 F.Supp. at 993. We approved this requirement. Rios II, 542 F.2d at 591 (affirming district court residence requirement as a reflection of class definition). On remand, the district court concluded that the six claimants who were undocumented aliens at the time they applied to the union were not “residents” of any of the specified counties, but rather were “non-resident aliens, illegally in the United States.” The district court reached this conclusion even though legal immigration status had never been an absolute requirement for admission to the union, the aliens had actually been admitted to the union dur[1172]*1172ing the affirmative relief stage of this case (although, the union contends, only because they concealed their alien status), and none of the aliens were ever subjected to deportation proceedings (with the single exception of Eric Wiston Campbell as to whom the Immigration and Naturalization Service advised by letter dated Feb. 20, 1980 that “[n]o efforts are being made to enforce his departure or terminate his employment during [the deportation] proceedings” in view of his marriage to a United States citizen). The district court cited no specific legal authority for its decision to exclude illegal aliens from any Title VII backpay award.
Although there are inconclusive arguments, on both sides, that the immigration status issue has been raised and settled at earlier junctures in this lengthy litigation,1 the main dispute here is over the meaning of the Supreme Court’s decision in Sure-Tan, Inc. v. NLRB, 467 U.S. 883, 104 S.Ct. 2803, 81 L.Ed.2d 732 (1984). Sure-Tan involved the application of the backpay provision of the National Labor Relations Act, 29 U.S.C. § 160(c) (1982), to illegal aliens. Sure-Tan’s construction of the NLRA provision is relevant authority in this Title VII case, because Title VIPs “backpay provision was expressly modeled on the backpay provision of the National Labor Relations Act.” Albemarle Paper Company v. Moody, 422 U.S. 405, 419, 95 S.Ct. 2362, 2372, 45 L.Ed.2d 280 (1975) (footnote omitted).
Sure-Tan held that the protections of the NLRA were applicable to illegal aliens. 467 U.S. at 891-94, 104 S.Ct. at 2808-10; cf. Espinoza v. Farah Mfg. Co., 414 U.S. 86, 95, 94 S.Ct. 334, 340, 38 L.Ed.2d 287 (1973) (Title VII protection from unlawful discrimination of “any individual,” 42 U.S.C. § 2000e-2(a)(l) (1982), extends to aliens). Sure-Tan found no conflict between this holding and the concerns embodied in the Immigration and Nationality Act, 8 U.S.C. § 1101 et seq. (1982), as it existed at that time and at all times pertinent to the instant litigation:
The INA envinees “at best evidence of a peripheral concern with employment of illegal entrants.” [DeCanas v. Bica, 424 U.S. 351] at 360, 96 S.Ct. [933] at 939 [47 L.Ed.2d 43 (1976)]. For whatever reason, Congress has not adopted provisions in the INA making it unlawful for an employer to hire an alien who is present or working in the United States without appropriate authorization____ Moreover, Congress has not made it a separate criminal offense for an alien to accept employment after entering this country illegally. See 119 Cong.Rec. 14184 (1973) (remarks of Rep. Dennis).
Sure-Tan, 467 U.S. at 892-93, 104 S.Ct. at 2808-09.2
Addressing the backpay issue, however, the Supreme Court held that “in computing backpay, the employees must be deemed ‘unavailable’ for work (and the accrual of backpay therefor tolled) during any period when they were not lawfully entitled to be present and employed in the United States.” Id. at 903, 104 S.Ct. at 2814. This conclusion was based in part on a concern for deterring unauthorized immigration. Id. The facts of the case explain this concern: the workers in Sure-Tan voluntarily departed the country (in lieu of imminent deportation) almost immediately after the NLRA violation, id. at 887, 104 [1173]*1173S.Ct. at 2806, and in order to be available for work, they would have had to return to the country. Because it was uncertain whether the claimants would ever be able to reenter the country legally, the court held that any relief must be conditioned on legal reentry. Id. at 903-04 & n. 12, 104 S.Ct. at 2814-15 & n. 12.
