
208 F.Supp.2d 634 (2002)
Charles ALBRIGHT, III, et al.
v.
THE CITY OF NEW ORLEANS, et al.
No. CIV.A. 96-0679.
United States District Court, E.D. Louisiana.
January 24, 2002.
*635 Frank G. DeSalvo, New Orleans, LA, for Plaintiffs.
Joseph Vincent DiRosa, Jr., Avis Marie Russell, Annabelle Hoppe Wlaker, George C. Wallace, Jr., Franz L. Zibilich, Greta L. Wilson, Eileen Patricia Comiskey, MArie Michelle Segu, City Atty's Office New Orleans, LA, for Defendants.

FINDINGS OF FACT AND CONCLUSIONS OF LAW DAMAGES
BARBIER, District Judge.
Plaintiffs in this action are white New Orleans police officers who filed suit against the City of New Orleans ("the City"), the Superintendent of Police, the Mayor, and the City's former Chief Administrative Officer, challenging the promotion policies of the New Orleans Police Department ("NOPD") and claiming they were passed over for promotions to the ranks of sergeant and lieutenant on March 3, 1995, in favor of black officers.[1] After a one-day bench trial on the issue of liability, the Court issued its Findings of Fact and Conclusions of Law (Rec.Doc. 279) on June 26, 2001,[2] finding in favor of Plaintiffs and determining that the City had impermissibly considered race when selecting officers for promotion to the ranks of sergeant and lieutenant in March 1995, in violation of Title VII and the United States Constitution.[3] On December 17, 2001, a one-day *636 bench trial was conducted on the question of what damages Plaintiffs have suffered as a result of the City's impermissible conduct.[4]

