Affirmative Action in Higher Education as Redistribution

North American Philosophical Publications

Affirmative Action in Higher Education as RedistributionAuthor(s): Louis M. GueninSource: Public Affairs Quarterly, Vol. 11, No. 2 (Apr., 1997), pp. 117-140Published by: University of Illinois Press on behalf of North American Philosophical PublicationsStable URL: http://www.jstor.org/stable/40435987 .

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Public Affairs Quarterly Volume 11, Number 2, April 1997

AFFIRMATIVE ACTION IN HIGHER EDUCATION AS

REDISTRIBUTION

Louis M. Guenin

action in higher education appears to be mired in a justificatory predicament. Provoked by the phenomenon of

reverse discrimination, a current of public opinion and some judicial rulings have recently exposed weaknesses in affirmative action's standard defenses. A successful justification, so I shall argue, may require a rationale heretofore not exploited.

To explore this justificatory predicament, it is helpful first to un- derstand whether there obtains some reason by which all cant of quotas should be anathema, as nowadays is often assumed. I begin with Michael Walzer's characterization of quotas (or what he calls "reservations") of publicly significant positions (or what he calls "offices"). For this purpose positions are publicly significant when their occu- pants are chosen by the public or chosen by publicly regulated proceedings. Postponing whether, all things considered, enrollment should be assimilated to an office, we may at least observe that educational institutions admit students in ways that are publicly regulated.

By virtue of a reservation, says Walzer, "the members of all those groups except the one for which the reservation is made are treated as if they were foreigners. Their qualifications are not attended to; they have no candidate rights."1 This is not to say that reservations are always bad. Justice for Walzer is an obligation binding upon those within a state toward each other. He holds that the choice of whom a state shall admit is one over which citizens enjoy wide latitude, and thus it is not unjust per se to categorize someone as a "foreigner." A justifi- able quota system might be realized, for example, in a binational state in which each nation elects a specified number of representatives to the state legislature. In a pluralist society, other offices might be reserved. A city might distribute positions on its police force so as to mirror the distribution of distinguishing features of its citizenry.

117



1 1 8 PUBLIC AFFAIRS QUARTERLY

We often imagine impartial consideration of candidates' characteristics according to criteria consistently applied. (The characteristics for which criteria select are commonly called "qualifications.") I shall call such treatment simply "impartial consideration."2 This regime has not always been prosaic. We owe the slogan "careers open to talents" to the French revolutionaries. The practices of impartial judging of qualifications and administration of examinations supervened only in relatively recent times upon a history of nepotism and simony. The latter practices, suggests Walzer, introduce an influence like kinship or money that may be appropriate for one "sphere of justice" into a sphere like office where they do not belong.

An alternative to impartial consideration issues from a disdain for office holders as persons who believe themselves entitled to their positions and perquisites and who display what "officiousness" captures. To repudiate these pretensions, the populist radical would insist that offices be distributed randomly or by rotation.3 The populist radical might suggest that one select students randomly from those qualified for training, and thereafter select professionals randomly from train- ees qualified for positions. That presupposes a way to reckon who is qualified in both instances; the rationale for impartial consideration revives. Even assuming such means, random selection from among the qualified would appear inefficient unless differences in talents and acquired proficiencies are immaterial. Such condition seems improb- able for roles such as teacher, engineer, scientist, and physician as to which gradations of talent and proficiency are observable, valuable, and sometimes even critical for protecting the public from harm.

Suppose that a society does arrange offices so as to represent subsets of the population. Can it meet the desideratum of impartial consideration? Impartial consideration need not be neglected when a polity forms a binational legislature or other body of citizen representatives. Group membership, notes Walzer, may tenably be a minimal qualification for serving as a representative of a group. Whether this is just, he suggests, may not be the question; it may suffice for a representative scheme that it achieve an accommodation among groups. The situation appears otherwise for the majority of publicly significant positions that qualify as "offices" in an industrialized democracy. These are likely to be civil service jobs or to require licensure by a public authority or credentials earned in an institution accredited by a public authority. It is not clear that any of these positions should be considered representative. Or even that they could be so. A given citizen is a member of many subsets of the population specified by ethnic, religious, economic, and other characteristics. The relation that pairs citizens to such subsets is not a function. There are good reasons to



AFFIRMATIVE ACTION IN HIGHER EDUCATION 1 1 9

oppose making it one, to applaud those who traverse boundaries.4 Hence group representation may be problematic even for a police force or legislature.

Concerning anyone who is not a representative - e.g., a student, regardless whether that role is an office - one may argue a fortiori that the only subset of the citizenry such that membership should be a necessary condition is the subset of citizens possessing relevant qualifications. Quotas typically require, as a necessary condition for a given station, membership in some subset other than the qualified. Quotas are expedient. They present a sure way to diversify a population by a characteristic. To assure that a college's band will be filled or that the Gilbert and Sullivan Society will have a full complement, a college may merely reserve places in an entering class for high school musicians and thespians. But even without explicating the notion of impartial consideration, it seems obvious that any consideration of applicants' nonartistic qualifications for reserved places is denied when, without considering their nonartistic qualifications, applicants are by an artistic reservation excluded. Any consideration of applicants' nonethnic qualifications for reserved places is similarly denied when, without considering their nonethnic qualifications, applicants are by an ethnic reservation excluded.