The present case is clearly distinguishable from Sure-Tan in this respect. The claimants here have never been deported or forced to leave the country to avoid deportation. Thus, there could be no enticement, by offer of employment or back-pay, for them to reenter the country illegally. Moreover, these claimants were available for employment during the entire period covered by the backpay order, since such employment would have violated no immigration law.3 We therefore disagree with the Union’s contention that the claimants were “legally unavailable” for employment.
We conclude, in agreement with the Ninth Circuit, that undocumented workers who have remained in the country are eligible for backpay as of the time of a violation. NLRB v. Ashkenazy Property Management Corp., 817 F.2d 74 (9th Cir.1987) (NLRA case); Local 512, Warehouse & Office Workers’ Union v. NLRB, 795 F.2d 705 (9th Cir.1986) (NLRA case). We find such awards to be consistent with Sure-Tan’s holding that the protections of the NLRA—and by analogy, Title VII— must apply to undocumented workers, at least to the extent that those protections do not conflict with immigration laws.
B. Claim of Isidro Diaz.
The claim of Isidro Diaz was dismissed by the district court, which accepted the finding of the Administrator Designee that Diaz had failed to establish that he made an oral application for union membership. See Rios II, 542 F.2d at 586-87 (to be eligible for backpay, claimant must show either written or oral application for union membership).
Diaz testified before the Administrator that he had gone to a union office where he had the following colloquy with a clerk:
I told her in English, "I’m looking for a job. I am a welder and pipefitter.” I told her, “Please, I don’t speak too much English.” She said, “What do you want?” I said, “I’m looking for work. I am a welder and pipefitter,” I said____ She told me that there was too much unemployed people and there was not a job for me, a vacancy.
The Administrator found that this exchange was merely “a request for a job,” rather than “an expression of interest in membership in Local 638.”
We hold that it was error to dismiss Diaz’s claim for backpay on this ground. It is clear that Diaz had difficulty communicating in English; even the Administrator recognized this at the hearing by allowing him to testify through an interpreter. Moreover, it is clear that Diaz’s “job request” was made to a union representative at a union office. Under these circumstances, it is unduly rigid to conclude that Diaz’s halting request could not constitute an oral application for membership in the union. We therefore reverse and remand for decision of the issues left unresolved in Diaz’s ease as a result of the erroneous determination that, accepting his version of the facts, he had not applied for union membership.
C. Disqualification of the Administrator.
Appellants cite 28 U.S.C. § 455(a) (1982), and numerous cases construing that provision, as authority for their claim that the district court erred in not disqualifying the Administrator Designee because of his representation of a union in an unrelated Title VII case where he was in an adversary posture to the EEOC. Section 455(a) reads: “Any justice, judge, or magistrate of the United States shall disqualify himself in any proceeding in which his impartiality might reasonably be questioned.”
As is apparent, the terms of this statute do not cover special masters, such as the Administrator Designee, but only [1174]*1174justices, judges and magistrates. Until 1974, in fact, section 455 only covered justices and judges. H.R.Rep. 1453, 93rd Cong., 2d Sess. 2, reprinted in 1974 U.S. Code Cong. & Admin.News 6351, 6352. When Congress undertook a general revision of section 455 in 1974, it chose to expand its coverage to include magistrates and bankruptcy referees,4 id. at 12, 1974 U.S.Code Cong. & Admin.News at 6362, but not special masters.
There is similar ambivalence in the case law. The First Circuit has applied a lower standard to masters than to judges, stating: “Since masters and experts are subject to the control of the court and since there is a need to hire individuals with expertise in particular subject matters, masters and experts have not been held to the strict standards of impartiality that are applied to judges.” Morgan v. Kerrigan, 530 F.2d 401, 426 (1st Cir.), cert. denied, 426 U.S. 935, 96 S.Ct. 2648, 49 L.Ed.2d 386 (1976). In Jenkins v. Sterlacci, 849 F.2d 627 (D.C.Cir.1988), however, the District of Columbia Circuit recently rejected that view, ruling that because of the “clearly erroneous” standard by which the factual determinations of special masters are reviewed, see Fed.R.Civ.P. 53(e)(2), “the district court’s oversight of a special master falls far short of plenary ‘control’,” id. at 631, and therefore a “special master must hold himself to the same high standards [of recusal] applicable to the conduct of judges.” Id. at 632 (citation omitted).