Applicable Law
In formulating relief in employment discrimination cases, district courts have broad discretion in fashioning remedies as the equities of a particular case compel. United States v. Criminal Sheriff, Parish of Orleans, 19 F.3d 238, 239 (5th Cir.1994) (citing LeBlanc v. Southern Bell Tel. & Tel. Co., 460 F.2d 1228, 1229 (5th Cir.), cert. denied, 409 U.S. 990, 93 S.Ct. 320, 34 L.Ed.2d 257 (1972)). Where possible, courts should fashion remedies that serve the purposes of Title VII, i.e., remedies that compensate the victims of past discrimination and deter employers from the inclination to discriminate in the future. See Walsdorf v. Board of Com'rs for the East Jefferson Levee Dist., 857 F.2d 1047, 1054 (5th Cir.1988).
Section 706(g) of Title VII allows the district court to award "make-whole" relief to victims when an employer has engaged in illegal discrimination. 42 U.S.C. § 2000e-5(g). Accordingly, the Court may order such affirmative action as may be deemed appropriate, including, but not limited to, reinstatement or hiring of employees, with or without back pay and/or any other equitable relief as the court deems adequate. Id. In addition, Title VII provides that the prevailing party may be awarded reasonable attorney's fees, including expert fees, as part of the costs. 42 U.S.C. § 2000e-5(k).
42 U.S.C. § 1981a also provides that a complaining party under Title VII may recover compensatory and punitive damages. However, punitive damages are only available under Title VII when discrimination results from malicious or reckless indifference and are not available against governmental agencies or political subdivision. 42 U.S.C. § 1981a(b)(1). See also City of Newport v. Fact Concerts, Inc., 453 U.S. 247, 271, 101 S.Ct. 2748, 2762, 69 L.Ed.2d 616 (1981) (holding that in employment discrimination cases falling under 42 U.S.C. § 1983, municipalities are not subject to punitive damages for the actions of government officials).
With respect to recovery of compensatory damages in employment discrimination cases involving more than one plaintiff, the Fifth Circuit has stated that where multiple job applicants failed to secure a position, "only those who can prove that they would have gotten the position but for the discrimination can recover compensatory damages." Arnold v. United States Department of the Interior, 213 F.3d 193, 197 *637 (5th Cir.2000).[5] While the Fifth Circuit's pronouncement appears to fashion a strict rule in such cases, it must be borne in mind that the facts of Arnold are unique, and, that subsequent to the decision in Arnold, the Fifth Circuit suggested that its finding in that case may not be dispositive in every case involving multiple applicants competing for a limited number of positions. See Pratt v. City of Houston, 247 F.3d 601, 607 (5th Cir.2001).
In Pratt, the Fifth Circuit reversed the district court's grant of summary judgment, finding that the two plaintiffs had presented enough evidence to create a question of fact regarding discriminatory motivation behind the City's failure to promote them. Pratt, 247 F.3d at 607. In a footnote, the court recognized, however, that "even if there is a finding of prohibited discrimination, a remedy in [that] case may be problematic in that only one position was available." Id. at n. 4. While citing its previous statement in Arnold, the court suggested that, despite that pronouncement, an appropriate remedy could still be fashioned: "[W]e simply note the problem and leave it to the district court to resolve in the course of further proceedings." Id. (Emphasis added). The Fifth Circuit, therefore, has not foreclosed the possibility that a district court may formulate an appropriate remedy in such a case.
Moreover, in employment discrimination cases involving multiple plaintiffs or class actions in other circuits, courts have applied a pro rata method for computing remedial relief when only a limited number of positions were available. See, e.g., United States v. City of Miami, 195 F.3d 1292, 1300 (11th Cir.1999); Ingram v. Madison Square Garden Center, Inc., 709 F.2d 807, 812 (2d Cir.1983); Hameed v. International Ass'n of Bridge, Structural, & Ornamental Iron Workers, Local Union No. 396, 637 F.2d 506, 519-21 (8th Cir.1980); Stewart v. General Motors Corp., 542 F.2d 445, 452-54 & n. 7 (7th Cir.1976). For example, in Dougherty v. Barry, 869 F.2d 605, 614-15 (D.C.Cir.1989), the appellate court reversed the lower court's ruling that eight white firefighters were to be promoted as compensatory relief for racial discrimination in the promotion process, when only two of the firefighters would have been promoted absent the discriminatory *638 practices. The court vacated the award, finding it "overly generous," and, instead, found that dividing the value of the promotions among the plaintiffs more closely achieved the goal of restoring the plaintiffs to the positions they would have occupied but for the discrimination. Id. at 615.
The court in Dougherty recognized that, ideally, if the district court had been able to ascertain which two plaintiffs would have been promoted in the absence of discrimination, the proper remedy would have been to award those two plaintiffs full relief and the other plaintiffs nothing. Dougherty, 869 F.2d at 615. However, the court concluded that
[b]ecause the court was unable to do so, however, one must assume that each appellee enjoyed less than a one hundred percent chance of being promoted. By awarding each appellee full back pay, however, the district court treated each as though he possessed a one hundred percent chance of receiving one of the promotions, counter to that court's own conclusion that one could not determine for certain which appellees, if any, would have been promoted. Thus, in order to restore appellees to the position they would have occupied absent discrimination, the district court should have awarded each appellee a fraction of the promotions' value commensurate with the likelihood of his receiving one of the promotions.
Id.
As this Court has already made known to the parties, it finds the reasoning of Dougherty persuasive and will apply a similar method of calculating compensatory damages in this matter.[6]

Evidence Presented
The primary evidence presented during the damages phase of trial on December 17, 2001, was testimony from the opposing sides' expert witnesses.

I. Plaintiffs
Plaintiffs called Dr. Bernard F. Pettingill, Jr., whom the Court qualified as an expert in forensic economics.[7] Dr. Pettingill testified with respect to the methodology he employed to calculate: (1) the present dollar value of the promotions, including past and future value, as to each individual plaintiff, (2) the average value of a promotion from police officer to sergeant with respect to these plaintiffs, and (3) the average value of a promotion from sergeant to lieutenant for these particular plaintiffs.
Dr. Pettingill explained that his calculation for each plaintiff represents the loss to that individual as a result of not being promoted on March 3, 1995, assuming that all plaintiffs were eligible to the next rank, that each would have worked at the higher rank until either the date of trial, retirement, or second promotion to higher rank, and that all would participate in D.R.O.P.[8] Dr. Pettingill's testimony and report explain that the figures were arrived at by calculating the present value of the lost retirement benefits[9] added to the income *639 lost per hour from March 3, 1995, up to the date of trial, promotion, or retirement, depending on the circumstance of each individual officer. Dr. Pettingill testified that he believed his figures were conservative as he did not consider sick or furlough leave, overtime earnings between March 3, 1995 and date of trial, potential impact of failing to be promoted on a second career, lost details, or non-pecuniary damages, and also because he used low figures in estimating the benefits from enrolling in D.R.O.P.
Upon calculating the loss as to each individual plaintiff, Dr. Pettingill then determined the average value of a promotion from officer to sergeant and from sergeant to lieutenant, based on these particular plaintiffs. During trial, he explained that in order to arrive at averages that he believed fairly represented the overall loss to these plaintiffs, he first dropped the lowest figures, which represented the losses to individuals who were promoted within a few years of March 3, 1995,[10] and the highest figure, which represents the loss to Sergeant Sam Bua.[11] Dr. Pettingill arrived at the following amounts as representing the average value of each promotion:

