Seventeen current and former members of the police force of the City of Milwaukee ("City") brought this action against the City, former Chief of Police Arthur Jones, the Milwaukee Board of Police and Fire Commissioners, and five of the Commissioners in their personal and official capacities. The officers, all white males, alleged that the City, the Chief and the Board had violated their statutory and constitutional rights by engaging in discriminatory promotion practices favoring women and minorities. The officers brought their claims under Title VII, 42 U.S.C. § 2000e et seq., as well as 42 U.S.C. §§ 1981 and 1983. Following a several-week bifurcated trial, a jury found the defendants liable on all counts; compensatory damages were awarded against all defendants and punitive damages were awarded against each of the individual defendants. Following a bench trial on economic damages, the district court also ordered back and front pay and costs. The defendants timely filed this appeal, challenging both liability and damages. For the reasons stated in the following opinion, we affirm in part and reverse in part the judgment of the district court.

* BACKGROUND

The plaintiffs in this action are seventeen police officers who, during times relevant to this action, held the rank of lieutenant on the City's police force. From November 18, 1996 until November 18, 2003, defendant Arthur Jones was the Chief of the Milwaukee Police Department. As required by Wisconsin law, the City maintains a five-member Board of Fire and Police Commissioners ("Board"), a citizen oversight body charged with various duties, including the responsibility to make certain general policies and standards for the departments, the authority over appointments on the police force and in the fire department, and the duty to conduct disciplinary hearings following referrals by department chiefs. See Wis. Stat. § 62.50. By statute, commissioners serve staggered five-year terms. Id. at § 62.50(1). Defendants, Commissioners Woody Welch, Carla Cross, Eric M. Johnson, Leonard J. Sobczak and Ernesto A. Baca, all served for some portion of Chief Jones' tenure.

The events at issue in this action revolve around a series of forty-one promotions from the rank of lieutenant to captain that occurred between 1997 and 2003. In accordance with Wisconsin law, when a vacancy in the rank of captain became available, Chief Jones nominated a candidate to fill it. The governing statute required that he select candidates "already in the service [who have] proven their fitness for the promotion." Wis. Stat. §§ 62.50(7)(b), 62.50(9). The process for selecting nominees for promotion in the relevant period was ill-defined: The City had no written procedures, and Chief Jones testified that he could not recall his thought processes with respect to the nominations, that he did not post a position announcement when a vacancy became open in the captain ranks and that he did not keep any records regarding nominations, R.273 at 391-93. Instead, Chief Jones stated that he personally evaluated potential candidates to determine the candidate he thought would be "the most qualified to fill [the] position." R.273 at 409. In making this determination, Chief Jones said that he considered an individual's skills, abilities and knowledge and in some measure also considered seniority. R.272 at 205, 228; R.273 at 394. His conclusions were based on his "personal observations of the individual over some — in most instances a long period of time," R.272 at 228, and verbal recommendations "from various individuals," R.272 at 232. He denied that race or gender was a factor in his decision, R.273 at 460, although the jury apparently disbelieved this statement.1

Having selected his nominee through this fairly amorphous and private process, the Chief would then forward the candidate's name to the Board and would request that the Board approve the appointment to the rank of captain in accordance with Wisconsin law. Wis. Stat. § 62.50(2). Along with the nomination, the Chief would forward the candidate's "hard card," which contained information from his or her service history and a resume, often prepared for this purpose. The Commissioners testified that they reviewed the documentation sent by Chief Jones and interviewed the candidates before conducting a vote on their approval of the appointment. They each specifically testified that they did not consider race or gender when approving promotions. They did, however, evaluate Chief Jones on his ability to foster diversity; over the course of an apparently deteriorating relationship in which his marks in a variety of other categories plummeted, he was determined consistently to be "exceed[ing] expectations" in valuing and achieving diversity on the force.2 R.298, Exs.59-64.

During the relevant period, there were forty-one promotional opportunities to the rank of captain. Chief Jones submitted forty-one nominees, all of whom were approved, and in all but one case, upon review of the record and interview of the candidate, the approval was unanimous.3

The Board kept records concerning the racial and gender diversity of the police force in part because of court orders issued in response to discrimination suits dating back to the 1970s. R.298, Ex.40 at 1. In fact, a consent decree governing affirmative action in hiring, but not promotions, was still in place during the beginning of Chief Jones' tenure. See R.298, Exs.537, 538. In 1996, on the twentieth anniversary of the first court order, a report was prepared by Joan Dimow, a researcher on the staff of the Fire and Police Commission ("FPC")4 and Kenneth Munson, Executive Director of the FPC, as a consultation paper to the United States Commission on Civil Rights. In that report, the authors discussed the affirmative action programs in the Milwaukee police force and stated that they believed that increased diversity on the force advanced two complementary goals: creating a representative force and better preparing all officers for culturally-diverse interaction in the community they serve. R.298, Ex.40 at 1. That same report noted continuing goals for diversity in recruiting and hiring, but stated that there were "no affirmative action goals for promotion," and that, because a variety of factors controlled a candidate's success in receiving promotions, the expected improvements in diversity among management were slower to take root. Id. at 7-8. In 2001, Dimow updated the findings in the earlier report, and in a portion examining diversity in command-staff rankings, noted that white men were under-represented at the rank of captain and higher, at just over forty-four percent, while their proportion in the entire department was nearly fifty-three percent, R.298, Ex.5 at 4; African-Americans were identified as over-represented.5 These reports apparently were made available to the Commissioners, although they were not discussed at a Board meeting. Only Commissioner Welch recalls any conversation regarding the reports. He testified that he and Dimow discussed the statistics from the later report and that he asked that the report be forwarded to Chief Jones. R.275 at 759.