If justice is not in point when devising a system of representation, for nonrepresentative roles it is prominent. A familiar defense of quotas is that they rectify past injustices such as discrimination on morally arbitrary grounds. To this the usual reply is that it is dubious to link the living with injustices of the dead (about which more later). Here we need only observe that the reply seems as applicable to a "temporary" quota system, a device sometimes imagined to function until it and other social policies can offset the effects of past discrimination, as to a permanent one. In any quota system, applicants are compared only to other members of the group in which they are classified. Un- less we assume that qualifications distribute evenly among groups (an assumption, notes Walzer, "that for any given applicant pool is bound to be false"), the minimum standard for selection will vary by group. It may be a distortion to regard the polity as a federation of groups rather than a community of citizens.

Despite their use in recent history precisely for the purpose of redressing discrimination, quotas are now seen by many as unacceptable. Eschewing the disfavored concept, the contemporary defense of affirmative action usually adverts to preferences.5 The judicial mien invokes a physical metaphor. When a scheme is "viewed" by the pseudo-optical device of "strict scrutiny," can the court espy a cou- pling between a preference and a "compelling state interest"? One might



1 20 PUBLIC AFFAIRS QUARTERLY

more straightforwardly say that ethnicity should be a qualification but not a necessary one. A scheme that treats ethnicity as a qualification but not a necessary one would appear to avoid a quota's defect of utterly excluding from consideration for some targeted number of places those who lack given ethnic qualifications.

It must be added that unless an ethnic qualification is treated by college admissions officers as a fairly important one, few who meet it will be chosen. Where grades and test scores are pivotal, how much weight should be given ethnicity as a qualification? Many nonacademic qualifications are, without much controversy, given considerable weight.6 These include proficiency in athletics, music, theatre, and the visual arts. Otherwise many an entering class would be bereft of musicians, thespians, and artists. If, as some have argued, a significant likelihood of enhancing the communal learning experience is an appropriate qualification, and if ethnic diversity enhances the communal learning experience, weight could be given to ethnicity just as weight is given to artistic talent.

Evidence of pedagogical enhancement by diversity may be lacking. Even if such evidence is adduced, it seems probable that for a given college class, there will be some threshold number or portion of students upon the admission of which the benefit to pedagogy of ethnic diversity is either achieved or begins to display significantly diminishing marginal returns. I shall call such threshold "pedagogical prime." For present purposes we do not need to imagine how we would calculate such quantity. We may employ it solely as a referent for purposes of drawing a contrast with that presumably larger number or portion of minority students that would be admitted if, instead of seek- ing merely to optimize learning among those enrolled, an institution's goal were to benefit a minority group by admitting as many of its members as possible. If rectification of injustice were a ground for affirmative action, then given many victims of discrimination and their descendants, one might argue for allotting most of the spaces in a given entering class to minority applicants. Or one could decide that the class should mirror the ethnic composition of the society. In any case it seems probable that the numbers and proportions of minority admittees sought by many affirmative action policies will greatly exceed pedagogical prime.

To implement preferences but avoid quotas, an institution must weight substantially, though not derivatively from targets, the elements of some set of qualifications for admission. The institution will expect that those who possess certain weighted qualifications will rise, just as students who present outstanding grades and test scores will rise, to the upper levels of the applicant pool. The case earlier noted against quotas will be as compelling for a quota of musicians as it is




for a quota of members of a given race. But if one adduces a cogent rationale for the presence of members of a given group (e.g., to reach pedagogical prime or to assure enough Savoyards), race as a highly weighted qualification should be no more objectionable than musical talent as a highly weighted qualification. The contrary view is that the difference between such a system of weighted qualifications and a system of quotas is merely cosmetic. If an institution's music program usually presents a fixed number of ensembles, each of which is optimal within a relatively narrow size range, there will be strong incentives to weight musical talent so as to admit the total number of musicians needed for such complement of ensembles. That number will be a disguised quota. On the other hand, unpredictability and failure of the number of admittees possessing a given qualification to fall within a narrow range from year to year might be evidence that a system of weighted qualifications differs meaningfully from a quota system. Here it is pertinent to note that pedagogical prime is at best imprecisely known. It hardly seems possible to infer what weightings are necessary to achieve it. The weighting of ethnicity with a view to enhancing the learning experience may thus be less vulnerable to objection as a disguised quota system than is the weighting of musical talent.

A critic of a system of weighted qualifications would be correct to interject that, when applied to a given applicant pool, such a system entails a particular distribution of qualifications among admittees. When a system assigns numerical scores for various traits, as did an admissions system employed by the University of Texas Law School that was recently held to violate the "equal protection" clause of the Fourteenth Amendment to the U. S. Constitution,7 the outcome for a given pool is determinate. One may be splitting hairs to claim that the weighting of any qualification effects anything other than a quota for it. In its first year of operation, a system of weighted qualifications may fairly be assimilated to quotas. As applicant pools later vary, even if weighting of qualifications is held constant, disparate distributions of qualifications from one class to another are likely. An institution may claim that the originally contemplated distribution is paid no heed. But of course it will continue to be the case that the system is predicated on the projected distribution of qualifications on which its authors doubtless relied when they designed it. Critics may further object that since a college, especially one without a rolling admissions policy, can ascertain the features of its applicant pool each year, as it admin- isters a system of weighted qualifications it merely operates a disguised though different quota system each year. An institution can manipu- late the distribution of qualifications just as powerfully by weighted qualifications as by quotas.




