183 F.3d 586 (7th Cir. 1999)
Paul Hill, Plaintiff-Appellant,v.Howard L. Ross, et al., Defendants-Appellees.
No. 98-3942
United States Court of Appeals, Seventh Circuit
Argued May 17, 1999Decided June 23, 1999

Appeal from the United States District Court for the Western District of Wisconsin. No. 97-C-0804-C--Barbara B. Crabb, Judge.[Copyrighted Material Omitted]
Before Easterbrook, Ripple, and Evans, Circuit Judges.
Easterbrook, Circuit Judge.


1
After the Psychology Department of the University of Wisconsin at Whitewater voted to offer Paul Hill a tenure- track position in clinical psychology, its chairman received a flurry of objections from Howard Ross, Dean of the College of Letters and Sciences. Ross wanted the Department to hire a woman instead. When the Department stood on its choice, Ross blocked the recommendation, and the position was left vacant. Sex discrimination in employment violates Title VII of the Civil Rights Act of 1964. Industrial Union, UAW v. Johnson Controls, Inc., 499 U.S. 187 (1991); Johnson v. Transportation Agency of Santa Clara County, 480 U.S. 616 (1987). Because the University is a state institution, the equal protection clause of the fourteenth amendment also applies. United States v. Virginia, 518 U.S. 515 (1996). Yet the district court granted summary judgment for the University, concluding that its decision was supported by a valid affirmative action plan.


2
Wygant v. Jackson Board of Education, 476 U.S. 267 (1986), and Johnson v. Transportation Agency, apply Steelworkers v. Weber, 443 U.S. 193 (1979), to public bodies, holding that affirmative action plans may justify employment decisions that otherwise would violate Title VII, the Constitution, or both. Wygant and Johnson follow up on the approach taken by Justice Powell, whose separate opinion in Regents of the University of California v. Bakke, 438 U.S. 265 (1978), concluded that under an affirmative action plan race or sex may be a factor in a hiring decision but can not be dispositive--not, at least, unless the plan is designed to overcome the effects of past discrimination. Both Wygant and Johnson stressed that the plans in question used race and sex only as factors in a more complex calculus, not as independently dispositive criteria. Some underpinnings of Wygant and Johnson were removed by Adarand Constructors, Inc. v. Pena, 515 U.S. 200 (1995), which held that race may not be employed as a thumb on the scale in granting public contracts or broadcast licenses. Cases such as Hopwood v. Texas, 78 F.3d 932 (5th Cir. 1996), and Lutheran Church-Missouri Synod v. FCC, 141 F.3d 344 (D.C. Cir. 1998), understand Adarand as forbidding a public agency to make any use of race or sex other than as a remedy for prior discrimination. But we need not enter this fray, for three reasons.


3
First, a jury reasonably could decide that Dean Ross used Hill's sex not as one factor among many, but as the sole basis for his decision. The Psychology Department proposed to make two appointments in spring 1995, one in clinical psychology and one in social psychology. Both candidates were male. Ross informed the Department: "As indicated on the recruitment signoff sheet, the hiring goals for the [psychology] department is [sic] 61.8 percent women and 9.8 percent minorities. According to the attached workforce utilization report, there are 4 women and 2 minorities in the department. Thus, the department needs 3.23 women to reach its target." (How it was going to appoint 23/100 of a woman Ross did not explain.) Ross stated in a later email message that "[t]wo male candidates cannot go forward." And still later: "We cannot send two male candidates forward, given the targets in the department." Memos signed by Dean Ross did not weigh other considerations in Hill's favor (such as his academic achievements or the strong and unanimous backing by the Department); these omissions could support a conclusion that sex played a role larger than that allowed by Wygant and Johnson in the absence of a finding of prior discrimination.


4
The University does not contend that its affirmative action plan is essential to eradicate the consequences of prior discrimination, either in the Psychology Department or elsewhere. To the contrary, the University denies that it has ever discriminated on the basis of sex. The University's Affirmative Action Review Committee concluded in a report dated September 12, 1994, that the Psychology Department had not discriminated against women in hiring. Although it found that two members of the Department exhibited discriminatory attitudes, this Committee concluded that these professors' "obstructionist or less than collegial behavior did not . . . prejudice [an applicant's] chance for employment." The University does not seek in this litigation to contradict the report's conclusion. Nor does the University contend that it has some other compelling justification, after the fashion of Wittmer v. Peters, 87 F.3d 916 (7th Cir. 1996).


5
Second, the University's affirmative action plan does not require Dean Ross's actions. According to the University, Dean Ross rejected the Psychology Department's recommendation not because Hill is male, but because the Department submitted one name rather than three for Ross to consider. Yet none of Ross's messages to the Department complained about the paucity of names (as opposed to the sex of the candidates). As the University's lawyer admitted at oral argument, nothing in the University's affirmative action plan requires departments to submit lists rather than single preferred candidates. Anyway, a trier of fact might see a multiple-name requirement as nothing but a smokescreen for discrimination. (Dean Ross may have wanted more names only to ensure that one woman was included, planning to appoint the woman without regard to the academic virtues of the candidates.)