Somewhat echoing the statement in Morgan v. Kerrigan, 530 F.2d at 426, of the “need to hire individuals with expertise in particular subject matters,” however, Jenkins v. Sterlacci recognized that since special masters are frequently attorneys, acco-modation is required to the likelihood that special masters will be engaged as advocates in matters other than those in which they serve as masters. Id., 849 F.2d at 632. A particular aspect of such involvement was noted in United States v. Lewis, 308 F.2d 453 (9th Cir.1962), where it was stated:
[T]here are very real practical problems in situations such as this: Those qualified to act as commissioners in a particular area are likely to have had prior association with those qualified as expert witnesses from that area.
Id. at 457; see also Scott v. Spanjer Bros., Inc., 298 F.2d 928, 931-32 (2d Cir.1962) (medical expert appointed by court to assist the court and jury not disqualified because he allegedly had a great deal of experience as a “plaintiff’s doctor”).
The reflection of these realities in the instant case was summarized in a statement by the Administrator Designee to the district court:
[I]f a person is involved in employment law or labor law, they [sic] are going to have occasions when their representation in one sense or another is going to bring them within the ambit [of] the EEOC or their related agencies, and if that were to be considered a disqualification or a situation which created predisposition or prejudice or an inability to dispassionately deal with issues that might be put before you, there would be few, if any, people with any experience in this field who could serve in any capacity similar to this.
This consideration is buttressed by 28 U.S.C. § 455(b)(2) (1982), which calls for a judge’s disqualification “[w]here in private practice he served as lawyer in the matter in controversy, or ... has been a material witness concerning it.” See also Code of Judicial Conduct for United States Judges, Canon 3C(l)(b), 69 F.R.D. 273, 277 (1975) (similar provision). The specificity of this prohibition is considerably at odds with the almost generic bar for which appellants contend in the instant litigation.
Furthermore, it is the general “rule that disqualification is a matter for the exercise of discretion by the district judge, unless actual bias has been demonstrated beyond reasonable possibility of disagreement.” United States v. Certain Parcels of Land, 384 F.2d 677, 681 (4th Cir.1967) (citation omitted). “A balancing of all considerations and probabilities should be the function of the district court and, in review of its action, the test should be whether abuse appears.” United States v. Lewis, [1175]*1175308 F.2d at 457. Under the circumstances here presented, we find no abuse of discretion in the district court’s denial of the motion to disqualify the Administrator Des-ignee.
There was no significant claim of particularized conflict between the two roles fulfilled by the Administrator Designee, other than his representation of a union client defending an EEOC action in unrelated litigation while acting as special master in the instant litigation where the EEOC is a party plaintiff. Furthermore, the Administrator Designee had been serving in that capacity for a number of years before any suggestion of recusal was made, and the district court was entitled to take into consideration the body of experience in these proceedings already acquired by the Administrator Designee at that juncture. See National Auto Brokers v. General Motors Corp., 572 F.2d 953, 958 (2d Cir.1978), cert. denied, 439 U.S. 1072, 99 S.Ct. 844, 59 L.Ed.2d 38 (1979); Rosen v. Sugarman, 357 F.2d 794, 797-98 (2d Cir.1966).5 Finally, we observe that the Administrator Des-ignee’s position vis-a-vis the EEOC, and Title VII plaintiffs generally, is not so uniformly hostile as appellants might imply. During the first disqualification hearing before the district court, the Administrator Designee informed the court that his office had clients who were plaintiffs in employment discrimination cases involving the EEOC, and that he had authored a set of training materials that was utilized by the EEOC for the training of hearing officers and commissioners in state agencies.