Police Officer to Sergeant = $111,817.00

Sergeant to Lieutenant = $137,045.00

II. City
At trial, the City presented the testimony of Dr. Kenneth J. Boudreaux, whom the Court accepted as an expert economist.[12] Dr. Boudreaux explained that his calculations represent the loss to the plaintiffs from March 3, 1995, until two alternative cut-off dates. Dr. Boudreaux first determined the amount of loss until October 7, 1995, when the most proximate non-discriminatory promotions were made. Alternatively, Dr. Boudreaux calculated the figures for losses ending on April 15, 1998, for promotions to the rank of sergeant, and April 16, 1999, for promotion to the rank of lieutenant, as those were the dates of the next approved final Civil Service Registers.
Dr. Boudreaux testified that he first calculated the loss to each individual plaintiff based on the assumption that each plaintiff would have been promoted to the higher rank. Those figures represent the difference in base wages, loss in retirement benefits, overtime pay, and D.R.O.P benefits for those plaintiffs actually enrolled in it, from March 3, 1995 to the alternative cut-off dates. Dr. Boudreaux testified on cross-examination that, while his calculations are significantly lower than Dr. Pettingill's, the difference was primarily a result of his use of cut-off dates, and that he otherwise would generally agree with Dr. Pettingill's evaluation. Dr. Boudreaux further speculated on cross-examination that their numbers would be similar if they had operated under the same assumptions regarding *640 cut-off dates for calculating damages.
After determining the value of the lost promotion to each plaintiff, Dr. Boudreaux adjusted those figures to reflect the actual probability of promotion each plaintiff would have experienced absent discrimination. This calculation was made by first determining what the statistical probability for promotion would have been absent any discrimination. Dr. Boudreaux explained that each plaintiff who had been eligible for a promotion to sergeant on March 3, 1995, would have had a 10.7% chance of being promoted absent any discriminatory conduct by the City.[13] With respect to a promotion from sergeant to lieutenant, Dr. Boudreaux determined that, absent discrimination, each eligible plaintiff had a 18.2% chance of being promoted.[14]
Next, Dr. Boudreaux determined the actual statistical frequency that white officers experienced promotion on March 3, 1995. For promotions from officer to sergeant, white officers actually experienced only a 1.1% chance, rather than a 10.7% chance, which results in a "% Differential" of 9.6%.[15] For promotions from sergeant to lieutenant, white officers actually experienced only a 3.6% chance, rather than the 18.2% chance, resulting in a "% Differential" of 14.6%.[16] In conclusion, Dr. Boudreaux opines in his report that applying the appropriate "% Differential" to the damages for each officer results in "the `least biased' method of adjusting for the extent to which officers that were not promoted actually experienced economic damage, under the assumption that all officers were to be treated `equally.'" Exh. 2a, at 4.