Thus the line between preferences and quotas is not sharp. One cannot easily defend an affirmative action program merely by saying that it is the former and not the latter. In both cases a rationale is needed. In both cases an institution must answer complaints of reverse discrimination. In both cases there is risked a discomforting experience for minority students about which there has recently been speculation, viz·, a realization that some majority students appear to assume that, were it not for affirmative action, the minority students would not be enrolled.

These pressures intensify scrutiny of an institution's articulated pedagogical aims. One can develop a cogent case for an institution's expertise in presenting the educational offerings its faculty judges best, and for a measure of autonomy in general. Statutes and courts, on the other hand, pay more attention to the grant or denial of admission in respect of what is just for a given applicant. To the extent that courts consider large scale societal or even institutional effects, they tend to subsume any consideration of a state institution's autonomy within the notion of a "compelling state interest." The latter conceptual crea- ture is hunted by courts, in the physicalist "scrutiny" earlier noted, across the terrain of everything from garbage disposal to zoning. It is a concept that lacks any specifically educational import. Yet since the law will often vindicate a reasonable commercial purpose when a re- straint of trade is attacked as violative of the Sherman Antitrust Act, one should think that the law might vindicate an educational purpose. One might contend that an admissions policy serves an educational purpose when, knowing that not every qualified applicant can be admitted, an institution preserves the optimal educational experience that it knows how to deliver for those it does admit.

While this is an interesting principle, it may only shift the battleground. Views may differ about how to provide the optimal educational experience. We know how profoundly a student's education is influ- enced by fellow students. Nonetheless educators have noted the lack of hard empirical evidence about the extent to which ethnic diversity enhances the educational experience.8 This concern is especially tell- ing in fields such as mathematics that may be relatively remote from social and cultural issues. When it is noted that colleges favor athletes, children of alumni, or children of potential donors in admissions, observers asked to respect pedagogical judgment may be sceptical. A question less often asked is whether the benefit of learning in the com- pany of especially bright students is such that places should be awarded to less talented students so that, inter alia, the pool of very bright students will be dispersed. Something of this dispersive effect may already occur because merit scholarships are scarce.

Here autonomy may be the academic administrator's refuge. Had the recently invalidated Texas system of weighted qualifications been



AFFIRMATIVE ACTION IN HIGHER EDUCATION 1 23

designed only for pedagogical prime, autonomy and expertise might have been a cogent defense of it. Like many other affirmative action programs, that scheme appeared to assign scores to applicants in virtue of their possession of various traits. It mechanistically established quantitative thresholds for automatic admission and for highly probable admission. The thresholds were lower for minority than for majority applicants. Such a system apparently was not conceived solely as a means to enrich the learning experience of all. For "all" consists predominantly of members of the ethnic majority. This suggests a different problem. While minority students also presumably benefit from a diverse cohort, their presence is often cited for what it contributes to others' learning. Are minority students impermissibly treated as means? The second form of Kant's categorical imperative is not violated unless minority students are treated solely as means. The authors of the Texas scheme appear to have striven to treat minority students as ends. Their ostensibly simple goal was to advance the welfare of a minority group by admitting as many of its members as possible.

When an institution is past the threshold of pedagogical prime, which is to say that the marginal contribution to learning that may be expected from admitting still more minority students is low, what jus- tifies assigning such weight to ethnicity as to generate admissions of more members of a given ethnic group? A standard reply earlier noted is the rectification of past injustice, or, as Fishkin more precisely renders it, the view that "compensation of previous violations of merit, that is, discrimination, require present violations of merit, that is, pref- erential treatment." But as we can readily see if we attempt to press hypothetical claims, the notion of tracing past injustices to living persons is a facile but usually incoherent one. It requires subjunctive claims about what would have occurred if injustice had not occurred. It requires specifying ways in which living persons are connected to past perpetrators.9 By dint of whatever dubious linkage is claimed, we must then deny some applicants impartial consideration of their qualifications. The law sometimes provides, after surmounting formi- dable questions about tracing and balancing of equities, that the legal rights of one who acquires or inherits transferable property are defea- sible because of a defect in a predecessor's title. But we do not regard admission to college as transferable. To regard it as such would con- tradict the premise that various qualifications are necessary for admission.

It seems more promising to propose a deliberate policy of assisting anyone who, regardless of history, is hampered by inferior developmental conditions. To do this, one might concede that no one inherits culpability and hence that no one should be disfavored because of their ancestry. Yet one might also take careful note that many of us enjoy




unearned benefits, including some benefits (e.g., the fruits of slave labor) whose etiology involves ancestral discrimination. Just as Rawls views talents, we might even say that all inherited benefits are unearned and for that reason may be exploited for redistributive purposes. Indeed it seems that to justify exceeding pedagogical prime, one must turn to some explicitly redistributive policy.