The Administrator Designee is exactly the kind of experienced employment law practitioner who could be of most use to the district court as a master in this case. It is virtually unavoidable that one so experienced in this area would represent workers and unions on both sides of EEOC enforcement actions. It is primarily up to the district court to control the master and to evaluate his conclusions. See Fed.R. Civ.P. 53(c) & (e). In sum, we find no abuse of the district court’s considerable discretion in its refusal to disqualify the Administrator Designee.
D. Backpay Calculation.
Appellants claim two errors in the Administrator Designee’s Phase II calculations of backpay, which were adopted by the district court. First, they challenge the “one-for-one” method, according to which each claimant was paired with a specific non-class applicant admitted to the Union, even though that admitted applicant may not have been the first non-class member admitted after the claimant was denied admission. Second, appellants challenge the inclusion of zero income years in the data base for determining the average yearly wage of successful non-minority applicants during the backpay period.
In determining whether the district court abused its discretion in fashioning the backpay remedy, we are guided by general principles pertinent to Title VII backpay awards. See Berkman v. City of New York, 705 F.2d 584, 594 (2d Cir.1983) (while district court has broad power to fashion relief, its discretion is bounded by purposes of Title VII). The purpose of the backpay provision of Title VII is to make victims whole for injuries sustained from past employment discrimination. Albemarle Paper Company v. Moody, 422 U.S. 405, 419, 95 S.Ct. 2362, 2372, 45 L.Ed.2d 280 (1975). Since the object of compensatory relief under Title VII is to make the victim whole, courts must “as nearly as possible, “ ‘recreate the conditions and relationships that would have been had there been no’ ” unlawful discrimination.” International Bhd. of Teamsters v. United States, 431 U.S. 324, 372, 97 S.Ct. 1843, [1176]*11761873, 52 L.Ed.2d 396 (1977) (quoting Franks v. Bowman Transp. Co., 424 U.S. 747, 769, 96 S.Ct. 1251, 1266, 47 L.Ed.2d 444 (1976) (in turn quoting Local 60, United Bhd. of Carpenters and Joiners v. NLRB, 365 U.S. 651, 657, 81 S.Ct. 875, 879, 6 L.Ed.2d 1 (1961) (Harlan, J., concurring))). It also follows from the “make whole” purpose that “such remedy as is given should not constitute a windfall at the expense of the employer, its union, or its white employees.” Ingram v. Madison Square Garden Center, Inc., 709 F.2d 807, 812 (2d Cir.), cert. denied, 464 U.S. 937, 104 S.Ct. 346, 78 L.Ed.2d 313 (1983).
Further, once a pattern and practice of unlawful discrimination has been proven and a claimant has established his individual entitlement to backpay, any “ ‘uncertainties in determining what an employee would have earned but for the discrimination, should be resolved against the discriminating [party].’ ” Rios II, 542 F.2d at 587 (quoting Hairston v. McLean Trucking Co., 520 F.2d 226, 233 (4th Cir.1975) (in turn quoting Johnson v. Goodyear Tire & Rubber Co., 491 F.2d 1364, 1380 n. 53 (5th Cir.1974))). For reasons hereinafter stated, we conclude that the calculations of back-pay made by the Administrator Designee and approved by the district court contravened this principle.
1. The One-for-One Method.
The original backpay eligibility order established that each claimant had the burden to prove, inter alia, that “[h]e was discriminatorily denied admission to the A Branch.” Rios I, 400 F.Supp. at 993. The order further provided that “[discrimination as to a claimant for the purposes of backpay will commence on the date on which the next applicant for membership in the A Branch who does not qualify as a member of the plaintiff class was admitted to the A Branch.” Id. This provision, which was not disturbed on appeal in Rios II although attacked in the appellate briefs of the class plaintiffs, is an extension of the general rule applying to proof of discrimination that claimant has the burden to prove that “after his rejection, the position remained open and the employer continued to seek applicants from persons of complainant’s qualifications.” McDonnell Douglas Corp. v. Green, 411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 36 L.Ed.2d 668 (1973).