Of the forty-one persons promoted to the rank of captain during the relevant period, the record shows that at least some women and minorities were promoted more quickly than white males, with four promoted during their one-year probationary periods in the rank of lieutenant. R.298 Ex.58. Of the twenty women and minorities promoted during Chief Jones' tenure, seventeen had spent less than five years in the lieutenant rank, while the same was true for only four of the twenty-one white males promoted during the same period. Id.

The seventeen plaintiffs in this action were, during the period of the forty-one promotions, qualified lieutenants eligible for promotion to the rank of captain. R.273 at 347. They were not promoted despite, in many cases, having seniority to a female or minority lieutenant selected for promotion.

The plaintiffs brought this action in the Eastern District of Wisconsin against the City, the Chief, the Board and the Commissioners, alleging violations of 42 U.S.C. §§ 1981 and 1983, and Title VII. The plaintiffs' theory was that Chief Jones had intentionally discriminated against white male members of the lieutenant ranks in promotions to captain and that the Commissioners knew about the discrimination and nevertheless approved every candidate for promotion. In special verdicts, the jury found that the City and Chief Jones had discriminated intentionally in favor of women and minority candidates in the selection of officers for promotion to captain and that the Commissioners had "personally participate[d]" in the discrimination. R.149 at 4-5.

In their initial answer, the defendants had raised a defense of qualified immunity.6 At trial, they introduced some evidence that there was a compelling interest in diversity in a police force, but they did not further request a ruling on their entitlement to qualified immunity until filing a motion for judgment as a matter of law and a renewed motion for judgment as a matter of law. R.140, R.224. Both these post-trial motions were denied by the district court.

Following a verdict in favor of the plaintiffs on liability, the jury calculated compensatory damages (ranging from $9,500 to $50,000, not including lost wages and benefits), and assessed $289,000 in punitive damages against each of the Commissioners ($17,000 from each Commissioner and Chief Jones to each of the 17 plaintiffs, each plaintiff receiving $17,000 x 6, or $102,000 in punitive damages). R.161 at 5. The court appointed a special master to determine the appropriate amounts of economic damages, particularly lost wages and benefits. R.200. The court instructed the special master to consider back pay from the date of the onset of discrimination, as found by the jury, and to "increase each Plaintiff's salary until the point at which the base pay reaches the highest base pay for the rank of captain." R.205 at 2. The defendants objected to this method of damages calculation and to the special master's report, R.211, and filed motions to vacate the punitive damages award and amend the compensatory damages awards, or for a new trial on damages, R.218, R.220. Their motions were denied. R.263, R.264.

The Commissioners and the City then brought this appeal, challenging liability and damages.

On appeal, the City, the Board and the Commissioners challenge four separate conclusions reached by the district court: (1) The Commissioners challenge the district court's ruling that they are not entitled to qualified immunity, insofar as their actions were not in violation of a clearly established constitutional right of the plaintiffs; (2) the City next challenges whether municipal liability is appropriate under the circumstances; (3) all defendants challenge the manner of calculation of compensatory damages; and (4) the Commissioners challenge the availability and amount of punitive damages. We shall address each of their arguments below.

The Commissioners assert that they are entitled to a defense of qualified immunity and, therefore, that the individual verdicts against them cannot stand.

The parties dispute the availability of this defense as a procedural matter. The defendant Commissioners first asserted a defense of qualified immunity in their answer and again in post-trial motions for judgment as a matter of law. Ordinarily, a district court is required to address the issue of qualified immunity at an early stage in the proceedings in order to ensure that public officials entitled to its protection are saved not only from ultimate liability for civil damages, but also from the burdens of litigation. See Harlow v. Fitzgerald, 457 U.S. 800, 818, 102 S. Ct. 2727, 73 L. Ed. 2d 396 (1982); Mitchell v. Forsyth, 472 U.S. 511, 526, 105 S. Ct. 2806, 86 L. Ed. 2d 411 (1985). In this case, however, given the failure of the defendants to raise the issue in pretrial or early trial motions for summary judgment, the district court stated in ruling on the defendants' motion for judgment as a matter of law post-trial:

The Defendants raised the affirmative defense of qualified immunity in their Answer, but they did not move for summary judgment on this or any other issue. Qualified immunity protects a public official sued in his or her personal capacity from suit. Once the trial has concluded, the opportunity for that protection is lost. Therefore, there is little reason to address the qualified immunity issue. In the case cited by the movants in support of their position, the court granted qualified immunity after trial without discussing timeliness. See Terry v. Richardson, 346 F.3d 781, 784, 787-88 (7th Cir.2003). The jury has found that the Defendants' conduct violated the constitutional rights of the Plaintiffs and those rights were firmly established at the time they acted. At this posttrial stage of these proceedings, the court will not delve further into this issue. See McNair v. Coffey, 279 F.3d 463, 475 (7th Cir.2002).