We are familiar with policies that enhance opportunities for various careers so as to achieve some collective goal.10 But because of barriers to mobility among social classes, it is not always the case that those of equal talents enjoy equal prospects of achievement. The full realization of "careers open to talents" is not trivial. Even neglecting discrimination, the benign institution of the family may in various cases aid or constrain the development of talents. One cannot easily counteract this unless the polity begins to legislate about family dynamics. Hence Rawls offers an indirect solution: the difference principle sus- tains inequalities in persons' lifetime expectations of primary social goods if and to the extent that they work to the benefit of the least advantaged. He holds that by implementing this principle, a society may permissibly counteract the effects of talents as developed.11

Given a history of "equal opportunity" as a slogan unfulfilled, various proposals would augment the armamentarium against its impediments. Rawls and Walzer both argue that society must not only enact prohibitions but must also actively interdict barriers erected on morally arbitrary grounds. Fishkin advocates a principle of "equality of life chances" according to which children's prospects for positions in society should not vary by arbitrary characteristics. He regards a characteristic as arbitrary if it is not one of those like IQ by which one can predict the development of suitable qualifications.12 Rawls shares this vision: "The school system, whether public or private, should be designed to even out class barriers."13 Rawls envisions that in a society that provides everyone an education to some level, talents will develop regardless of students' social classes. Walzer contends that since all children have the same need to know, society should provide all with the same "basic education" up through some level. All students, he holds, enjoy the right that "insofar as they are prepared for office holding in the public schools, they should, so far as possible, be equally prepared."14 To the extent that one believes that society should provide an education for all, redistribution is already underway.

Even in Rawls 's strong sense of "fair" (vis-a-vis merely formal) equality of opportunity, employers are not compelled to create new jobs for minority citizens. Instead they are merely enjoined from prac- ticing discrimination on impermissible grounds when they award such jobs as there are. Consequently, life chances will remain unequal when




talents are unequal. One response to this would be to claim that, owing to developmental handicaps, a person's talents may not be fully realized, and for that reason it is not enough to assure that careers are open to talents. Such an assurance only leaves the race to the swiftest, the meritocratic result against which Rawls's difference principle mili- tates. One could argue that society should indirectly distribute educational opportunities via sweeping redistributive policies. These might attack every condition by dint of which members of an ethnic minority fail to develop the qualifications for admission that one might imagine in the absence of discriminatory social practices. Such policies might enjoin minimal provision of food, clothing, housing, and education. Or should education appear on this list when it is the opportunity that we are trying to allot? The answer appears to be that one level of education is requisite for a higher one. If members of a given group frequently fail to qualify for admission to college, that failure may impel society to implement programs that enhance their elementary and secondary educations.

May society enhance primary and secondary education for blacks but not for whites? Where truancy laws operate, a place awaits every child in public elementary and high schools. In such case to admit one student is not to displace another. (I neglect those secondary schools that practice selective admissions.) The question that we must instead ask is whether there arises warrant for providing extra measures to less advantaged students but not to all. We might expect to find support for such favored treatment from Rawls. Rawls argues that the education of the less talented must not be neglected because education enables one to take part in society's culture and affairs and thereby to gain a secure sense of one's own worth. Subject to that constraint, however, Rawls supports arrangements that favor more talented students in education. This is the way to achieve a more productive economy and thus greater welfare for all. Where the least advantaged gain shelter indirectly in his theory is from the difference principle. The difference principle effectively directs that the fruits of exercise of superior talents be deployed as a common asset, a resource that, among other things, pays for the education of the least advantaged.15 The antimeritocratic difference principle sets justice as fairness apart from other liberal views. The others, affirming only that careers shall be open to talents, leave the race to the swiftest. What Rawls does not do is to direct anything as specific as extra pedagogical aid. The origi- nal theory of Rawls deals only in the distribution of primary social goods like income and wealth. It fails to handle the difficulty that, from a given quantity of goods, some people will realize much less welfare, perhaps perilously less, than will others who are more talented or




lack a handicap. In school, some students need more help than do others in order to reach a given proficiency. Thus the race is to the swiftest after all.

To meet this problem requires a stronger version of egalitarianism. We find an adumbration of one when Rawls talks of an adjustable in- dex of primary goods.16 A more precise notion is Amartya Sen's view that justice should be concerned with equating persons' "capability sets."17 Nonetheless the capacities of the severely ill may be so low that "normal" realization of rudimentary functionings requires a large if not boundless drain of resources.18 On the other hand, one can imagine many functionings whose realization depends on education and as to which, in the absence of severe learning disabilities, the incremen- tal cost to raise a student's capacity or attainment to that of others would be tolerable.

Already costs of extra measures are incurred in the special education of physically or emotionally handicapped children (either of which conditions confers eligibility for special education according to the Education of All Handicapped Children Act). It seems that one could, mutatis mutandis, muster the rationale for expenditures on special education in support of a more general obligation to enhance instruc- tion of students who do not qualify as handicapped but who otherwise perform poorly. This would not state a case for apportioning extra pedagogy by any ethnic characteristic. It could be a contingent fact that members of ethnic minorities constitute a large portion of those who perform poorly and thereby qualify for enhanced schooling, but the warrant for extra measures may remain general. Rectificatory justice would suggest that extra measures should be provided if under- performance can be traced to some past injustice, but in special education we have a counterexample of extra measures about which we do not ask an applicant's ancestry.