6
Affirmative action plans may be arranged along a spectrum. See Christopher Edley, Jr., Not All Black and White: Affirmative Action and American Values 18-24 (1996); David Benjamin Oppenheimer, Understanding Affirmative Action, 23 Hastings Const. L.Q. 921, 926-33 (1996). On the one end are detailed hiring quotas designed to overcome past discrimination. On the other end are the sort of plans that all federal contractors must adopt, under President Johnson's Executive Order 11246, a directive enforced by the Office of Federal Contract Compliance Programs. Plans of the latter kind promise to search intensively for minority candidates and to ensure equal opportunity by clearing away barriers to employment; they do not entail preferential treatment for any group in making offers of employment.


7
According to the University's brief, it has the sort of plan that every federal contractor adopts "to comply with the federal government requirements". The University's "Equal Employment Opportunity and Affirmative Action Policy", which we take to be its affirmative action plan, is a four-page document, issued by the University's Provost, very much in the spirit of Executive Order 11246. It prohibits discrimination and promises outreach to find and assist members of underrepresented groups. The only portion of this plan even arguably relevant to Dean Ross's decision is this platitudinous paragraph:


8
UW-Whitewater is committed to a positive, continuing, result-oriented program to assure meaningful employment opportunities to all segments of the community and specifically to ethnic minorities, women, and the handicapped. These groups have suffered in the past from barriers to employment and promotion. The Affirmative Action program includes a continuing analysis of the employee structure to discover where there is under-utilization of ethnic minorities, women, and the handicapped; to establish goals to remedy deficiencies and guidelines and procedures to maximize opportunities for the recruitment of ethnic minorities, women, and the handicapped. Every position vacancy announcement must invite applicants from the aforementioned categories. Every person or committee charged with the responsibility of filling an unclassified vacancy must indicate to the Affirmative Action Officer the specific means to be used in directly contacting potential candidates in the respective categories.


9
Dean Ross did not conclude that the Psychology Department had failed to solicit applications from women; he did not mention any shortcomings in how the Department evaluated the candidates; he cared only about the bottom line. Whatever the phrase "result-oriented program" may mean, it does not (and can not) jettison the statutory and constitutional anti-discrimination principle and establish a quota system at the University of Wisconsin--though, as we have said, a jury could conclude that this is how Dean Ross administered it.


10
Third, any preference for one sex in making offers of employment, however slight the preference may be, must be justified. The Court said in Virginia that the justification must be "exceedingly persuasive." 518 U.S. at 531, 533. Nonetheless, the University insists that it need not offer any justification. On its view, so long as an employer has any kind of affirmative action plan, the burden is on the plaintiff. Things can't be that easy, however. Employers may not shed their responsibilities under Title VII and the Constitution by intoning "affirmative action."


11
Wygant says that "[t]he ultimate burden remains with the employees to demonstrate the unconstitutionality of an affirmative-action program" (476 U.S. at 277-78), and Johnson adds: "we see no basis for a different rule regarding a plan's alleged violation of Title VII." 480 U.S. at 626. Whether these decisions survive Adarand and Johnson Controls is a question for another day, because Hill has done all that he need do under Wygant and Johnson. In Johnson the Supreme Court adapted the burden-shifting approach of McDonnell Douglas Corp. v. Green, 411 U.S. 792 (1973), to affirmative action plans, stating that once the plaintiff establishes that race or sex "has been taken into account in an employer's employment decision, the burden shifts to the employer to articulate a nondiscriminatory rationale for its decision. The existence of an affirmative action plan provides such a rationale. If such a plan is articulated as the basis for the employer's decision, the burden shifts to the plaintiff to prove that the employer's justification is pretextual and the plan is invalid." Johnson, 480 U.S. at 626. Hill has done what needs to be done to show that reliance on the plan may be pretextual by demonstrating that (i) the written terms of the plan do not support Dean Ross's decision, and (ii) the University denies having engaged in prior discrimination. An employer that wants to use sex (race, religion, etc.) as a factor in hiring decisions and yet denies ever engaging in discrimination (and therefore denies that a remedy is in order) must supply some other "exceedingly persuasive" justification. Once it does, Johnson holds, the plaintiff bears the burden of overcoming it; but neither the University's plan nor its brief advert to any justification. Cf. Janowiak v. South Bend, 836 F.2d 1034 (7th Cir. 1988).