R.262 at 2-3. The defendants claim this procedural ruling, which we construe as a ruling that qualified immunity had been forfeited, was error.

We note that we have not determined with precision how a defendant must preserve a qualified immunity defense.7 However, we need not decide this question here because we conclude that, in any event, the Commissioners are not entitled to an immunity defense.8

In determining whether a defendant is entitled to qualified immunity, we engage in a two step analysis. Riccardo v. Rausch, 375 F.3d 521, 526 (7th Cir.2004). We first ask whether a constitutionally protected right has been violated; if we determine that there has been such a violation, we examine whether this right was clearly established at the time of the violation. Saucier v. Katz, 533 U.S. 194, 201, 121 S. Ct. 2151, 150 L. Ed. 2d 272 (2001); Payne v. Pauley, 337 F.3d 767, 775 (7th Cir.2003). Because the jury has rendered a verdict against the Commissioners now seeking immunity, we must view the facts in the light most favorable to the plaintiffs; because the substance of a constitutional right is a question of law and therefore not within the authority of the jury, whether the acts done by the Commissioners violate the Constitution and whether the law was clearly established at the time of any violation are, as questions of law, subject to our de novo review. Mitchell, 472 U.S. at 528, 105 S. Ct. 2806; Reynolds v. City of Chicago, 296 F.3d 524, 527 (7th Cir.2002); McNair v. Coffey, 279 F.3d 463, 466 (7th Cir.2002).

The jury found that the Commissioners "personally participate[d] in discriminating against ... the plaintiffs," R.149 at 5, and held the Commissioners liable under 42 U.S.C. § 1983 for violating the officers' rights under the Fourteenth Amendment to equal protection of the law. We first must determine whether the acts found by the jury indeed constitute a constitutional violation in this context. See McNair, 279 F.3d at 466.

The Equal Protection Clause of the Fourteenth Amendment provides that "[n]o State shall ... deny to any person within its jurisdiction the equal protection of the laws." U.S. Const. Amend. XIV, § 1. The Clause protects the right to be free from certain types of discrimination in promotion in public employment absent justification of constitutional proportion. Race-conscious employment decisions made by the state are presumptively unconstitutional and will satisfy the requirements of equal protection only where they are consistent with strict scrutiny. Adarand Constructors, Inc. v. Pena, 515 U.S. 200, 227, 115 S. Ct. 2097, 132 L. Ed. 2d 158 (1995); City of Richmond v. J.A. Croson Co., 488 U.S. 469, 493-94, 109 S. Ct. 706, 102 L. Ed. 2d 854 (1989). To satisfy strict scrutiny, classification schemes involving race must serve a compelling state interest and be narrowly tailored to further that interest. Adarand, 515 U.S. at 235, 115 S. Ct. 2097.9 Although the ultimate burden of defeating a qualified immunity defense rests with the plaintiff and thus it is the plaintiff's burden to establish a constitutional violation, Sparing v. Village of Olympia Fields, 266 F.3d 684, 688 (7th Cir.2001), on review of an equal protection challenge, we ordinarily require only that the plaintiff establish a racial classification; it then becomes the Government's burden to prove that the classification satisfies strict scrutiny, Johnson v. California, 543 U.S. 499, 505, 125 S. Ct. 1141, 160 L. Ed. 2d 949 (2005).

Neither the parties nor the district court appear to dispute the compelling nature of the state's interest in diversity in law enforcement.10 See Jury Instruction 3, R.164 at 18; Instruction Conference, R.284 at 2176; McNamara v. City of Chicago, 138 F.3d 1219, 1222 (7th Cir.1998). Our precedent supports this view. See Petit v. City of Chicago, 352 F.3d 1111, 1114 (7th Cir. 2003) (considering the Supreme Court's decision in Grutter v. Bollinger, 539 U.S. 306, 327-31, 123 S. Ct. 2325, 156 L. Ed. 2d 304 (2003), and concluding that, in the case of the City of Chicago, "there is an even more compelling need for diversity in a large metropolitan police force charged with protecting a racially and ethnically divided major American city"); Wittmer v. Peters, 87 F.3d 916, 919 (7th Cir.1996) (stating that law enforcement is among "the very clearest examples of cases in which departures from racial neutrality are permissible" in rejecting the plaintiffs' claim that appointment of a black correctional officer as a lieutenant in a young-offender boot camp was discriminatory).