A problem that may arise in extending the rationale of special education is that many students may claim, some even disingenuously, that they should receive enhanced educaional services by reason of circumstances other than race or handicaps heretofore recognized. The circumstances might be social, economic, familial, genetic, political, or geographical. This prompts us to reflect whether more students merit extra help than presently receive it, and illustrates why we must draw some lines. It does not state an objection to extra measures in general. In particular it does not show that only responses to injustice are warranted.

An overt policy of favoring, without regard to ethnicity, students who need extra help also seems more promising than one familiar argument. Sometimes admissions preferences are defended with the claim that prevailing methods of secondary grading and testing fail to detect




important talents of minority applicants, and in particular, that they fail to predict success in college. If this be true, one would expect that college performance of minority students would surpass what conven- tional measures predict. To the extent that evidence of such unpredicted performance is lacking, the defense stumbles unless it is successfully argued that methods of evaluating college performance are themselves culturally biased and should not be so.

For completeness, we may also observe that as compensation for the college education that may be missed by minority students who fail to qualify for admission, society could provide goods other than education. Society could pay compensation to the uneducated. The obvious disadvantage of such a scheme is that, if education truly is the key to social advance, compensation alone would leave persons without valuable benefits that money cannot supply. Lost benefits might include the experience of racial intermingling and the example to younger minority students that older minority students provide when they enroll in college. A libertarian would also object to such compensation as an unprincipled taking in violation of entitlements.

It is because he believes that equal opportunity inexorably leads to redistribution (as indeed I am suggesting here) that Robert Nozick ob- jects to equal opportunity in general.19 His well-known entitlement theory asserts that one is entitled to (a) the fruits of one's labor and other previously unheld things legitimately acquired, and (b) what one has received in lawful transfers. Hence he holds that it is wrong for society to violate such entitlements by taking any such things through taxes, even to distribute the proceeds to the needy. Whether this view neglects the contribution made by society to each of its members, and most especially society's contribution to each member's accumulated wherewithal for making and buying things, is a major question, but two observations suffice for present purposes. First, though Nozick maintains that it is just to rectify violations of (a) and (b), we know that the rectificatory rationale for affirmative action founders about tracing across generations, and indeed as Nozick observes, problems of subjunctive reasoning render rectificatory justice indefinite in general.20 Second, the entitlement theory raises no objection peculiar to the policy of enhancing the primary and secondary education of disadvantaged minorities. It opposes redistribution in general. The case for improving the education of any underperforming group rides on the case for a welfare state or for something more extensive than the minimal state allowed by the entitlement theory. The same may be said for public education in general. J. S. Mill understood utilitarian- ism to enjoin elementary education for all, but Herbert Spencer maintained that education should be privately supported.



128 PUBLIC AFFAIRS QUARTERLY

The case for extra help, for enhancing precollegiate education of ethnic minorities, might extend to similar help for enrolled minority college students. But a rationale has not yet been stated for weighting ethnicity as a qualification for admission, beyond pedagogical prime, to higher education. Returning to a point postponed at the outset, one might offer a rationale by denying that enrollment is an office. While we speak of an individual's "qualifications for" admission to higher education, we may also view education as purely instrumental. Edu- cation provides a means of qualifying for society's offices. Rawls's strong principle of equal opportunity applies to "positions of authority" and "offices of command," a universe that excludes many jobs21 and nonjobs. We might choose to classify education as a role and a privilege but not as a job. This would place education outside the pre- cept that candidates for office deserve impartial consideration on the basis of qualifications. Surely one is not obliged to select for every role by qualifications. Someone (not necessarily a populist radical) might suggest that society distribute scarce resources by lottery or by "first come, first serve." Another might suggest distributing admission to higher education so as to counterbalance some prior random distribution (e.g., of talents, what Rawls calls the "unearned outcomes of the natural lottery"). The welfare system effectively does this with food and income support. Demographic characteristics might become decisive.22

Many theories allow or endorse meritocracy, a system in which superior talents garner superior welfare. Rawls's justice as fairness exemplifies a design to avoid meritocracy. It as well as the other distributive policies just noted will surely annoy a candidate of sterling qualifications who fails to gain admission. The disappointed candidate may complain that education should, in Walzer 's phrase, be "a monopoly of the talented." As it happens, the brunt of reverse discrimination is unlikely to fall predominantly on sterling applicants. Many of them may gain admission no matter how ethnicity is weighted. More likely to be burdened by reverse discrimination are qualified but not outstanding applicants such as the plaintiffs in the Texas case who at one point were called "mediocre." We may contrast this stratum of disappointed candidates with faculty and administrators who devise and debate programs of affirmative action. The latter appear to share at least one demographic characteristic. Many scholars and educational leaders have not tasted rejection in quest of admission. Most were outstanding students. The youngest among them gained admission during the very era of affirmative action quotas and preferences. The scholarly attainments of those who did not attend prestigious institutions often evince exceptional talent and dedication. Scholars may unwittingly fail to appreciate the resentment of qualified but less outstanding majority




applicants who are denied admission. We risk inflaming that sore point by pressing the contention that education is not an office and that impartial consideration of applicants is not owed.