Analysis

I. Compensatory Damages
After reviewing both experts' reports and considering the testimony presented at trial and the applicable law, the Court concludes that the most equitable remedy can be fashioned by combining the methods and calculations used by both experts. First, the Court accepts Dr. Pettingill's calculations of the value of the lost promotion to each individual plaintiff as the most accurate, given that the City's calculations are based on the artificial cut-off dates described above and the Court was not persuaded by the City's arguments as to why damages should only be calculated through those dates. The Court was impressed by Dr. Pettingill's method and individualization of the loss as to each plaintiff. In addition, Dr. Boudreaux testified that he generally agreed with Dr. Pettingill's calculations and that there was a likelihood that their numbers would be similar had Dr. Boudreaux not computed the promotions' values using the City's cut-off dates.
However, rather than average the values and then divide the total worth of the promotions made among the eligible plaintiffs, *641 as the Court originally suggested it might do, the Court was persuaded by Dr. Boudreaux's testimony and report that the measure of damages suffered by the plaintiffs must take into account the probability each plaintiff had of being promoted in the first place, absent discriminatory conduct. As the City has argued, it is obvious that not all of the plaintiffs would have been promoted, even if all eligibles had been treated equally. However, the evidence reveals that each plaintiff was deprived of a fair chance of being promoted because of the City's discriminatory actions. Dr. Boudreaux's report demonstrates that this loss of a fair opportunity for promotion can be quantified in mathematical terms, through adjusting the value of a promotion by the lost statistical probability of receiving the promotion.
Accordingly, the Court concludes that each plaintiff suffered a decreased probability of being promoted, as a result of the City's discriminatory conduct. Because the Court cannot determine which plaintiffs would actually have been promoted but for the discrimination, the Court finds that the most precise calculation that can be made of each plaintiff's damages is the value of the promotion as to each individual plaintiff, according to Dr. Pettingill's report, multiplied by the "% Differential" applicable to the relevant promotion, as computed in Dr. Boudreaux's report, to reflect each plaintiff's actual loss, which are as follows:


 1. Charles Albright, III: $117,281.00 × 9.6% = $11,258.98
 2. Michael L. Allsbrook: $98,876.00 × 9.6% = $9,492.10
 3. Bruce Bono, Sr.: $117,916.00 × 14.6% = $17,215.74
 4. Pete Bowen: $121,328.00 × 9.6% = $11,647.49
 5. Samuel Bua: $197,240.00 × 14.6% = $28,797.04[17]
 6. Anthony Caprera: $15,789.00 × 9.6% = $1,515.74
 7. John Castelluccio, Jr.: $105,827.00 × 9.6% = $10,159.39
 8. David Daughtry, Sr.: $117,585.00 × 9.6% = $11,288.16
 9. Dennis Dejean: $102,667.00 × 9.6% = $9,856.03
10. Stephen Dunn: $121,339.00 × 14.6% = $17,715.49
11. John Favaloro, III: 130,218.00 × 9.6% = $12,500.93
12. Garold Fayard: $118,221.00 × 9.6% = $11,349.22
13. Earl Frisard: $111,885.00 × 14.6% = $16,335.21
14. Walter Gifford: $131,636.00 × 9.6% = $12,637.06
15. Michael Glasser: $133,345.00 × 14.6% = $19,468.37
16. Michael Goodson: $103,193.00 × 9.6% = $9,906.53
17. Edward Hirstius: $131,774.00 × 9.6% = $12,650.30
18. Stanley Hoogerwerf: $12,150.00 × 14.6% = $1,773.90
19. Gary Lee: $100,221.00 × 9.6% = $9,621.22
20. Isidro Magana: $105,317.00 × 9.6% = $10,110.43
21. Paul McCaskell: $24,530.00 × 9.6% = $2,354.88
22. Norman McCord: $131,116.00 × 9.6% = $12,587.14
23. Marjorie Powell: $90,414.00 × 9.6% = $8,679.74
24. Michael Rice: $140,957.00 × 14.6% = $20,579.72
25. John Ronguillo: $113,577.00 × 9.6% = $10,903.39
26. Jay Saaks: $133,540.00 × 9.6% = $12,819.84
27. Troy Savage: $98,047.00 × 14.6% = $14,314.86
28. James Scott: $2,772.00 × 14.6% = $404.71
29. Fenner Sedgebeer: $127,559.00 × 14.6% = $18,623.61



*642
30. David Slicho: $96,073.00 × 14.6% = $14,026.66
31. Leroy Smith: $110,883.00 × 9.6% = $10,644.77
32. Larry Stokey: $143,686.00 × 9.6% = $13,793.86
33. James Ward: $125,581.00 × 9.6% = $12,055.78
34. Julie Wilson: $135,995.00 × 14.6% = $19,855.27
35. Clifford Wood: $119,003.00 × 9.6% = $11,424.29

These figures result in a total compensatory damages award of $428,367.85 against the City and in favor of Plaintiffs. As discussed above, no punitive damages may be awarded against the City.