However, as we noted earlier, in order for the defendants to demonstrate that their actions comport with strict scrutiny, they must demonstrate not only a compelling state interest, but also evidence sufficient to establish that they have narrowly tailored the remedy consistent with that interest. Adarand, 515 U.S. at 235, 115 S. Ct. 2097. Upon examination of the record, we must conclude that, in this case, the Commissioners have not made this second showing. The evidence adduced at trial regarding the "plan" to increase diversity in the command staff ranks was limited at best. Although it had been subject in the past to court orders to increase diversity in hiring and had been under one during the first part of Chief Jones' tenure, the City was under no specific court orders directing it to increase promotional opportunities for women and minorities. Reports prepared by FPC staff expressly noted that there were "no affirmative action goals" for the command staff ranks. R.298, Ex.40 at 7. Each Commissioner in his or her own testimony denied the use of race-conscious policies in their votes to approve potential candidates for promotion. The record therefore discloses no policy, no set parameters and no means of assessing how race should be weighed with other promotional criteria. Faced with any evidence of a plan in the trial record, the defendants are left to urge that the Commissioners' testimony demonstrates that, even though they considered each candidate individually, they embraced a view of increasing diversity. They contend that the Commissioners took a flexible approach, in which diversity was important, but under which the individual qualifications of each candidate were considered before promotion. They further contend that this approach is supported by evidence that they undertook review of Chief Jones' performance and that his ability and successes in promoting diversity were cornerstones of their review.

Our cases approving of a race-conscious promotion policy for a public employer as a narrowly tailored response to a compelling governmental interest have never approved such a loose and indeed effectively standard-less approach. See, e.g., Petit, 352 F.3d at 1115-17 (approving of a limited-time standardization of examinations scores based on race for promotion to sergeant where the examination had an adverse racial impact); Reynolds, 296 F.3d at 525-26 (noting that "promotions were made pursuant to an affirmative action plan"); McNamara, 138 F.3d at 1224 (noting the precise increase in minority promotions identified as an affirmative action plan goal and the manner in which it was achieved to have "the minimum adverse impact on whites"); Billish v. City of Chicago, 989 F.2d 890, 892 (7th Cir.1993) (en banc) (identifying the challenged plan's goals, although ultimately not finding evidence sufficient to justify dismissal on the ground that the plaintiffs had not stated a claim of discrimination). On one occasion, we have approved a race-conscious promotion without an admitted plan with appropriate standards, see Wittmer, 87 F.3d 916, but it is of little relevance in the present case. In Wittmer, we evaluated the necessity of appointing a single black officer to the rank of lieutenant in a boot camp populated primarily by black inmates. By contrast, the present situation stretches through several years and dozens of promotions. Id. at 920.

Therefore, we cannot say that the defendants' actions comport with the Constitution. There simply is no evidence in the record of the actual content of their policies — policies that we must examine under the most searching form of judicial scrutiny. A race-conscious promotion system with no identifiable standards to narrowly tailor it to the specific, identifiable, compelling needs of the municipal department in question cannot pass constitutional scrutiny. Accordingly, we must proceed to determine whether this deficiency was "clearly established" at the time of the Commissioners' actions.

2. Clearly Established Law During the Relevant Period

Qualified immunity protects officials from suit and from liability for civil damages when, at the time of the challenged action, the contours of the constitutional right were not so defined as to put the defendant officials on notice that their conduct amounted to a constitutional violation. See Hope v. Pelzer, 536 U.S. 730, 739, 122 S. Ct. 2508, 153 L. Ed. 2d 666 (2002) (equating the right of an official sued for damages under 42 U.S.C. § 1983 to fair notice to that of an official charged with criminal liability under the § 1983 criminal counterpart, 18 U.S.C. § 242). "The relevant, dispositive inquiry in determining whether a right is clearly established is whether it would be clear to a reasonable officer that his conduct was unlawful in the situation he confronted." Saucier, 533 U.S. at 202, 121 S. Ct. 2151 (citing Wilson v. Layne, 526 U.S. 603, 615, 119 S. Ct. 1692, 143 L. Ed. 2d 818 (1999)). In order to determine whether the law is clearly established, we must inquire whether, "in light of preexisting law, the unlawfulness [of the conduct was] apparent." Hope, 536 U.S. at 739, 122 S. Ct. 2508 (citing Anderson v. Creighton, 483 U.S. 635, 640, 107 S. Ct. 3034, 97 L. Ed. 2d 523 (1987)).

Accordingly, we must determine whether the state of the law with respect to affirmative action during the relevant period would have put a reasonable official on notice that the approach taken by the Board was unconstitutional. We have little difficulty in concluding that the law was clear. Following the Supreme Court's opinions in City of Richmond v. J.A. Croson Co., 488 U.S. 469, 109 S. Ct. 706, 102 L. Ed. 2d 854 (1989), and Adarand Constructors, Inc. v. Pena, 515 U.S. 200, 115 S. Ct. 2097, 132 L. Ed. 2d 158 (1995), it was clear that "all racial classifications, imposed by whatever federal, state, or local government actor" must comport with strict scrutiny. Adarand, 515 U.S. at 227, 115 S. Ct. 2097. Our own precedent during the period in question supports the view that the approach taken would not pass constitutional muster. In Cygnar v. City of Chicago, 865 F.2d 827 (7th Cir.1989), we stated that the onus is on state defendants to "fully and properly articulate the factual predicate for their [affirmative action] `plan'." Id. at 840. Cygnar arose relatively early in the development of affirmative action jurisprudence, at a time when courts were more concerned with statistical evidence of past discrimination to justify present remedial affirmative action. Here, however, we are concerned with the separate compelling interest in diversity as a justification. Nonetheless, we clearly placed the burden on defendants who act in a racially discriminatory manner to do so only on the basis of established facts demonstrating real necessity.11 We ultimately affirmed the district court's ruling that the City was not liable for the constitutional violation in Cygnar; we did so, however, by concluding that, although the defendants' conduct in using an insufficiently justified affirmative action plan "may well violate today's established constitutional law standards," the law in 1984 (at the time of the challenged transfers) was not sufficiently clear to deny the defendants qualified immunity. Id. at 844 (emphasis in original).