Just the opposite of such contention is discernible in various contemporary views of justice. Walzer describes the contemporary debate as one in which many seek justice by imbuing every job with public significance. An example is the legal prohibition of discrimination in employment. Walzer detects a tendency to attach public significance to any role for which persons compete and the attainment of which affords some social or economic advantage. "Any employment for which academic certification is required," he observes, "is a kind of office, since the state . . . controls the accreditation of academic institutions and often runs them itself."23 Walzer does not appear correct in locating this expansive tendency within Rawls's equal opportunity principle. We have seen that it is confined to "positions of authority" and "offices of command," that it does not embrace all jobs (to say nothing of nonjobs), and that it does not apply to all institutions but only to society's basic structure. Nonetheless the inclusive tendency may be prevalent.

Should we decide to treat being a student as an office? Many a hard- working student would be prepared to say that education is a job. Education also seems to be a privilege. With less ambiguity, it can be acknowledged that to be a student is a role for which persons compete and that confers obvious advantages. In that sense being a student can be said to be an office. For the proponent of meritocracy, this entails that candidates for admission should receive impartial consideration. The populist radical might insist on random distribution of both education and offices, but as earlier mentioned, this would be unlikely to produce a reliable corps of teachers, scientists, engineers, physicians, and numerous other critical and specially trained workers. I suggest that impartial consideration of candidates appears to be owed regardless whether one classifies enrollment as an "office." Consider merely how numerous are the jobs that we already recognize as offices. Turn- ing on its head the instrumentalist view that enrollment is a means to but not itself an office, one could argue that precisely because enrollment is such a means, whatever rules obtain about evenhandedness in selection for jobs ought to apply to the selection of students. One might say that if impartial consideration is owed to candidates for office, the same consideration is owed to candidates for preoffice training, i.e., education.24 We would think it peculiar to say that licensure in medi- cine is open to all on the basis of qualifications if admission to medical schools were systematically denied to members of some ethnic group.

One rationale, Rawls's in fact, for holding equal opportunity to be a social duty is not that material wants must be met but that equal




opportunity protects self-esteem against the damage inflicted by the experience of discrimination. Education enables persons to take part in their society's culture and affairs and thereby to gain a secure sense of their own worth. Education "underwrites" equal opportunity for jobs.25 One may also fashion reasons - e.g., to protect against damage to self-esteem - by which no one should be denied impartial consideration on the basis of qualifications, regardless whether education connects with jobs.

Given these considerations, for any affirmative action policy it seems that we at least recognize what will not be a cogent defense. It will not avail to deny that education is a privilege for which candidates should receive impartial consideration on the basis of their qualifications. In consequence, to argue for extending the rationale of special education to sustain extra academic help for minority students or to argue for sweeping redistributive policies to attack every social condition that bounds the academic development of minority students is not sufficient for the present justificatory task. To defend those measures is only to defend expenditures. Whereas to defend admission of minority students to an extent that a college exceeds pedagogical prime requires one to defend preferences that compromise impartial consideration.

What may be the clinching defense employs the claim that no individual deserves admission. Consider a case in which (i) there exist more qualified candidates, persons who satisfy the standard of performance for a function, than there are places, and (ii) proficiency surpassing that standard does not render its possessor more suitable for such a place. This, we may conclude, is an instance in which a qualification is a necessary condition for selection but in which none of the qualified can be said to deserve selection. We might then declare that places should be awarded by lottery or other scheme in which desert plays no part. Military conscription is such a scheme. But even though (ii) may obtain for some menial jobs, (ii) seems implausible for a subtle en- deavor like academic work in which differences in talents matter. Relying on tests and other concededly imperfect indicia of qualification, what an admissions committee attempts to do when reviewing more qualified candidates than it has places, is to impose an ordering on the set of qualified candidates. It envisions a set of ordered pairs <jc, y>, each signifying that "y is 'more qualified' than λ;."26 The committee will claim to select "the most qualified" as those who outrank many others. One might be inclined to say for this case where (ii) is false that the most qualified deserve selection.

I should like to adduce four strategies that the defender of affirmative action at this point might pursue in order to maintain that admission is not indefeasibly deserved. First, it might be contended that no one




deserves admission on account of talents and character. For this there may be invoked the view that talents, as well as character traits such as perseverance by which one makes the most of one's talents, are merely outcomes of a natural lottery and of fortunate family and social circumstances for none of which any of us deserves credit.27 That neither genotype nor phenotype is deserved and the related consequence of the Rawlsian difference principle that talents are common assets whose fruits are available for redistribution is likely to offend anyone who respects the status of being well-born or the ethic of hard work. The most penetrating opposition is that of Nozick. But Nozick's reply to Rawls does not purport to resolve the issue of desert. Nozick merely claims that even if persons do not deserve their natural assets, they are entitled to them. Indeed it seems more plausible to say that applicant χ is entitled to jc's natural assets than to regard someone else, or society as a whole, as entitled to them. But Nozick's arguments only purport to show that the use of *'s natural assets may engender entitlements to material things. Nozick does not adduce an argument that a person's natural assets entitle the person to be selected for any role or office.28 It remains to be shown that χ deserves admission to those colleges for which the talents to which χ may be entitled and the use χ has made of them may qualify x.