On remand, the Administrator Designee decided not to commence the backpay period with just the next non-class admission, but instead matched each claimant with a specific non-class applicant, whether or not that non-class member was the next applicant admitted after the claimant was rejected. In other words, where more than one class member was denied admission prior to a single non-class admission, that admission would “trigger” the initiation of back-pay for only one of the immediately preceding discriminatee class members; the initiation of backpay for any other class member would have to await a further triggering admission of a non-class member.
The Administrator Designee, however, did not consistently utilize this approach. In the Decision of Administrator Designee dated May 14, 1985, he stated:
There are, however a few instances where applying a strict “one for one” formula leaves a back-pay claimant in a position of losing many months of potential back-pay until a point is reached where that claimant can be matched with a qualified non-minority admittee. In some cases the result is more arbitrary than equitable. When this has occurred, specially where there has been a number of non-minorities admitted on or about the same date, I have utilized the same admission date for all class members even if there where [sic] fewer non-minority admittees then [sic] back-pay claimants. I believe that this effectuates the language and intent of the Back-Pay Order and is a reasonable accomadation [sic] between the positions of the parties. It appears as important to me to achieve a fair and equitable result as to mechanically apply the “one for one” principle. It is for this reason that I have deviated from the strict “one for one” in the case of several claimants who fell into the March 6, 1972 admission date. I believe [1177]*1177this result is amply supported by the record.
Id. at 7.
The foregoing decision established eligibility dates for thirty-three claimants. Of that number eleven were determined to have an eligibility of March 6, 1972, as to an unspecified “several” of which the Administrator Designee deviated from the “one-for-one” rule in establishing an eligibility date. In addition, he departed from that rule in establishing eligibility dates for three “named” plaintiffs, George Rios, Eugene Jenkins and Eric Lewis. Id. at 7-8. Finally, there were further unspecified deviations from the “one-for-one” rule in the final revisions to the eligibility dates made, in response to further factual presentations by the Union, in the Final Report of Administrator Designee dated June 30, 1986 at 2-7.
The prior consideration of this issue in Rios I and Rios II, which resulted in triggering backpay on “the date on which the next [non-class] applicant for membership in the A branch ... was admitted to the A branch,” Rios I, 400 F.Supp. at 993, did not address the complication which we must now consider, and therefore established no “law of the case” one way or the other. We are now required “to balance the equities of each employee’s situation in allocating the limited number of vacancies that were discriminatorily refused to class members.” International Bhd. of Teamsters v. United States, 431 U.S. 324, 372, 97 S.Ct. 1843, 1873, 52 L.Ed.2d 396 (1977). In doing so, we should “ensure that the number of minority [applicants] to be paid back-pay dating back to a given date does not exceed the number of non minority [applicants] hired on that date.” Association Against Discrimination in Employment, Inc. v. City of Bridgeport, 647 F.2d 256, 288 (2d Cir.1981) (emphasis added).6
Applying these criteria, we cannot conclude that the basic approach taken by the Administrator Designee was irrational or inappropriate. On the other hand, we are certainly given pause by his departure from the “one-for-one” rule with respect to a substantial (but unspecified) number of determinations in order to achieve a result that was “equitable” rather than “arbitrary.” See Decision of Administrator Des-ignee dated May 14, 1985 at 7, quoted supra at 1176. Ultimately, the lack of an adequately articulated rationale for the Administrator Designee’s rulings on this issue precludes meaningful review here. Cf. Ballard v. Rockville Centre Hous. Auth., 605 F.2d 1283, 1289-90 (2d Cir.1979) (findings below inadequate for appellate review).
