Full opinion text
Opinion for the Court filed PER CURIAM. Concurring opinion filed by Circuit Judge SILBERMAN. Opinion concurring and dissenting in part filed by Circuit Judge SENTELLE. Opinion concurring and dissenting in part filed by Circuit Judge GARLAND. PER CURIAM: This case presents what we hope to be the penultimate chapter in a 23-year-old litigation involving racial discrimination by iron workers’ unions against a class of African-American construction workers. We upheld the unions’ liability a decade ago, and all of the remaining issues in the case concern the remedy due, if any, to those claimants who have thus far not settled with the unions. Although we are reluctant to prolong this unduly protracted litigation any longer, the district court’s failure adequately to resolve the questions presented on appeal compels us to remand many of these challenges to the district court for further factual findings and supporting explanation. In those instances in which the district court’s findings and explanations make it possible for us to resolve an issue definitively, we affirm or reverse the district court’s award. I. Background The background of this case is set out in full in our prior opinion, see Berger v. Iron Workers Reinforced Rodmen Local 201, 843 F.2d 1395, 1405-07 (D.C.Cir.1988) {Berger I), and we see little need to' repeat the details here. Suffice it to say that in 1975 a class of African-American rodmen — construction workers who handle and position steel rods for reinforcing concrete and other building materials — sued Local 201 of the Iron Workers Reinforced Rodmen and the International Association of Bridge, Structural and Ornamental Iron Workers for discriminatorily denying them union membership in violation of Title VII, 42 U.S.C. § 2000e et seq., and 42 U.S.C. § 1981. Rodmen obtained work for construction employers in the Washington, D.C. area through referrals distributed at Local 201’s hiring hall, and although referrals were available to non-union “permit men,” priority, along with the other benefits of union membership, went to the union members. See Berger I, 843 F.2d at 1405. The class pursued and succeeded on several theories of liability at trial, but we essentially upheld the district court’s liability determination on one theory alone. We held that the unions were liable for imposing training and apprenticeship prerequisites to taking the journeyman’s examination — the entrance examination for union membership. The class demonstrated with statistical evidence, to which the unions offered no rebuttal, that the educational prerequisites to taking the entrance examination worked to discriminate against “experienced” African-American rod-men (those rodmen with at least two-years’ experience which, according to the class’ expert, approximated 2,150 rodmen hours). See Berger I, 843 F.2d at 1414-15. We reversed the district court’s finding that the unions’ various entrance prerequisites from 1967 to the filing of the suit in 1975 constituted a single, continuing pattern of intentional discrimination. Central to this holding was our conclusion that the so-called “Open Period” from February to June 1971, during which all experienced rodmen were permitted to take the union entrance examination (though a more difficult one), marked a sharp break in the unions’ admissions practices. See id. at 1422-23. We thus limited the liability period to the time between June 1971, the close of the “Open Period” and the beginning of the Training and Apprenticeship prerequisites, and the filing of the suit on October 21,1975. See id. at 1422. Since the trial bifurcated liability and damages, the district court on February 15, 1989, referred the case to a Special Master, Magistrate Patrick J. Attridge, and directed him in an “Order of Reference” to conduct proceedings to calculate the amount of back pay to be awarded to class members and to determine whether class members were entitled to compensatory and punitive damages and any other relief that might be appropriate. The Order stated that the class consisted of the eight named plaintiffs, and any other claimant who could make a grima facie case that he was a member of the class — subject to the unions’ rebuttal by clear and convincing evidence. It specified the applicable back pay period as follows: Each individual class member may present a claim for back pay for the period commencing on the date when he first attempted to become, or was deterred or discouraged from becoming, a member of Local 201 and/or the International, and concluding on the date when he first was allowed to take the journeyman examination, passage of which is required for membership in Local 201 and the International, or was given a bona fide opportunity to take the examination. However, in no event shall the back pay period of any class member commence earlier than October 21, 1972, which is three years prior to the filing of the complaint in this case. The Order also set forth procedures governing the burdens of proof for establishing the amount of back pay and other relief (grima facie case by claimants subject to the unions’ rebuttal by clear and convincing evidence), notice to the class, a schedule for submitting claims, the formula for determining back pay awards, creation of a Relief Account in which the unions would deposit awards for each successful claimant, adjustment of pension records, legal representation of claimants at individual hearings, and status reports to be filed by the Special Master every six months. The parties conducted discovery in 1989, and in 1990 the Special Master held individual trials for the 64 remaining claimants and heard the parties’ respective expert witnesses. By March of 1991, 47 claimants remained, and the parties submitted proposed findings to the Special Master. Nearly two years later, the class filed a request for a ruling from the district court. The district court did not respond to this request, nor to a renewed request by the class filed in April 1993. In July 1993, the class sought a writ of mandamus from this court compelling the Special Master to rule, which we denied, expressing confidence (unfortunately unjustified) that the district court would promptly issue a final order resolving all matters covered by the Order of Reference. When the Special Master still had not filed his report by March of 1994 (and thus the district court obviously had not issued a final order either), the class filed a second petition for a writ of mandamus with this court. Finally, on April 14, 1994, three years after the parties submitted proposed findings, the Special Master issued his report resolving the claims of the 35 remaining claimants. In making the class membership determinations, the Special Master defined “experience” ón a case-by-case basis, rejecting the unions’ contention that 2,150 hours of Local 201 rodmen experience was a prerequisite to class membership, as well as their position that a claimant’s failure to pass the journeyman’s examination is a per se bar to class membership. The Special Master concluded that 11 claimants failed to prove membership in the class, and he awarded the remaining 24 claimants back pay, based on a formula multiplying the hourly rodmen wage rate for each year times the difference between the number of hours the claimant actually worked each year as a rodman and the number of hours he would have worked as a union member (less any non-rodwork