In Billish v. City of Chicago, 989 F.2d 890 (7th Cir.1993) (en banc) (reversing a district court's dismissal of plaintiffs' equal protection claims), we relied on our ruling in Cygnar when we again evaluated Chicago's attempt to remedy past discrimination, an interest that, by then, the Supreme Court had identified as sufficiently compelling under some circumstances to justify a narrowly tailored remedy, see City of Richmond, 488 U.S. at 493, 109 S. Ct. 706. The city's remedial efforts involved a race-conscious promotion plan; in our review, we stated that the measures adopted could survive only where they had been "carefully designed to avoid unnecessary injury to white persons," Billish, 989 F.2d at 893. Several years later, we further stated, in Wittmer, that to demonstrate such careful crafting consistent with the Constitution, the defendant must

show that they are motivated by a truly powerful and worthy concern and that the racial measure that they have adopted is a plainly apt response to that concern. They must show that they had to do something and had no alternative to what they did. The concern and the response, moreover, must be substantiated and not merely asserted.

87 F.3d at 918 (emphasis added). Wittmer then approved of the promotion of a single black staff member to lieutenant because a compelling interest in some representation of African-Americans on the command staff at a boot camp with a predominantly African-American inmate population had been shown and because a single promotion was the least discriminatory remedial action the state could take under the circumstances. Id. at 920-21.

These cases clearly establish that narrow tailoring means precisely what it says: Race-based preferences must be constructed carefully to discriminate no more than necessary to meet whatever compelling state interest is at issue. Moreover, defendants must substantiate both the need and the remedy sufficient to permit our meaningful review. The defendants in this action had fair notice that their actions were outside the permissible bounds of racial preferences at the time that they acted.

Because we conclude that the acts of the Commissioners, as found by the jury, in participating in discrimination against the plaintiffs, violated the constitutional rights of the plaintiffs and because we conclude that, at the time of their acts, the constitutional violation was clearly established, we also must conclude that the defendants are not entitled to qualified immunity. Accordingly, we affirm the judgment of the district court with respect to the liability of the Commissioners under 42 U.S.C. § 1983.

The City of Milwaukee challenges the finding of liability against it for the actions of the Commissioners and the Chief under §§ 1981 and 1983 and Title VII. The basis for municipal liability under § 1983 is that the municipality sanctioned or ordered, through official policy, the unlawful discriminatory conduct in issue. Pembaur v. City of Cincinnati, 475 U.S. 469, 479-80, 106 S. Ct. 1292, 89 L. Ed. 2d 452 (1986). Liability may be found either with a widely-adopted policy, or for even the single actions of municipal employees, if those employees had final policy making authority for the municipality, a question of state law. Id.; City of St. Louis v. Praprotnik, 485 U.S. 112, 123-24, 108 S. Ct. 915, 99 L. Ed. 2d 107 (1988) (plurality opinion). Section 1981, like § 1983, also requires a plaintiff to demonstrate an official policy or custom in order to allow for municipal liability. Jett v. Dallas Ind. Sch. Dist., 491 U.S. 701, 736-37, 109 S. Ct. 2702, 105 L. Ed. 2d 598 (1989). The jury was instructed that the Commissioners were final policymakers for the City and found, on the basis of their actions, that the City was liable. See R.285 at 2273.

As the defendants correctly note, under Monell v. Department of Social Services, 436 U.S. 658, 693, 98 S. Ct. 2018, 56 L. Ed. 2d 611 (1978), if the final policymakers for the City did not engage in unlawful conduct, the City cannot be liable on the basis of a municipal policy under § 1983; because we have already concluded, however, that the Commissioners did violate the plaintiffs' constitutional rights because their race-conscious promotion plan was not consistent with strict scrutiny, this principle is of no assistance to the City with respect to the actions of the Commissioners.

We need not decide whether Chief Jones is a policymaker, thus making the City liable under § 1981 and § 1983 for his actions. The City remains liable for his actions under the respondeat superior theory of liability embraced by Title VII. See Geier v. Medtronic, Inc., 99 F.3d 238, 244 (7th Cir.1996). Because the City has declined to challenge whether the actions of Chief Jones violated the plaintiffs' constitutional rights, see Appellants' Br. at 41-42 n. 17, his actions form an appropriate basis for a valid Title VII claim against the City as the employer.

Accordingly, because we reject the City's contention that the actions of the Commissioners can withstand strict scrutiny and because we conclude that, in any event, the City is responsible for Chief Jones' actions under Title VII, we affirm the district court's finding of liability against the City.

The defendants next challenge numerous legal rulings made by the district court with respect to the jury's award of compensatory damages. We review the challenged legal determinations de novo and the factual determinations made by the court for clear error. Todd v. Corp. Life Ins. Co., 945 F.2d 204, 207 (7th Cir.1991).