Second, while partial orderings are mathematically interesting, a claim that Jones deserves admission because Jones is better or more qualified than some others would ordinarily be taken to imply a weak linear ordering of the applicant pool or of some subset containing Jones. Admissions committees will often contend that theirs is partly an in- tuitive task of reviewing many nonquantifiable qualifications, but that granted, judgments that are not reduced to a linear ordering will not avail claims of desert of the foregoing sort. Are any such orderings attainable? In evaluating applicants, a college effectively constructs many relations, each a set of ordered pairs of applicants, each pair reflecting how one applicant compares with another in respect of some single qualification such as quantitative ability, verbal ability, or musical proficiency. If one imagines such relations mapped into some single linear ordering in which persons admitted rank higher than those rejected, which I shall call a "final ordering," one runs headlong into the voting paradox.29 A college may rank three applicants, in view of their mathematical promise, in the order A, B, C; in view of their verbal ability, B, C, A; and in view of their musical proficiency, C, A, B. Thus by a majority of criteria, A is preferred to Β and Β is preferred to C, which suggests that A should be preferred to C. Yet by a majority of criteria, C is preferred to A. One cannot find any candidate as to which there is not another candidate that a majority prefers. Majority rule




here yields no transitive relation and hence no ordering. If A, B, and C are compared two at a time, someone will prevail, but the outcome will vary with the order of the matches. Not every situation presents this paradox. But the situations in which majority rule yields a transitive relation are unusual.30 Such is the predicament for merely three candidates, three criteria, and a univocal admissions process. When relations are constructed according to many more criteria and when committee members declare separate rankings, the relations become ever more numerous and diverse.

It might be thought that this predicament could be avoided at least as to multiplicity of criteria by a scheme that weights criteria. But then it will be noticed that weightings are seldom uniform. Superior- ity in mathematical and verbal skills often will explain the admission of one outstanding student and the rejection of another proficient student, but then too a musician or athlete may be admitted whose mathematical and verbal skills are decidedly less than those of the rejected applicant. Nonuniform weightings are the predictable result of partitioning a set of applicants into subsets of scholars, science students, thespians, and so on, as quotas effectively do. In quest of a final ordering of at least some subsets, one could partition each subset included in the partition just mentioned, then partition each subset of those subsets, and so on. But in constructing chains, Le.9 linear orderings on subsets, even for a single qualification (e.g., musical or analytical ability) there will usually be no single feature or measure. Hence more than one chain will be constructed for each subset of any significant size, the voting paradox will recur, and intransitivity will be among its consequences.

More is also true. Even if every qualification-based relation, regardless of criterion or author, were a linear ordering, Arrow's impossibility theorem shows that one cannot construct a function that, consistently with Arrow's minimal description of rationality, maps every set of diverse linear orderings into a linear ordering - unless that function ignores the linear orderings of its domain or selects one of them to dominate.31 To accept either of the latter alternatives would be to renounce the purportedly comprehensive methods of admissions decisions. Expressed for the present context, Arrow's conditions of rationality are that no bounds obtain on the number of applicants or orderings of them, no qualification is allowed to dominate, anyone superior to another by all criteria will in the final ordering be ranked ahead of the other, and the rank of χ and y in the final ordering will depend solely on the order of χ and y (and not of any other z) in the qualification-based orderings (the last condition being known as the "in- dependence of irrelevant alternatives" ["IIA"]). In light of the theorem,




one asserting a claim of desert might pursue the following alternatives, (a) One might challenge the applicability of IIA to admissions. One of Arrow's arguments for IIA is that it precludes the Borda count (the familiar scheme in society elections and polls in which for each voter, the /th-ranked of η candidates is assigned η - i points), a scheme noto- riously susceptible to manipulation by insincere voting. Strategic voting has been shown to be a possibility in any voting scheme,32 but admissions do not seem to risk it. Admissions decisionmakers ordinarily have no incentive to rank applicants insincerely in respect of qualifications. Hence, one might argue that IIA is unnecessary for admissions. One might then seek a final ordering that meets the other three conditions, however difficult that may be. Still there remains at least one important reason to retain IIA, v/z., that it precludes considering intensities and their differences - the cardinal measure of Allan's and Robert's musical ability and the extent to which Allan's is greater, the measure of their mathematical ability and the extent to which Robert's is greater - which may not be amenable to reliable comparison, (b) An alternative to a final ordering is offered by Sen's result that any set of linear orderings of a finite set, such as an applicant pool 5, can be mapped, consistently with Arrow's rationality conditions, into an acyclical relation.33 Under an acyclical relation, every subset of 5 has a set of maximal members (i.e., members preferred or viewed indif- ferently to all others). In theory, a college could choose to admit the maximal members of 5. This would leave a set 5' of applicants not chosen whose maximal members the college could next admit, leav- ing a smaller set 5" of members not yet chosen whose maximal members it could then admit, and so on until it had reached some target number of admittees. The mapping is only assured, however, if the qualification-based relations are connected, which is to say that it is known how every applicant compares with every other in every qualification. Morover, the mapping needed to generate an acyclical relation may not make sense for admissions. The illustration offered by Sen, for example, a mapping that selects the Pareto-superior candidate, leaves all candidates ranked equally.34 Even when it obtains, although acyclicity averts the voting paradox, it is a weaker condition than transitivity and fails to assure an ordering. There may occur many near cycles, making it difficult to separate candidates, (c) A more ambi- tious claim is that transitivity is not necessary for rational choice. One can describe relations that become intransitive (e.g., "close to") by dint of intensities. It has also been argued that when a "more qualified" or "better than" relation is predicated on a variety of criteria whose significance varies from one comparison to another, we should expect a rational choice sometimes to display intransitivity.35 Nonetheless, it




would seem difficult to advocate an intransitive final relation in a system that leans conspicuously on percentile groupings, class rank, and relative grading systems. For the rare polymath virtuoso quarterback, some claim of desert may seem incontrovertible, but for others, claims about who is more qualified than whom may founder. Admission or rejection may significantly reflect the velleities of the decisionmakers.