interim earnings pursuant to 42 U.S.C. § 2000e-5(g)). The Special Master derived the number representing the average hours a claimant “would have worked” — the so-called “benchmark proxy” — from the pension records of Local 201, and rejected alternative benchmark figures proposed by experts for both the class and the unions. He also awarded prejudgment interest at a rate of 6% compounded annually, awarded 22 claimants compensatory damages for mental or emotional distress, and denied all of the requests for punitive damages. The parties filed objections to the report, and before the district court could rule, five of the successful claimants and two of the dismissed claimants settled. We denied the class’ second petition for mandamus after the Special Master issued his report in April 1994, and assumed in that order that the district court would act promptly on the report “in light of the long delays in this case.” The district court issued its opinion and order on January 26, 1995. The court adopted the Special Master’s report with respect to the class-wide issues and the awards to the 19 remaining successful claimants, making small corrections in the amount of the award where appropriate, but specifically noting that its order would not constitute a final, appealable order until the court’s subsequent order addressing the excluded claimants’ claims issued. That March 16, 1995 order upheld the Special Master’s exclusion of the nine remaining claimants from the class, and amended the January 26 order by finding clear error, in light of the parties’ 1990 stipulation to the contrary, in the Special Master’s failure to include overtime in the back pay calculations of the successful claimants. The next two years of this litigation involved premature appeals by the unions and six of the excluded claimants; although the district court indicated in its January 1995 order that the order would become final upon issuance of the March 1995 order, the court ordered the plaintiffs to submit proposed judgment orders and did not certify any of the claims for appeal pursuant to Federal Rule of Civil Procedure 54(b). Accordingly, this court dismissed the unions’ appeal pursuant to the class’ motion, and dismissed the remainder of the excluded claimants’ appeals on its own motion. The district court entered an order of judgment on January 3, 1997, from which the unions, the class on behalf of the 19 successful claimants, and three excluded claimants, appealed to this court. The unions challenge a number of legal conclusions and factual findings, both class-wide and with respect to individual claimants, in the district court’s opinion (and the Special Master’s report that the opinion adopted), including: the method for calculating the “benchmark proxy” from which individual awards were derived; the standard of review used to determine class membership; the conclusion that several individuals were properly included in the class; the calculation of several class members’ awards; the conclusion that some class members did not fail to mitigate their damages; and the award of compensatory damages and prejudgment interest. The class members obviously defend all of those decisions. In addition, the class argues that the district court erroneously calculated several back pay awards in the unions’ favor; incorrectly concluded that four claimants abandoned their efforts to join the union and forfeited their right to back pay subsequent to their abandonment; erred by failing to award punitive damages; and should have awarded even more prejudgment interest. Three individual class members also appeal the district court’s decision to exclude them from the class. II. The Benchmark Determination The unions advance numerous arguments against the benchmarks chosen by the Special Master, and the consequent awards of back pay to the members of the plaintiff class. We are convinced that the Special Master, and thus the district court, did commit clear error in two respects. The Special Master failed to include “zero-hour” workers (workers who for a number of years worked zero hours as union rodmen) in the determination of the average number of hours worked by a union rodman in the relevant time period, and he failed entirely to address the “fixed-pie” issue raised by the unions’ expert, Dr. Farrell Bloch. First, the zero-hour workers reflect the inherent risk in the work, and failure to adequately account for their absence is clear error. If the risk of injury is calculated back into the equation when individual back pay awards are determined, it needs to be done explicitly, and the specific experiences of individual rodmen can be measured against the baseline risk of injury to see if they surpass it. Individual claimants whose injury-time exceeds the statistical average should then be adjusted downward to reflect the difference between their actual experience and the average. Second, as we explain below, the fixed-pie analysis permits the court to determine what would have happened in the absence of the discrimination, International Bhd. of Teamsters v. United States, 431 U.S. 324, 372, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977), and the burden for showing what those conditions would have been falls on the plaintiff, who is responsible for proving damages. A. The Special Master’s Methodology We review the findings of fact by the district court, including the findings of the Special Master to the extent that they were adopted by the district court, under a clearly erroneous standard. See Cuddy v. Carmen, 762 F.2d 119, 123-24 (D.C.Cir.), cert. denied, 474 U.S. 1034, 106 S.Ct. 597, 88 L.Ed.2d 576 (1985); 28 U.S.C. § 636(b)(2); Fed. R. Civ. P. 53(e)(2). “The findings of a master, to the extent that the court adopts them, shall be considered as the findings of the court.” Fed. R. Civ. P. 52(a). The basic standard for devising back pay awards in a Title VII case is undisputed by the parties. A court 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. at 372, 97 S.Ct. 1843 (quoting Franks v. Bowman Transp. Co., 424 U.S. 747, 769, 96 S.Ct. 1251, 47 L.Ed.2d 444 (1976) (internal quotations omitted)). The Order of Reference directed the Special Master to determine how many additional hours class members would have worked in the absence of discrimination, and award back pay by multiplying the expected hours worked by the average wage rate in effect during the year that the class member would have worked. The back pay period began for each individual class member when he was denied access to the examination or deterred from applying for the examination for union membership by the educational requirement, and ended when he either took or had a bona fide opportunity to take the entrance examination. No back pay award could be granted for periods before October 21, 1972, three years before the suit was filed, or after April 10, 1986, when the district court issued its remedial order granting comprehensive injunctive relief. The amount of back pay awarded to any given member of the plaintiff class is the product of the average wage rate in effect during the time during which the union discriminated against him multiplied by the number of hours worked by the average rodman during that time period. Each side put on expert testimony and presented documentary evidence sponsoring a method for computing the number of hours worked by the average rodman for purposes of determining the proper