In Doll v. Brown, 75 F.3d 1200, 1206-07 (7th Cir.1996), this court commended "to the consideration of the bench and bar" the loss of a chance doctrine for evaluating damages due to a plaintiff in a competitive-promotion employment discrimination case; we then applied that rule in Bishop v. Gainer, 272 F.3d 1009, 1016-17 (7th Cir.2001), and in Biondo v. City of Chicago, 382 F.3d 680 (7th Cir.2004). The loss of a chance doctrine is a familiar doctrine in tort law, and although not all jurisdictions accept it as a basis for calculating damages, we have stated that, in our view, it is basically sound. Doll, 75 F.3d at 1206. We described the usual application of the doctrine as follows:

[Loss of a chance] is illustrated by cases in which, as a result of a physician's negligent failure to make a correct diagnosis, his patient's cancer is not arrested, and he dies — but he probably would have died anyway. The trier of fact will estimate the probability that the patient would have survived but for the physician's negligence — say it is 25 percent — and will award that percentage of the damages the patient would have received had it been certain that he would have survived but for the negligence.

. . . . It is an extension of the routine practice in tort cases involving disabling injuries of discounting lost future earnings by the probability that the plaintiff would have been alive and working in each of the years for which damages are sought. It recognizes the inescapably probabilistic character of many injuries. It is essential in order to avoid under-compensation and thus (in the absence of punitive damages) under-deterrence, though to avoid the opposite evils of overcompensation and overdeterrence it must be applied across the board, that is, to high-probability as well as to low-probability cases. If the patient in our example was entitled to 25 percent of his full damages because he had only a 25 percent chance of survival, he should be entitled to 75 percent of his damages if he had a 75 percent chance of survival — not 100 percent of his damages on the theory that by establishing a 75 percent chance he proved injury by a preponderance of the evidence. He proves injury in both cases, but in both cases the injury is merely probabilistic and must be discounted accordingly.

Doll, 75 F.3d at 1205-06 (internal citations omitted) (emphasis in original). As we have recognized when applying this doctrine in other discriminatory promotion cases, it appropriately quantifies each plaintiffs' monetary loss when what they in fact lost was a chance to compete on fair footing, not the promotion itself. See Biondo, 382 F.3d at 688.

The parties in this case acknowledge that our precedent supports the use of the loss of a chance method of calculating damages in the factual scenario at issue in this case. They dispute, however, whether the district court appropriately applied the doctrine to the facts and whether, as a consequence, it erroneously instructed the jury.

At the damages phase of the trial, the defendants requested a damages instruction that would take into account all other lieutenants eligible for promotion at each of the dates the jury found that the plaintiffs had been wrongfully passed over for promotion. That instruction would have required the jury to consider the entire number of officers who were qualified for promotion to the position of captain at the time of the discrimination. R.109 at 24. The district court rejected the proposed instruction's language and ruled that it would eliminate all references to other qualified candidates in the instruction, because there was no mechanism by which the qualifications of other officers was established. R.291 at 299-300. Specifically, the district court stated that no evidence had been produced with regard to other candidates seeking promotion and that, unlike the Biondo plaintiffs, the plaintiffs in this action were not among a group that had pre-qualified and expressed interest by virtue of sitting for a promotional examination. Id. at 300. The court apparently believed that, if other candidates were qualified and interested, they necessarily would have joined as plaintiffs in the present action. Id. at 300-01. The court therefore instructed the jury by referencing only the probability that each individual plaintiff — not each officer eligible for promotion — would be promoted on any particular date. R.165 at 5. A special verdict form asked the jury only to determine the "percentage chance that each Plaintiff would have been promoted to captain of police ... keeping in mind other qualified Plaintiffs" on each date of discrimination. Id. (emphasis added). As instructed by the district court, the Special Master used the dates of discrimination and probabilities of promotion found by the jury in calculating the economic damages owed to each plaintiff. See R.209 at 2-4 (Special Master's Report).

We believe the district court's approach was inconsistent with the dictates of our lost-chance precedent. Although our cases have evaluated situations in which the administration of exams and other identifiable benchmarks have resulted in a more definite and certain list of potential promotees, it is not the case that, in the absence of such a measure, the district court was entitled to assume that each plaintiff was virtually assured promotion ahead of any other available lieutenants. The district court believed that our ruling in Biondo, which rejected as implausible a jury's findings of high probabilities of promotion for the plaintiffs in that case, distinguishable; in Biondo, the plaintiffs had rested on their desire for the promotion, whereas, in the present case, the plaintiffs produced evidence regarding their fitness for promotion. 382 F.3d at 688. We acknowledge this distinction, but conclude that it misapprehends the nature of the burdens in the lost-chance damages inquiry. The district court treated the issue as though once the plaintiffs had proved discrimination, the lost-chance doctrine was effectively a measure by which the defendants could reduce their liability by showing that the plaintiffs were not the likeliest candidates for promotion in the absence of discrimination. See R.289 at 2531 ("[I]t seems to me at some point the shifting occurs."). Our mention of the absence of evidence of the plaintiffs' qualifications in Biondo did not mean that a plaintiff is entitled to rest on a presentation of his or her qualification. Indeed, we noted that the Biondo plaintiffs had each chosen to present "a non-comparative case," a failing, on their part, because potential promotees "do not strive to meet an absolute standard; they compete against their colleagues." Biondo, 382 F.3d at 689. We stated that the plaintiffs should have demonstrated that they were better suited than their rivals — indeed, much better suited, as the jury in that case found the plaintiffs had a one hundred percent chance of promotion absent discrimination — and noted that the plaintiffs "suffer from the omission" of appropriate comparative evidence and actual evidence of how the plaintiffs subsequently fared in attempts toward promotions against other candidates. Id.12