12
Where, for example, does the Dean's 61.8% target come from? Having insisted that it bore no burden, even a burden of production, the University did not reveal the answer in discovery. We gather from references in other documents, and in the University's brief, that it is the proportion of all doctorates in clinical psychology, awarded since 1980, that are held by women. Let us suppose that all members of the Psychology Department have been hired since 1980 (avoiding any need to account for the possibility that fewer women received advanced degrees in earlier years), that male and female doctorates are equally likely to seek teaching positions, and that the University views all holders of doctorates as eligible for appointment. This may not be so; many universities want to hire only people with a track record of publications; but again we will make the simplifying assumption. Then if the Department had hired a large number of professors, say, 250 or 500, any significant departure from 62% female would be surprising and require justification to dispel the possibility that the departure was caused by sex discrimination (or a failure of outreach). But the Psychology Department is not large. In spring 1995, when it proposed to hire two additional tenure-track faculty, the department had ten members with tenure or on the tenure track. Four of the ten were women. If it had hired two more tenure-track faculty, to reach twelve, then a ratio of seven women to five men would have produced the closest approximation of 62% female. This appears to be the source of Dean Ross's statement that the Department needed an additional three women to meet its target.


13
Suppose the University hired blindly from a pool that is 62% women. How likely is it that exactly seven of twelve would be female? What the University appears to have in mind is a world in which the absence of discrimination means that every department would exactly mirror the population from which its members are hired. But that is statistical nonsense. Suppose a university has 64 departments or faculties, each with five members; that half of all persons meeting its standards for appointment are women; and that the university makes appointments by drawing blindly from an urn containing infinitely many balls, each representing a candidate. Then the most likely outcome is that two of the 64 departments would be all male (25 = 32) and two would be all female. Ten of the 64 departments would be 80% male, and another ten 80% female. The remaining forty would have three men and two women, or three women and two men. The existence at this hypothetical university of 24 departments that were composed 80% or more of one sex would do nothing at all to imply discrimination or a need for corrective action; such a distribution is simply the result of chance.


14
This particular distribution, with four all-male or all-female departments, is only one possible outcome of repeated draws from the urn. Suppose a given university turned out to have six or eight such departments. Fairly simple statistical inquiries can reveal the probability that a circumstance less wholesome than chance was to blame. Some of these methods are discussed in Paul Meier, Jerome Sacks & Sandy L. Zabell, What Happened in Hazelwood: Statistics, Employment Discrimination, and the 80% Rule, 1984 Am. Bar Foundation Research J. 139, 158-70; and Mister v. Illinois Central Gulf R.R., 832 F.2d 1427 (7th Cir. 1987). We do not pursue the issue, however, because the University, which must provide an "exceedingly persuasive" justification for its actions, has not supplied the essential data. This record does not reveal the sizes of the departments at the University, the distribution of faculty by sex among the departments (and the populations from which they hire), and so on. It is therefore impossible to estimate the probability that nondiscriminatory hiring would have produced the observed pattern. The affirmative action plan in Johnson covered 238 skilled craft positions, of which none was held by a woman. Justice O'Connor remarked in a concurring opinion that, when such large numbers are involved, the "inexorable zero" is all the justification needed for some kind of response. 480 U.S. at 656-67, quoting from Teamsters v. United States, 431 U.S. 324, 342 n.23 (1977). Zero of 238 is exceedingly improbable, if chance alone is an explanatory variable. When the pool is 5% female (as it was in Johnson), 0 for 238 will occur by chance once per 200,000 employers (1 ÷ 0.95238). Four of ten--the situation at the Psychology Department in 1995 when Dean Ross blocked Hill's appointment--is much more likely to occur by chance, even when the pool is 62% female. A proposal to hire two men (or two women) for two new positions likewise easily could reflect merit hiring.


15
Knowing the full distribution of academic staffs at the University could cast a more sinister light on things. To return to the 64-department hypothetical, suppose that university had four departments with five men and no women, and no all-female departments; suppose it had 20 departments that were 80% male, and none 80% female. Instead of the expected bell-shaped distribution, this university would have only one side of the bell. Truncation or skewness of the distribution would speak loudly, as the "inexorable zero" did in Johnson, and could justify intervention to make things look more like the outcome of a nondiscriminatory process. Nothing in this record suggests that the University of Wisconsin at Whitewater has any such problem, however. Dean Ross wanted to look at the Psychology Department in isolation, which no statistician would do, and to collapse the distribution by compelling every academic department to mimic the population from which it was hired. That would be as sure a sign of discrimination as is a lopsided or truncated distribution, and a plan to have every department duplicate the pool from which it is drawn cannot be sustained as a valid affirmative action plan. Such a plan neither rests on a powerful justification nor uses sex in a way that is narrowly tailored to the justification. See Britton v. South Bend Community School Corp., 819 F.2d 766 (7th Cir. 1987) (en banc) (discussing the importance of the "narrow tailoring" requirement for affirmative action plans).


16
Perhaps the University can offer more in defense of its decision, now that it knows where the burden lies. On this record, however, Hill comes closer than does the University to establishing entitlement to victory. The judgment is reversed, and the case is remanded for further proceedings consistent with this opinion.