amount of a back pay award. The Special Master noted that one of the primary difficulties with the calculation was the fact that the union did not employ people, but referred them to employers, who individually determined the terms and length of employment. The Special Master rejected the methods proposed by the expert witnesses in this case, Marc Ben-dick, Jr. for the claimants and Daniel Quinn Mills and Dr. Bloch for the unions, and created a method of his own based on the documentary evidence in the record. The Special Master determined that the best proxy for hours worked in the absence of discrimination was the hours actually worked by union members during the years in question. He therefore examined the pension records of Local 201 and calculated how many hours fully employed rodmen worked on average. The Special Master noted that the “pension records automatically take into account the unemployment levels of District of Columbia union rodmen and the average number of days lost due to injury, sickness and attrition.” Report of Special Master, J.A. 341. He explained his choice as follows: From the Local 201 pension records, a representative group of workers is readily identifiable. The representative group are those workers who received steady referrals during the relevant time period, as evidenced by a consistent number of hours worked per year. Workers with consistent referrals worked remarkably similar total numbers of hours for any given year. Excluded from this group are non-representative workers, i.e., those who for several years during the relevant time period worked no hours at all. By taking an average of the number of hours worked by those engaged in full time employment and checking that figure for ball-park accuracy against certain indicators of local iron worker productivity during the relevant time periods, the undersigned arrived at the representative or “proxy” number of hours per year that an iron worker could be expected to work. Based upon these indicia, and taking into account the testimony regarding the relatively recent concept of “double breasting” [in which contractors worked both union and non-union crews], and having also considered all the testimony and exhibits received in evidence, the Special Master finds that the annual hours reasonably expected to be worked by a member of Local 201 is as follows: Year Hours Worked 1972 1711 1973 1557 1974 1627 1975 1447 1976 1419 1977 1253 1978 1179 1979 1230 1980 1210 1981 1263 1982 1168 1983 1126 1984 953 1985 1397 1986 1549 See Report of the Special Master at 50-51, J.A. 342-43. Based on his calculations, he arrived at an average of 1,339 hours per year- B. Alleged Errors in the Master’s Method The unions argue that the Special Master committed clear error in the method he adopted for devising a benchmark for purposes of awarding back pay. Specifically, they argue that he did not sufficiently explain his choice, or show why he failed to adopt the methodology of their expert, Dr. Bloch, which has been endorsed for Title VII remedies in the past. Like the Special Master, Dr. Bloch used a cohort analysis based on pension records, but he used a smaller category of workers, those who were admitted to the union during the period when the union discriminated against the plaintiff class. Dr. Bloch’s calculations also differed from the Special Master’s in that they included the zero-hour workers, on the reasoning that a longitudinal analysis of the cohort should incorporate the risk of disabling injury. Finally, Dr. Bloch limited the number of hours that could be awarded with a “fixed-pie” analysis. He adjusted the benchmark by adding the total number of hours worked by all rodmen, including union members, traveling members from another local, and permit men (non-union workers who were referred to jobs from the union hall). Members of the plaintiff class, he assumed, would have become union members if the discrimination had not occurred, and would have replaced non-union members on jobs that were referred by the union. In some years, however, there were limited referrals to nonunion members, which Dr. Bloch assumed was due to limited employment in the industry generally. In such years, since only a limited number of hours were available to non-union workers, class members could not possibly have replaced only nonunion workers, but would also have displaced other union members. Reflecting this, the total hours available for such years was placed in a “fixed-pie,” and the hours were divided by the total number of union workers plus the number of proven members of the class. The assumption is that the hours would have been divided equally between all members. See Declaration of Farrell Bloch Ph.D., at 9-11, J.A. 1383-85. The unions argue that the reason the Special Master gave for rejecting Dr. Bloch’s analysis — that the cohort group for 1973, consisting of 38 individuals, was a statistically insignificant sample — was wrong as a matter of fact and as a matter of law. The unions point out that Dr. Bloch’s proxy group included the aggregate of all 135 journeymen admitted between 1971 and 1975, and that the size of the group used by Dr. Bloch exceeds the sample size of union and nonunion workers used by the class to establish liability in the first instance. See Berger, 843 F.2d at 1415. The unions also argue that the Special Master misunderstood Segar v. Smith, 738 F.2d 1249 (D.C.Cir.1984), which he cited for the proposition that the sample was too small. They distinguish Segar by noting that it applied to a liability decision, not a damages decision. Further, the Segar panel’s analysis took issue with breaking cohorts into smaller and smaller subgroups, until they did become insignificant. The unions claim that Dr. Bloch’s much larger cohort does not resemble those found objectionable in Segar. The unions cite a line of eases beginning with Pettway v. American Cast Iron Pipe Co., 494 F.2d 211, 262 (5th Cir.1974), for the proposition that matching the plaintiff class with a comparable group is a favored method of determining what would have happened absent discrimination. See also Green v. United States Steel Corp., 640 F.Supp. 1521, 1526-29 (E.D.Pa.1986) (calculating damages based on comparable class, and adjusting cohort class for attrition rate), modified on other grounds, Green v. USX Corp., 843 F.2d 1511 (3d Cir.1988), vacated USX Corp. v. Green, 490 U.S. 1103, 109 S.Ct. 3151, 104 L.Ed.2d 1015 (1989); Stewart v. General Motors Corp., 542 F.2d 445, 453-54 (7th Cir.1976), cert. denied, 433 U.S. 919, 97 S.Ct. 2995, 53 L.Ed.2d 1105 (1977) (same). They also cite a series of eases that have adopted the comparison group methodology in determining Title VII remedies in the construction industry. See Hameed v. International Ass’n of Bridge, Structural and Ornamental Iron Workers, Local Union No. 396, 637 F.2d 506, 520-21 (8th Cir.1980); Rios v. Enterprise Ass’n Steamfitters Local 638 of U.A., 651 F.Supp. 109, 111-12 (S.D.N.Y.1986), modified and remanded, 860 F,2d 1168, 1177 (2d Cir.1988). The class counters that we should adopt the Special Master’s analysis, and argues that if he erred, he did so on the low side,, because the total he reached, 1,339 hours, was well below the 1,400-hour estimate published by the Institute of Ironworking Industry. The Special Master as trier of fact was free to accept or reject expert testimony, and was free to draw his own conclusion. See United States