II. Attorney Fees
Under Title VII, in addition to compensatory damages, the Court "may allow the prevailing party ... a reasonable attorney's fee (including expert fees) as part of the costs." 42 U.S.C. § 2000e-5(k). In fact, the prevailing Title VII plaintiff is usually awarded attorney fees unless except in unusual situations. See Christiansburg Garment Co. v. EEOC, 434 U.S. 412, 98 S.Ct. 694, 54 L.Ed.2d 648 (1978). Thus, "a prevailing plaintiff in a civil rights action is presumptively entitled to reasonable attorney's fees, unless a showing of `special circumstances' is made that would deem such an award unjust. See Scham v. Dist. Courts Trying Criminal Cases, 148 F.3d 554, 557 (5th Cir.1998).
Accordingly, the Court concludes that Plaintiffs in this case are entitled to an award of reasonable attorney fees, including expert fees. Counsel for Plaintiffs are therefore instructed to file any application for attorney and expert fees they feel are appropriate on or before Wednesday, February 13, 2002. The City will have until Monday, February 25, 2002 to respond.

Conclusion
Plaintiffs have demonstrated that they suffered damages in that each lost a fair opportunity to be promoted as a result of the City's discriminatory conduct. Because it is impossible to determine which Plaintiffs would actually have been promoted in the absence of the City's actions, the Court has applied the reasoning in Dougherty and awarded each Plaintiff compensatory damages in the amount of a fraction of the lost promotions' value corresponding to the statistical probability of each Plaintiff having received a promotion but for the City's discriminatory promotion policy on March 3,1995. See Dougherty, 869 F.2d at 615. Accordingly;
The Court finds that the City is liable to the individual Plaintiffs for the amounts detailed above, which total $434,278.90 in compensatory damages, and for any post-judgment interest that accrues on those amounts pursuant to 28 U.S.C. § 1961(a). In addition, the Court finds that Plaintiffs are entitled to reasonable attorney and expert fees, in the amount of which is to be determined at a later date.
NOTES
[1]  As detailed in the Court's previous ruling on the issue of liability, Plaintiffs were patrolmen and sergeants on a list of eligibles for promotion to the ranks of sergeant and lieutenants, respectively.
[2]  The procedural and factual history of this matter are detailed in the Court's previous opinion. Accordingly, the Court does not find it necessary to repeat those facts here.
[3]  The Court dismissed all claims against the Superintendent, the Mayor, and the former Chief Administrative Officer in any capacity, and found that the City is the liable party under the applicable law.
[4]  The plaintiffs who, on March 3, 1995, were eligible for promotion from patrolmen to sergeants are: Charles Albright, Michael Allsbrook, Forest Austin, Pete Bowen, Anthony Caprera, John Castelluccio, David Daughtry, Dennis DeJean, John Favalora, III, Gerald Fayard, Walter Gifford, Michael Goodson, Edwin Hirstius, Gary Lee, Isidro Magana, Paul McCaskell, Norman McCord, Jr., Marjorie Powell, John Ronquillo, Jay Saaks, Leroy Smith, Jr., Larry Stokey, James W. Ward, and Clifford Wood. However, Plaintiffs agreed at trial that Forest Austin and Steven Smegal have not suffered any damages in the form of lost income and lost retirement benefits, because they were both promoted retroactively with back pay and benefits to March 3, 1995.