The plaintiffs bear the burden of establishing their losses, and, in the case of promotional opportunities, it is the plaintiffs' burden to establish the probability that they would be promoted over all other potential candidates. Only in the face of evidence that they would have been promoted over any other non-plaintiff candidates absent discrimination would the district court have been justified in instructing the jury to limit its consideration of the plaintiffs' lost chances to the consideration only of other plaintiffs. Although the evidence in the record strongly supports the conclusion that the lieutenant-plaintiffs were qualified — indeed, that is uncontested — it necessarily does not follow from our case law that the plaintiffs were entitled to an instruction that treated them as though they were the only qualified individuals.13

We further conclude that the error in instructing the jury on how to establish probabilities of promotion infected more than the economic damages award to which the percentages were directly applied. Specifically, although the defendants asked the district court, in their motion for remittitur, to apply the lost-chance percentages to the compensatory damages as found by the jury, the district court read this court's opinion in Biondo as not requiring a reduction in compensatory damages for emotional injury on the basis of the probability of promotion. R.264 at 3. This was error. As we have noted, the purpose of compensatory damages is to compensate for what was lost, and under the damages rubric that applies, what was lost is only a chance. In Biondo, we vacated compensatory damages awards that were not properly scaled to the lost chance. Biondo, 382 F.3d at 690. We acknowledged expressly that compensatory damages for a lost chance must be linked to promotional likelihood. Id. In fact, we specifically stated that "[a] change in the promotion probabilities and dates requires everything else to be redone." Id. Accordingly, on remand, compensatory damages must be redetermined taking into account the applicable probabilities of promotion, consistent with this opinion.14

In addition to the claimed errors with respect to the application of the lost-chance doctrine, the defendants also contend that the district court erred in refusing to offset certain interim earnings against back and front pay. Although lieutenants were in a lower pay grade than were captains, they were eligible for overtime, which was often a source of substantial additional income for a lieutenant. Instead of earning overtime, when captains were required to work additional hours, they received no additional compensation, but they could accrue flextime for certain of those hours worked.

Before the district court, and again on appeal, the defendants urge that a captain's base pay should be compared to a lieutenant's base pay plus overtime earnings. See Appellants' Br. at 48-54. The district court rejected this method of economic damages assessment, concluding that there was "no sure way, a way that this court could be comfortable with in attempting to calculate a dollar amount for either the flextime or the overtime." R.291 at 303-04. Instead, the district court fixed the measure of wage loss at the base pay of a lieutenant after completion of the probationary period to the base pay of a captain. R.291 at 304; R.205 at 2.

We note that there is actual record evidence of the amounts of overtime pay in the plaintiffs' past earnings. See R.298, Ex.565 (admitted payroll records). We also note that the district court heard testimony regarding the relationship of flextime to overtime, but struck the testimony because the defendants had failed to comply with a continuing discovery order for ongoing flextime records. R.291 at 249-53. The defendants had produced evidence that flextime would not produce additional compensation, except in rare circumstances involving retirement before certain flextime rules were in place. R.291 at 289; R.298, Ex.120. Accordingly, at least with respect to back pay, there were admitted amounts of overtime earnings, and evidence that flextime would have treated those extra hours as simply a reallocation of the hours a captain was expected to work in the course of a salaried year absent some application of the special retirement pay-out rules. With respect to front pay, there was some testimony regarding the tightening of overtime earnings that would have drawn into question whether future rates of overtime could be in any way comparable to past rates. R.291 at 262-63.

We believe that both overtime and flextime had economic value and therefore must be considered in determining economic damages. With respect to back pay awards and overtime earnings, hard numbers are available, and the simple fact that the economic value of flextime is more difficult to quantify is simply not a justification for ignoring both issues in determining compensatory damages. On remand, the district court must take these matters into consideration.15

3. Determining a Cut-off Point for Front Pay Awards

The defendants seek review of one final matter on the measure of compensatory damages. Upon the district court's instruction, the Special Master considered front pay awards to end on the earlier of the date of a plaintiff's retirement, or after two years of service as a captain. See Special Master Report, R.209 at 2. The defendants submit that the appropriate cut-off point should have been the first unhindered opportunity for promotion.

The defendants are correct that our ruling in Biondo sets an end-point for front pay at the time of the first unimpeded promotional opportunity, not a particular plaintiff's actual date of promotion. Biondo, 382 F.3d at 691. This approach reflects Biondo's general application of lost chance principles: The plaintiff who suffered discrimination in promotion did not lose a promotion, but some quantifiable chance at a promotion; when that chance is unimpeded by discrimination, the injury ceases.