Especially since this case must be remanded for other reasons, we direct that upon remand a principled basis be articulated and utilized in applying the “one-for-one” rule to, or varying therefrom in, the determination of eligibility dates for back-pay. It will still be the general rule that “[discrimination as to a claimant for purposes of back pay will commence on the date on which the next [non-class] applicant for membership in the A Branch ... was admitted to the A Branch,” Rios I, 400 F.Supp. at 993, but any uncertainties concerning the application of that rule are to be resolved against the Union and in favor of the class of discriminatees. See Rios II, 542 F.2d at 587; Cohen v. West Haven Bd. of Police Comm’rs, 638 F.2d 496, 502 (2d Cir.1980).
2. Inclusion of Zero Income Years in Average Wage Calculation.
The original 1975 backpay order specified that “[m]onetary damages will be computed on the basis of the average monthly wage paid to members who were admitted to the A Branch on or after October 15, [1967].” Rios I, 400 F.Supp. at 993, as modified by Rios II, 542 F.2d at 590-91. In order to compute the average monthly [1178]*1178wage, the Administrator Designee utilized the wages during the pertinent periods of a non-random group of persons admitted to the A Branch, i.e., the twenty-seven non-class applicants who were used to trigger the backpay starting dates in the “one-for-one” match discussed immediately above. The Administrator Designee computed the total earnings from steamfitting by these twenty-seven non-minority Branch A members during the entire backpay period and arrived at an average yearly wage. This calculation included four union members who had no income from steamfitting during the period. Twenty-five zero-income steamfitting years from other members of the sample group were also included. In all, forty-eight zero-income years were thus included in the average wage calculation.
The Administrator Designee made a “weighting” adjustment, however, to compensate for the four “triggering” members who had no steamfitting income at all throughout the relevant period. As he described the process:
Because of the significant effect of no earnings for the entire period by four (4) individuals I further calculated the average between the high and low average. A pure average [of the earnings of all twenty-seven triggering persons] yielded $6,846.39 [per year], an average eliminating all persons with no earnings yielded $8,037.07. The average of the high and low yielded $7,441.73 which I find to be a fair and proper average wage figure given the necessity of “weighting” persons with no earnings.
Final Report of Administrator Designee dated June 30, 1986 at i n. 1.
For all we know, this approach may have resulted in rough justice under the circumstances. No effort apparently was made, however, to determine whether the earnings of the twenty-seven triggering persons were a representative sample of members who were admitted to the A Branch on or after October 15, 1967. Further, while the Administrator Designee justified the inclusion of zero-income years as being a reflection of the unavailability of steamfitting work during the backpay period, he made no findings concerning the extent to which the zero-income years were the result of voluntary decisions by the “triggering persons” not to be employed at steamfitting during the period, or the extent to which the zero-income years in the non-random sample corresponded to the unavailability of steamfitting work during the period.
We therefore remand for reconsideration of the average yearly wage. The district court or Administrator Designee may choose to abandon the “triggering persons” sample altogether and select some random sample from which to calculate the average wage. Alternatively, the burden may be imposed upon the Union to support the assumption that the zero-income years in the sample employed by the Administrator Designee actually reflect the degree of involuntary unemployment during the backpay period. Some other approach may be taken in light of the available data. In any event, a rational basis must be provided for the “average monthly wage” determination.
Conclusion
The judgment of the district court is affirmed as to the denial of disqualification, and reversed and remanded for recalculation of the backpay awards, for determination of any unresolved issues concerning the backpay claims of Isidro Diaz and the six claimants improperly dismissed on the ground of immigration status, and for any further proceedings not inconsistent with this opinion. With respect to the calculation of backpay awards, we recognize that both the length of time which this litigation has been pending and the greater familiarity of the district court and the Administrator Designee with the particulars of the backpay claims will call for considerable deference in any future appellate review of the backpay determinations made upon remand. We hope there will be none; this litigation is already assuming a Dickensian aspect. We require, however, that a reasoned, systematic approach be [1179]*1179taken which can be subjected to meaningful appellate review.