The remaining plaintiffs who were sergeants and were eligible for promotion to the rank of lieutenant on March 3, 1995, are: Bruce Bono, Sam Bua, Stephen Dunn, Earl Frisard, Jr., Michael Glasser, Stanley Hoogerwerf, Michael Rice, Troy Savage, James Scott, Fenner Sedgebeer, David Slicho, and Julie Wilson. While Stanley Hoogerwerf and James Scott have both been promoted to the rank of Lieutenant, neither was promoted retroactively to the date of the City's discriminatory conduct.
[5]  The facts in Arnold are unique, however. The three plaintiffs in that case, Joe Arnold, Allen McDaniel, and Bobby Maxwell, all white men, applied for a supervisory position in the Mineral Management Service ("MMS"), a division of the Department of Interior. Arnold, 213 F.3d at 194-95. A woman was hired for the position, and the plaintiffs filed administrative complaints, alleging, among other things, gender discrimination. After a hearing, the administrative judge issued an opinion finding that the hiring decision had been based on gender discrimination, and the MMS determined that the three were entitled to compete in an unbiased selection process and reconducted the job search. The plaintiffs filed suit anyway. However, thereafter, the woman originally hired was transferred, and Maxwell was selected to replace her. Even so, Maxwell remained a plaintiff in the suit. Id.

Prior to trial, the district court ruled that Arnold and McDaniel could not present any evidence as to compensatory damages on their discrimination claim, because the subsequent promotion of Maxwell precluded them from proving that "but for" the discrimination, they would have gotten the job. The jury did find in favor of all three plaintiffs, but only awarded compensatory damages to Maxwell. Id. at 195.
On appeal, the Fifth Circuit affirmed the district court's ruling regarding Arnold and McDaniel, and agreed that they could not recover compensatory damages because they could not prove that they would have gotten the position, but for the discrimination, especially as they did not contend discrimination, played a role in the selection of Maxwell to fill the position. Id. at 197.
[6]  The Court previously ruled that it would apply the Dougherty Court's reasoning in determining damages in this case, during the hearing in open court on the City's Motion for Partial Summary Judgment on November 14, 2001.
[7]  Dr. Pettingill's expert report was admitted into evidence as Exhibit 1 in globo.
[8]  D.R.O.P is a deferred retirement plan for which NOPD officers may volunteer, which essentially allows them to receive early retirement pay, while continuing to work for a limited period of time. See Exh. 2a, at 36.
[9]  The formula used by Dr. Pettingill to determine the lost retirement benefits to individual officers was based on the following: 3.3% times the number of years of service times the highest three years of base income plus the state supplemental pay, projected over the course of each officer's normal life expectancy and reduced to present money value applying a 2% net discount rate. See Exh. 1a, at 2.
[10]  For example, Sergeant Anthony Caprera was overlooked for a promotion from officer to sergeant in March 1995, but was subsequently promoted on June 7, 1998, resulting in a smaller loss of $15,789.00, according to Dr. Pettingill. That figure was not included in arriving at the average value of a promotion from officer to sergeant, as it was significantly lower than the majority of the plaintiffs' losses.
[11]  Plaintiffs argue that Sergeant Bua's circumstances are unique. Sergeant Bua testified that had he been promoted on March 3, 1995, to the rank of lieutenant, he would subsequently have been promoted again to the rank of captain in August 1998. Plaintiffs point out that he was on the list of eligibles for both promotions and that all lieutenants eligible for captain were promoted out of his band, before promotions were made out of the next band.
[12]  Dr. Boudreaux's expert report was admitted into evidence as Exhibit 2 in globo.
[13]  This percentage reflects that there were 121 eligible officers for the promotion and that 13 were actually promoted, meaning each of the 121 eligibles had a 10.7% chance of being promoted, all other factors being equal.
[14]  This percentage reflects that there were 33 eligible sergeants for promotion and that 6 were actually promoted, meaning each of the 33 individuals had a 18.2% chance of being promoted, all other factors being equal.
[15]  These numbers reflect that out of the 90 white eligibles, only 1 was promoted, whereas, but for the discriminatory conduct, 9.7 white officers would have been promoted.
[16]  These numbers reflect that out of the 28 white eligibles, only 1 was promoted, whereas, but for the discriminatory conduct, 5.1 white officers would have been promoted to the rank of lieutenant.
[17]  The Court finds that, as it is impossible to determine whether Sergeant Bua would have been promoted to the rank of lieutenant, so that he subsequently would have been promoted to the rank of captain, the most equitable solution is to accept Dr. Pettingill's calculation of the value of both lost promotions to Sergeant Bua, and adjust it by the % Differential applicable to the promotion from sergeant to lieutenant.