In this case, the district court erred in concluding that the plaintiffs' promotional opportunities would not be "unhindered," as Biondo requires, because they would be placed back in the pool of eligible applicants, not given preferential treatment for the first promotional opportunities. R.291 at 299 ("[W]hen I first read [about the unhindered promotional opportunities claimed by the defendants], I understood it to mean there would be no hindrance to them being the next promotion. Now from what I have heard I'm inclined to believe that that does not mean unhindered, it just means that they're back in the pool that is eligible."); id. at 294 ("To argue [as defendants have] that there are still other candidates seems to defeat the defendants' earlier argument that nine of the plaintiffs will have unburdened promotional opportunities."). On remand, the district court must determine "the time a reasonable person needs to achieve the same or an equivalent position in the absence of discrimination," Biondo, 382 F.3d at 691, which in this context, as in Biondo itself, means an opportunity to compete on equal footing with other candidates of any race. We note that, because the City promotes officers to captains only when a vacancy in the rank of captain arises, the frequency of this availability should be among the relevant considerations in determining when each of the seventeen plaintiffs, and in particular, those who have not yet been promoted or have not yet retired, would have an unimpeded promotional opportunity.

The individual defendants also challenge the punitive damages awards assessed against them. Specifically, they contend that there was insufficient evidence of malice to submit the issue to the jury and that, in any event, the punitive damages awards are excessive and cannot stand.

In Smith v. Wade, 461 U.S. 30, 56, 103 S. Ct. 1625, 75 L. Ed. 2d 632 (1983), the Supreme Court enunciated the appropriate standard for the availability of punitive damages in an action under § 1983: "[A] jury may be permitted to assess punitive damages in an action under § 1983 when the defendant's conduct is shown to be motivated by evil motive or intent, or when it involves reckless or callous indifference to the federally protected rights of others." This court reviews whether the issue of punitive damages was properly submitted to the jury for an abuse of discretion. Gentry v. Export Packaging Co., 238 F.3d 842, 851 (7th Cir.2001).

As the plaintiffs correctly note, there is some evidence in the record that the defendants at times failed to require the Chief to comply with their policies mandating that he submit various paper records to the Board along with a candidate for promotion. R.298, Ex.18 at 20 (requiring written explanation of reasons for promotees); R.275 at 834 (noting an absence of information regarding assignments for captains); R.275 at 770 (noting a lack of resumes). During the liability phase, the jury found the personal participation of the Commissioners in discrimination, and this finding would suggest that the jury concluded that the Commissioners had done more than simply evaluate single candidates that had come before them, as the statute requires. The plaintiffs' also produced evidence of the apparent racial animus of Chief Jones of which the Commissioners were aware, and introduced the 2001 Dimow report. This evidence could be interpreted as having put the Commissioners on notice that the promotional policies in effect in the Police Department, over which they had authority, were resulting in a quickly changing racial make-up exhibiting an under-representation of white males on the command staff. Taking that evidence in the light most favorable to the plaintiffs and in light of the jury's verdict, the Commissioners knew about a problem, failed to act to control it, as the responsibility of their office required them to do, and knowingly participated in its continuance. This evidence permitted a jury to find reckless or callous indifference to the federally protected rights of the plaintiffs, and we must therefore conclude that the district court did not abuse its discretion in submitting the issue of punitive damages to the jury.

Finally, relying on the Supreme Court's recent decision in State Farm Mutual Automobile Insurance Co. v. Campbell, 538 U.S. 408, 418, 123 S. Ct. 1513, 155 L. Ed. 2d 585 (2003), the defendants submit that, if the punitive damages stand as supported by the evidence, they should be reduced because they exceed reasonable limits. Although it is true that the Supreme Court expressed concern about some awards in excess of four times compensatory damages, see id. at 425, 123 S. Ct. 1513 (and here, ten of the seventeen plaintiffs received punitive damages awards of between 4 and 10.73 times their compensatory damages, R.215 at 2-3), the compensatory damages in this case are relatively low; the Supreme Court has indicated that greater punitive damages ratios may comport with due process under that circumstance. State Farm, 538 U.S. at 425, 123 S. Ct. 1513. Accordingly, State Farm does not require us to reduce the award as excessive as a matter of law. See Mathias v. Accor Economy Lodging, Inc., 347 F.3d 672, 678 (7th Cir.2003) (approving, post-State Farm, a $186,000 punitive damages award, a thirty-seven-fold increase over the compensatory award of $5,000).16

We note that the punitive damages award was equal with respect to each Commissioner and with respect to Chief Jones, apparently irrespective of the fact that some Commissioners sat on the Board over a significantly smaller number of promotions than others and the concededly discriminatory acts of Chief Jones. "[P]unitive damages should be proportional to the wrongfulness" of each defendant's actions. Mathias, 347 F.3d at 676. Although the jury was instructed to consider the "reprehensibility of the Defendants' conduct" and the likelihood that a defendant would repeat the conduct absent an award of punitive damages, R.165 at 3, it should have been more clearly instructed that each individual defendant's actions and fault must serve as the basis for fashioning an appropriate punitive damages award.

For the reasons stated above, we affirm the judgment of the district court with respect to liability and reverse the judgment of the district court as to damages. We remand the case for further proceedings consistent with this opinion. The parties shall bear their own cost on this appeal.

AFFIRMED in part, and REVERSED and REMANDED in part