v. Jackson, 425 F.2d 574, 577 (D.C.Cir.1970); Powers v. Bayliner Marine Corp., 83 F.3d 789, 797-98 (6th Cir.1996); Michel v. Total Transp., Inc., 957 F.2d 186, 192 (5th Cir.1992); United States v. 0.161 Acres of Land, 837 F.2d 1036, 1040-41 (11th Cir.1988). The Special Master rejected Bloch’s figures because his cohort group was too small, and because the Special Master did not credit the fixed-pie theory. The Special Master found that the union could have found sufficient work for its members, so the pie was not fixed. The class suggests that this court can recreate the Special Master’s results from the record, and should affirm because he cannot be found to have committed clear error. While we agree that the use of a cohort methodology substantially similar to that used by Dr. Bloch has met with approval in the cases cited by the unions, those cases do not require us to hold that the methodology adopted by the Special Master for defining the cohort to include all union members was clear error. The eases relied upon by the unions establish neither a specific minimum size of the cohort nor a particular degree of similitude needed to meet the mandates of Title VII. We therefore hold that rejecting the specific cohort methodology urged by Dr. Bloch was not clear error. C. Zero-Hour Workers Nonetheless, the Special Master is required to establish, as nearly as possible, what would have occurred in the absence of discrimination. International Bhd. of Teamsters, 431 U.S. at 372, 97 S.Ct. 1843. After reading the full report submitted by Dr. Bloch, it becomes clear why he included the zero-hour rodmen in his calculation. “The mean based on all journeymen including those working zero hours in a given year is appropriate to use in the back pay calculations because it incorporates individual attrition from Local 201 resulting from such factors as temporary illness or injury, aversion to rodmen [sic] work, a geographic move away from Local 201’s jurisdiction, or the decision to become a contractor.” Report of Dr. Farrell Bloch at 6-7. Dr. Bloch did not include zero-hour rodmen who had died, retired, were incarcerated or permanently disabled, all conditions which would have limited the unions’ liability. Id. at 7. The more cursory explanation by the Special Master does not make it clear why he removed the zero-hour workers from the calculation, other than his feeling that they are not representative. See Report of Special Master at 50. By removing them from the calculus, the Special Master removes from the equation the risk of disabling injury, or of finding another more desirable job, or whatever other reason a person might not work full time. It is a false assumption that all of the members of the plaintiff class would have remained full time in the industry, given the dangers and disincentives inherent in the work. The very real risk that they would have been unable or unwilling to continue working has been improperly removed. The amount an individual would work at full employment should be multiplied by the likelihood that they would remain fully employed. By leaving the zero-hour workers in, Dr. Bloch removed the need for coming up with a figure to approximate that risk. The historic value of that risk is represented by the zero-hour rodmen. Discounting of this type is a common practice when attempting to fix speculative damages. The failure to account for the risks inherent in the industry does amount to clear error. The Special Master did limit awards where he found that claimants had been disabled for lengthy periods. However, as we explain in Part IV, because there is no quantification of the amount of lost time built into the hours calculation, it is impossible to determine when a claimant is injured for a period that exceeds the anticipated lost time, and the Special Master’s inconsistent treatment of claimants when determining individual back pay awards shows the need for further analysis on this factual issue. A specific number can be calculated that quantifies the risk of injury, and then individuals’ actual experience should be compared against that figure. We are not deciding today that each claimant’s award must be reduced for excessive injury-time. It is only because the district court appeared to operate on that assumption, yet applied that assumption without sufficient facts and in an inconsistent manner, that we are compelled to remand these questions. In this regard, we think it is necessary to note the interrelationship between the inclusion or exclusion of the “zero-hour” workers in the benchmark proxy and the injury-time calculation for each claimant. Both of course are means of discounting back pay awards to reflect unavailability for work during the liability period. The district court might conclude, if he includes the “zero-hour” workers in the benchmark proxy to reflect the overall risk of injury, that individual re-adjustments for individual claimants with “excessive” injury-time would not be necessary. In other words, treating all claimants like hypothetically average claimants might obviate the need to analyze unavailability for work due to injury for individual claimants. We do not in any way endorse that outcome, and indeed think the analytical differences between the overall discounting of the proxy caused by inclusion of the “zero-hour” workers and the specific discounting of an individual’s award caused by excessive injury-time reductions easily could support doing both. We wish only to emphasize the interrelationship between these two inquiries, and to direct the district court to consider that relationship when it resolves these issues on remand. D. “Fixed-Pie” Analysis [6] We now turn to the Special Master’s fixed-pie analysis, and the flawed assumption that underlies it. The Special Master assumed that the union could have found additional work for its members if it wanted to, had the numbers been increased by admitting the plaintiff class. See Report of the Special Master at 47-48. There is no evidence in the record to suggest that there was additional work in the D.C. area for Local 201 rodmen. In fact, the evidence on the issue of double-breasting suggests that the portion of rodwork available to unions generally was declining, as evidenced by the limited work available for permit men. There is no evidentiary basis for the assumption made by the Special Master. Common sense and experience suggest that a union will attempt to bring as many projects as possible under union control, and that it will not slow its attempts when the additional work will be allocated to non-members, ie., permit men, much less when the number of hours available to union members is declining. Nonetheless, the Special Master cited such a determination on the part of Dr. Bloch as speculative. The Special Master impermissibly switched the burden of proof on this issue. If the class wished the court to award damages on the basis of hours not referred through the hall, it follows that they would have the burden of at least making a prima facie showing that additional hours were available to Local 201. Local 201 cannot be faulted for not allocating work that was never brought under its control. The Special Master placed the burden on the unions to prove that those hours were not available: “There was no evidence presented that the union would not have solicited other employment opportunities for its members had it been faced with an influx of members, or taken other actions to expand its piece of the rod work ‘pie.’ ” Report of the Special Master at 47. The unions made a prima facie showing that the hours were not available based on the declining hours referred out of the hall and the evidence they introduced of the declining market share available to the union due to double-breasting. As the unions noted in their brief, the record showed that “[tjhe percentage of union jobs in the metropolitan Washington D.C. area was 77% in calendar years 1973 and 1974; peaked at 89% in 1975; and then dropped precipitously to 66% in 1976 and 47% in 1977, and then gradually declined to 22% in 1984 before rising to 33% in 1986.” Def. Br. at 16. We remand to the district court to consider the effect of the fixed-pie on the number of hours available to be allocated to the plaintiff class, and to apply the correct burden of proof. The district court should bear in mind the goal of recreáting as nearly as possible the situation that would have occurred in the absence of discrimination. International Bhd. of Teamsters, 431 U.S. at 372, 97 S.Ct. 1843. That means that it should make findings as to the number of members of the original plaintiff class who actually would have been awarded union membership, and for any given year calculate how many had actually gained membership, and how many remained to be added into the fixed-pie calculation. It may well be that the difference by the end of the period is insignificant. Nonetheless, the failure to consider the issue, based as it was on the flawed and factually unsupported assumption that additional work was necessarily available to the union, leaves us with no option but to remand. Judge Garland’s dissent takes issue with our holding that the Special Master’s failure to consider the “fixed-pie” when calculating damages, and the district court’s subsequent adoption of his report, amounts to clear error. First, he argues that the unions did not argue that the district court erred in failing to consider this issue. The unions argued that the district court erred in failing to adopt Dr. Bloch’s methodology. Among the points they enumerate in favor of Dr. Bloch’s analysis is the following: “Once the actual number of claimants in each year was known, Dr. Bloch would adjust each annual average so that the recalculated claimant hours did not produce a total hours figure for all workers that exceeded the actual total hours worked through Local 201, as derived from the Local 201 pension records.” Def. Br at 28. While it does not use the specific term “fixed pie,” as Judge Garland notes, the argument raised by the unions’ brief is the argument described by that term. The fact that the brief argued that all of the methodology used by their expert be adopted does not mean that we may examine either all or none of the points raised. As we note in our opinion, it is the Special Master’s outright rejection of the issue, based on the unsupported assumption that the union could have found more jobs if it had so chosen, that we find to be clearly erroneous. Judge Garland also misconstrues our reasoning with regard to the assumption that the union could bring more rod work under its control if it so chose. The fact that some 1,649 job requests went unfilled over a 10-year period does not mean that the union had enough work for the 173 putative class members to be fully employed over that same 10-year period. Fluctuations on a given day that would result in a specific job referral being listed as unfilled are not the same as a finding that hundreds of thousands of hours were available. As we note, the evidence on double-breasting and the steadily declining share of work available to permit men, annual drop-offs of tens of thousands of hours, shows just the opposite. Moreover, the work available, according even to the Special Master’s calculations, showed significant disparities over the period. For instance, in 1972, the average rodman would have worked 1,711 hours, in 1973, 1567 hours, and in 1974, 1627 hours. By 1977, that number had dropped to 1,253 hours, and stayed below that level until 1985, bottoming out at 953 hours in 1984. It makes no sense to conclude a fortiori that a union could readily have found full-time work for 173 additional union members when its existing members were working some 400 fewer hours per year than during the full employment period. We agree with Judge Garland that it is the gross hours available for referral, not trends, that are relevant to the validity of the fixed-pie theory. While a more detailed examination of the record, considering such factors as an increasing percentage of class members gaining union membership in the years in question, may once again yield the same conclusion reached below, we cannot affirm, on the record before us, on the basis of the court’s stated reasoning, which we find to be clearly erroneous. III. Class Membership A. Burden of Proof We now turn to the issue of the burden of proof at the remedial phase of a Title VII class action suit. Class action lawsuits brought under Title VII are typically bifurcated into two phases, a liability phase and a damages phase, as was done in this case. The first phase establishes whether the employer is liable to the class because of a pattern or practice of discrimination. See International Bhd. of Teamsters, 431 U.S. at 359, 97 S.Ct. 1843. The second phase addresses questions of class membership and the degree of damage suffered by individual class members. The district court, in its February 1989 Order of Reference, required each claimant to make a 'prima facie showing of class membership, which could in turn be rebutted by the defendants by “clear and convincing evidence.” This instruction was in keeping with D.C. Circuit precedent, requiring the defendant to disprove class membership by clear and convincing evidence at the second phase of a Title VII class-action suit. See Trout v. Lehman, 702 F.2d 1094, 1107 (D.C.Cir.1983), rev’d on other grounds, Lehman v. Trout, 465 U.S. 1056, 104 S.Ct. 1404, 79 L.Ed.2d 732 (1984); McKenzie v. Sawyer, 684 F.2d 62, 75-78 (D.C.Cir.1982). The unions argue that a supervening Supreme Court case, Price Waterhouse v. Hopkins, 490 U.S. 228, 109 S.Ct. 1775, 104 L.Ed.2d 268 (1989), decided weeks after the Order of Reference, established that the proper standard of proof in Title VII cases is a preponderance, for both plaintiffs and defendants. After careful consideration, we agree. We review this question of law de novo. See United States of America v. Perkins, 161 F.3d 66, 69 (D.C.Cir.1998). The unions acknowledge that Hopkins involved a mixed-motives case finding discrimination against an individual, not a disparate-impact class action. However, they note that “in both situations it remains for a particular individual to prove the defendant’s liability to him.... Each claimant is relieved of the burden of proving that defendants discriminated against the class, not that he is part of the class.” Def. Br. at 33. This is because in the remedial stage of a class action, “as to the individual members of the class, the liability phase of the litigation is not complete.” Hopkins, 490 U.S. at 266, 109 S.Ct. 1775 (O’Connor, J., concurring). The class counters that the district court applied the correct burden of proof for three reasons. First, in the damages phase of a class action suit, the defendant is already a proven discriminator, therefore, they argue, increasing the defendant’s burden of proof as to class membership is appropriate. Second, the class argues that the Hopkins case is distinguishable because it wás the liability phase of a mixed-motives ease, not the damages phase of a class action suit. Finally, they argue that the unions made no attempt to show a business justification for their testing requirement, and the court is not weighing liability. Therefore they contend, the court should retain the clear and convincing standard established in McKenzie. In McKenzie, we read the Supreme Court’s precedent as requiring that once the employer was a proven discriminator, “ ‘all doubts are to be resolved against the proven discriminator rather than the innocent employee.’ ” McKenzie, 684 F.2d at 77 (quoting International Bhd. of Teamsters, 431 U.S. at 372, 97 S.Ct. 1843). We went on to hold that the finding of liability in the first phase of the trial established the prima facie case against the employer, and that the employer “should be required to rebut the plaintiffs’ individual showings by clear and convincing evidence.” Id. at 77-78. Since our holding, the Supreme Court has revisited the issue of the burden of proof in Title VII lawsuits. In Hopkins, the Court overturned this circuit’s holding that an employer in a Title VII sex discrimination case who had allowed a discriminatory motive to play a motivating part in an employment decision was required to show by clear and convincing evidence that it would have reached the same decision in the absence of the discriminatory motivation. Hopkins, 490 U.S. at 238 n. 2, 109 S.Ct. 1775, reversing Hopkins v. Price Waterhouse, 825 F.2d 458, 470-71 (D.C.Cir.1987). The proposition specifically applicable to this case states that no heightened burden is required in Title VII cases, even where a burden shift has occurred. Conventional rules of civil litigation generally apply in Title VII cases, and one of these rules is that parties to civil litigation need only prove their case by a preponderance of the evidence. Exceptions to this standard are uncommon, and in fact are ordinarily recognized only when the government seeks to take an unusual coercive action — action more dramatic than entering an award of money damages or other conventional relief — against an individual. Only rarely have we required clear and convincing proof where the action defended against seeks only conventional relief, and we find it significant that in such cases it was the defendant rather than the plaintiff who sought the elevated standard of proof — suggesting that this standard ordinarily serves as a shield rather than, as ■Hopkins seeks to use it, as a sword. Hopkins, 490 U.S. at 253, 109 S.Ct. 1775 (plurality opinion) (internal citations omitted). While Justice Brennan was writing for himself and Justices Marshall, Blackmun, and Stevens, Justice White concurred in the judgment “[bjecause the Court of Appeals required Price Waterhouse to prove by clear and convincing evidence that it would have reached the same employment decision in the absence of improper motive, rather than merely requiring proof by a preponderance of the evidence.” Id. at 260, 109 S.Ct. 1775. We think Hopkins mandates that in this case the clear and convincing standard is inappropriate, and the ordinary preponderance of the evidence standard must apply. Hopkins makes it clear that the heightened burden should not apply in Title VII cases where the heightened burden would be used as a sword not a shield. While this case may not be on all fours with Hopkins, as the distinctions noted by the class demonstrate, the basic principle stated by the Court applies. Raising the burden of proof to clear and convincing evidence is not justified in Title VII cases; instead a preponderance applies as to all factual issues, regardless of which party bears the burden, as in other civil actions. The Court relied on the basic principle it articulated — in Title VII cases, the standard burden of proof in civil cases will apply — to decide Hopkins. The distinctions to which the class points therefore make no difference to our determination that the preponderance of the evidence standard, and not a clear and convincing standard, should apply in this case. The burden shift itself is sufficient to meet the Court’s admonition that doubts be resolved in favor of the employee, because the party that bears the burden also bears the risk that he will be unable to carry that burden due to doubts on the part of the factfinder. With these principles firmly in mind, we now go on to consider how that decision affects the facts in this case. B. Disputed Findings The district court’s adoption of an incorrect standard for the unions’ rebuttal burden requires remand of the Special Master’s findings of class membership with respect to two claimants, because we are unable to determine whether the Master would have made the same findings if he had applied the correct burden of proof. In the remaining disputed cases, the validity of the Master’s findings turns not on the quantum of the parties’ evidence, but on issues that can be resolved without reference to the burden of proof. Our disposition of the findings disputed by the parties is as follows: 1. O.C. Brown. The plaintiff class includes those experienced rodmen who attempted to become, or were deterred or discouraged from becoming, members of Local 201 during the liability period-i.e., between June 1971 and October 21, 1975. See Order of Reference, J.A. 216; see also Berger I, 843 F.2d at 1411. Although there was uncontested evidence to support the Special Master’s finding that O.C. Brown was “discouraged and deterred from admission” to Local 201, J.A. 86, the conclusion that this occurred during the liability period depends upon disputed inferences from circumstantial evidence. Because we are unable to determine whether the Master would have reached the same conclusion had he applied the correct burden of proof, we remand Brown’s case for redetermination. 2. Silburn Francis. There was conflicting testimony and other evidence as to whether Silburn Francis sought union membership during, rather than after, the liability period. See J.A. 400-04. Because the Special Master weighed this evidence according to an incorrect standard, we remand for re-determination under the correct burden of proof. 3. John Offer. The unions do not dispute that John Offer sought union membership in June 1972. They contend, however, that this “predat[es] the critical period,” which they define as October 21, 1972 to October 21, 1975. The unions are mistaken as to the start of the liability period. October 21, 1972 starts the period for which the remedy of back pay is available under 42 U.S.C. § 1981. See Order of Reference, J.A 216. However, as Berger I held, membership in the class is established by having sought (or having been deterred from seeking) entry into the union “from the end of the Open Period [June, 1971] until the filing of suit on October 21, 1975"-notwithstanding that back pay may not be awarded for the early part of that period. See 843 F.2d at 1422. See generally Thomas v. Denny's, Inc., 111 F.3d 1506, 1513-14 (10th Cir.1997) (discussing distinction between a liability limitation period, which may effectively be extended by a continuing violation, and "the period within which damages can be recovered," which is fixed by statute). The unions also contend that Offer was ineligible for the Apprenticeship Program for the "lawful reasons" that he could not meet that Program's educational (high school diploma) and age requirements. However, because Berger I established that the Apprenticeship Program itself was an unlawful prerequisite to union membership for experienced rodmen, see 843 F.2d at 1414, 1421, that Program's own prerequisites are irrelevant. Offer's membership in the class is affirmed. 4. Wordia Parks. Wordia Parks appeals from the Special Master's finding that he abandoned efforts to join Local 201 prior to the eligibility period, and that he therefore neither sought nor was discouraged from ~eeking membership during that period. See J.A. 461. The Special Master also found that Parks' evidence was "inconsistent and contradictory," and that he had "repeatedly impeached his own responses to interrogatory questiolis." J.A. 462. The Master's findings regarding Parks" are not clearly- erroneous and therefore are affirmed. - 5. Charles Dean and Eldridge Harmon. To be a member of the class, a claimant must have been an "experienced" rodman. The unions challenge the Special Master's finding that Charles Dean and Eldridge Harmon were sufficiently experienced, on the ground that the Master counted nonunion rodwork toward the number of hours required to be regarded as "experienced." This, the unions contend, is contrary to the "law of the case," because Berger I assertedly established that only union-referred rodwork could be counted as experience. We reject this contention because nothing in Berger I limited the definition of experience to union-referred rod-work. See 843 F.2d at 1414-15, 1421-22. Counting non-union-referred experience, the Special Master accepted the deposition testimony that Charles Dean had the 2,150 hours of experience that all agree is sufficient to establish the necessary experience. See J.A. 990. The Master further noted in his report that "by 1974, Dean had performed rodwork for seven years," J.A. 391, which is far in excess of the two-year figure from which the 2,150-hours number was extrapolated. See Berger I, 843 F.2d at 1414. Because the unions offer no evidence to rebut this prima facie case-no evidence at all that Dean's total hours were less than 2,150-Dean's membership in the class is affirmed. With regard to Eldridge Harmon, the Special Master expressly credited Harmon's testimony that he had worked over 2,150 hours by December 1972. J.A. 407. Although the unions complain that the Master should have required Harmon to provide documentation to substantiate his testimony, they offer no evidence to rebut Harmon's prima facie case. Accordingly, Harmon's membership is affirmed as well. 6.. Alfonzia Berger. Claimant Alfonzia Berger appeals the Special Master's decision to deny him class membership on the ground that he had no rodwork experience prior to 1974. Although Berger now argues that he was discouraged from seeking the very experience that would have made him a class member, the holding in Berger 1 was limited to discrimination against experienced rod-men. 843 F.2d at .1419. Alfonsia Berger is not a member of the class of experienced rodmen, and the Special Master's determination is therefore affirmed. 7. Paul Brown, James Hicks, and James Brown. The unions contend that the Special Master should have excluded from the class two claimants who failed the Open Period exam (Paul Brown and James Hicks), and one claimant who assertedly failed to take that exam despite being given an opportunity to do so (James Brown), because those failures allegedly demonstrate that these claimants were not qualified to be union journeymen. Berper I, however, made clear that the relevant question is not whether a claimant was qualified during the Open Period, but whether he was qualified during the liability period-which did not begin until the Open Period ended. The union is liable, we said, “to those class members who were experienced workers, but were delayed entry to union ranks by the particular educational prerequisites affecting them from the end of the Open Period until the filing of suit on October 21, 1975.” 843 F.2d at 1422. That is the issue upon which the Special Master properly focused. See, e.g., J.A. 383, 412. Although a failure on the Open Period exam may have rendered a claimant unqualified to enter the union during that period, contrary to Judge Sentelle’s dissent it did not by itself render him unqualified to do so during the liability period. The Local did not have a rule that an applicant who failed the Open Period exam (or any other pre-liability period exam) was ineligible to gain entry by subsequently taking and passing the exam during the liability period. Indeed, claimant Hicks was permitted to do just that, and passed the exam in 1974. J.A. 412. Failing to pass the exam during the Open Period is no different than having had less than 2,150 hours of rodwork experience during that period. It may mean a claimant was unqualified to be a journeyman at that time; it does not mean he could not become qualified by the time of the liability period. Nor was a failure on the Open Period exam conclusive evidence that a claimant would have failed had he been permitted to take the exam during the liability period. As we noted in Berger I, the Open Period exam was different from and notably more difficult than the exam offered during the liability period. During the Open Period, only 70.6% of white examinees and 35.3% of black examinees passed the exam. By contrast, 100% of white rodmen and 97.6% of black rodmen who took the exam given during the liability period passed. 843 F.2d at 1405-06 n. 2. The Special Master’s determination of class membership for these claimants is affirmed. 8. Albert Berger. Finally, claimant Albert Berger appeals the Special Master’s decision to deny him class membership on the ground that he failed the exam and then failed to avail himself of an opportunity to retake the exam during the Open Period. This denial is inconsistent with the Master’s correct decision not to exclude the preceding claimants for the same reason. Berger’s failure prior to the liability period neither rendered him unqualified to retake the exam during the liability period, nor indicated he would fail again if permitted to do so. Indeed, like Hicks, Berger ultimately did retake and pass the exam in 1974. J.A. 361. He was not permitted to do so, however, until he completed the Training Program — a requirement we held unlawfully discriminatory in Berger I, 843 F.2d at 1414, 1421. Accordingly, Albert Berger’s exclusion from the class is reversed. IV. Back Pay The unions challenge as clearly erroneous the back pay awards to several class members, contending that the district court failed to deduct from these claimants’ awards for certain periods of time during which, for one reason or another, they were not entitled to recover back pay. The class disagrees, but also challenges as clearly erroneous the district court’s decision to reduce several other awards for a period of time during which, the class argues, the claimant was entitled to recover. We consider each contested claim below. 1. James Brown. As we noted above, the district court’s Order of Reference entitles a claimant to back pay “for the period commencing on the date when [the claimant] first attempted to become, or was deterred or discouraged from becoming, a member of Local 201 and/or the International,” such period not to begin prior to October 21, 1972. The unions contest the $242 back pay award to James Brown in 1973 because, according to Brown’s own testimony, J.A. 797, Brown first attempted to join the union in 1974. The class counters that, although Brown’s attempt to join the union in 1971 predates the applicable liability period, the 1971 attempt gave the unions knowledge, or should have given them knowledge, that Brown wanted to join the union. According to the unions, Brown presented no evidence below that he was discouraged from joining the union in 1972 or 1973, and the class does not point to any such evidence in their brief. The Special Master awarded Brown 1973 back pay without addressing this question. J.A. 375. In its discussion of class-wide issues, the district court approved of the class’ knowledge theory, J.A. 528 n.10, and appeared to agree that it was unnecessary for the Special Master specifically to identify the date on which a claimant first attempted to become a union member, or was discouraged from doing so, since the Special Master implicitly did so when he determined the years of applicable back pay for each claimant. In its discussion of Brown’s award, the district court adopted the Special Master’s findings without further comment. J.A. 547. We think the 1973 back pay award to James Brown is clearly erroneous. Despite the district court’s apparent acceptance of the class’ “knowledge” theory, the district court’s Order of Reference authorizes back pay only for those claimants who attempted to join the union, or were discouraged from doing so, within the relevant period — not, as the class would have it, those who did nothing during that period, but whom the union knew or should have known wanted to join because of prior attempts. Although evidence of discouragement in joining would be sufficient, the class points to no such evidence as to Brown. And we think the district court’s suggestion that the Special Master implicitly found discouragement from whatever date that he began the back pay award is too much of a stretch, even for deferential review. We note that the district court’s resolution of this award is not affected by our instruction to the court on remand to apply the correct burden of proof as to class membership, since the complete absence of evidence supporting Brown’s position entitled the unions to prevail even under the more stringent standard. 2. Sherman Johnson. The unions challenge the 1972 award to Sherman Johnson for substantially the same reason that they challenge James Brown’s award. In Johnson’s case, however, we affirm the back pay award because the Special Master specifically found that Johnson sought to join the union in 1972. J.A. 434. It is true that Johnson testified that he only sought entrance to the union in 1970, 1971, and 1973, but the Special Master acknowledged that testimonial omission and pointed instead to Johnson’s certification form, which stated that Johnson sought to join in 1972. J.A. 431 n.100. The unions do not challenge the Special Master’s findings on the certification form and thus have waived any objection to it. We therefore affirm the 1972 award to Johnson, subject of course to- any necessary re-calculation if the district court alters the benchmark figures on remand. 3. Robert Posley. The unions challenge the back pay award to Robert Posley for the portion of 1974 (29%) in which he did not have 2,150 hours of Local 201 union experience. The class’ only response is that the Special Master did not err by measuring experience in union and non-union hours. As we held above, although we agree with the class that experience can be measured in union and non-union hours, a showing of 2,150 hours of experience is a prerequisite to class membership. Because of the Special Master’s contrary position on this latter point, we cannot be confident at this juncture that his conclusion that by October 1972 Pos-ley “had been doing iron work for both union and non-union contractors for over four years” is consistent with the 2,150 hour prerequisite. Indeed, the Master said nothing about the number of hours Posley worked at all. This uncertainty is complicated by the stringent burden of proof that the Special Master erroneously imposed upon the unions to rebut Posey’s testimony. We leave it to the district court on remand to decide whether Posley’s award for 1974 is consistent with the principles we have outlined in this opinion. 4. Randolph Jackson and Ernest Bellamy. The district court’s Order of Reference directed that a class member’s entitlement to back pay ends on “the date when he first was allowed to take the journeyman examination ... or was given a bona fide opportunity to take the examination.” J.A. 216-17. The unions challenge the 1975 back pay award to Randolph Jackson to the extent the award postdates Jackson’s failure of the exam in March 1975. The class challenges the back pay award to Ernest Bellamy for the opposite reason; they claim that the Special Master erroneously denied Bellamy back pay for the period after September 30, 1974, the date on which Bellamy failed the journeyman’s examination. We think it obvious that the Special Master’s findings, which the district court adopted without comment, are inconsistent. In discussing Jackson’s award, the Special Master awarded Jackson back pay for all of 1975, even though Jackson failed the exam in March of that year. But in discussing Ernest Bellamy’s award, the Special Master cut off back pay after the date on which Bellamy failed the exam, noting the Order of Reference and the fact that there were no challenges to the validity of the examination itself at the merits stage. J.A. 365 & n.61. We reconcile the inconsistency by reversing the 1975 award to Jackson and affirming the truncated award to Bellamy. The class’ sole argument in support of the contrary result is that the Order of Reference should be read to cut off back pay when a claimant is given a bona fide opportunity to take the exam. The class reads “bona fide opportunity” to mean “bona fide exam,” and argues that neither Jackson’s nor Bellamy’s exam was a bona fide one. The class further argues that the Special Master implicitly credited Jackson’s contention that Ronnie Vermillion, the union business manager, was lying when he claimed that Jackson failed the exam in March 1975 because Jackson, an experienced rodman, did not know the steel tubing sizes. J.A. 424-25. In addition, the class contends that the Special Master erroneously excluded evidence that Bellamy intended to use to demonstrate that his exam too was not a bona fide one. We think the unions are quite correct in contending that these arguments are really challenges to the administration of the journeyman’s exam—challenges which were not made at the merits stage and which we cannot, and will not, entertain at this late stage. The Special Master recognized this point in his discussion of Bellamy’s award, and in his discussion of another claimant not part of this appeal, J.A. 398-99, but awarded Jackson a full award because he did not believe that Jackson’s exam was bona fide. Moreover, as the unions point out, this court has repeatedly noted that the Title VII liability of the unions in this case is not related to the journeyman’s exam itself or to its administration, but solely to the educational prerequisites to taking the examination. Berger I, 843 F.2d at 1440; Berger II, 852 F.2d at 621. And although we do not cast doubt on the Spec