Third, there avails a distinction between reward for past performance and selection in anticipation of future performance.36 The rationale for admitting a student to an entering class may be said to differ from the rationale of awarding an academic degree. Admission is not offered solely for a past performance, for an historical datum, for an attainment. Admission is offered in anticipation of future performance. As an employer decides which among many qualified candidates it will invite to join it, the employer may properly implement preferences, so long as they are not morally arbitrary, about how the employer's business will evolve. An academic institution would seem entitled to do likewise. It would seem permissible for an institution to admit students according to its predictions of what they will contribute to what it wishes to be. If subjectivity, inaccuracy, and intransitivity are unavoidable in retrospective rankings, they would seem more likely still when admissions officers predict performance. Predictive admissions decisions may not easily be called correct or incorrect. We affirm the notion of impartial consideration by saying that every applicant deserves to be considered according to uniform criteria, but it may always be gainsaid that any given applicant deserves to be selected or rejected.

Fourth, an applicant may not deserve his or her qualifications, but we may agree with Nozick that the applicant is entitled to them. We might then say that the applicant deserves what they procure. We could next concede that admission on the basis of qualifications is deserved. But with Thomas Nagel, we could also insist that deserved admission may be denied if to do so will ameliorate a connected injustice greater than the injustice of such denial. The connected, greater injustice here would be that worked by the labor market. In that market, persons receive widely varying economic rewards for the same effort performed in various occupations for which they are selected in virtue of educational attainments. Nagel contends that persons are equal in the respects relevant to deserving economic rewards for their work.37 Nearly all characteristics, he is prepared to argue, are irrelevant to what people who expend equal effort deserve. Hence he holds that everyone should be treated equally. When persons contribute the same effort, there is no morally compelling reason why greater intellectual ability, beauty, or athletic ability should garner greater rewards - why bankers should




be better rewarded than construction workers, movie stars than computer programmers, professional athletes than teachers. Supply and demand in the labor market entail that persons' rewards will not be equal, but that empirical fact does not count as a moral claim of desert. The admissions policies of educational institutions may of course be helpless to revise wages in the labor market. Hence, Nagel concludes that, ostensibly because "ought" implies "can," a departure from impartial consideration of qualifications in admissions can be shown to be just only to the extent that it rectifies injustices exogenous to the labor market. Any further departures from impartial consideration are unjust. But Nagel goes on to emphasize that economic rewards for various jobs are effectively predicated on the educational qualifications for them. By virtue of this link, he holds that injustice in departing from impartial consideration of qualifications, the effect of which is to de- feat legitimate claims of desert, may be overshadowed by the salutary effect of such departures in redressing the injustice of economic rewards. Simply put, justice in economic rewards may supersede justice in college admissions.

This position will be compelling for some in defending affirmative action as the lesser of two injustices. The libertarian will nonetheless deny that market wages effect injustice in economic rewards. Wages, the libertarian will urge, are prices of talents and other qualifications. They are reckoned justly in any market that is free of illegitimate gov- ernment interference. Against libertarianism, the first three strategies are more promising defenses of affirmative action inasmuch as they deny that admission, predicated on predictions of future performance, is deserved in the first place.

If by means of the foregoing four strategies or otherwise, it can be maintained that admission is not ultimately deserved, what follows? Society might adopt policies of manipulating admissions so as to achieve worthy goals. Goals might include raising the average welfare, raising the welfare of the least advantaged, achieving greater equality, training specialists for a perceived national or regional need, fostering racial harmony, or enhancing productivity. Whatever pat- terned distribution of entering places is the target, no entitlements to material holdings would be breached by manipulating admissions. Hence not even Nozick's objections would reach such manipulations. Of course the position that admission is not deserved allows action in many directions. It allows preferences for a minority over a majority, but it also allows the reverse. The choice of collective goals is crucial.

It seems unlikely that we shall be able to prefer an ethnic classification alone. Consider Fishkin's view that one may sacrifice impartial consideration or the principle of merit if to do so renders life chances




more nearly equal across a population. The problem is that reverse ethnic discrimination fails that test. It does not single out those indi- viduals within an ethnic minority whose life chances in fact are impaired by the environment in which they must develop their qualifications.38 Thereby reverse discrimination leaves competition to turn on morally irrelevant characteristics - just as does the discrimination against minorities that the former was designed to counteract. At least it can be said that reverse discrimination will not visit on an ethnic majority as extensive a burden as that imposed by discrimination against a minority. The diminished self-esteem that follows from knowing that one is disfavored because all members of one's class are disfavored will not burden members of a majority since they belong to the group that dominates.

It seems more defensible to contemplate preferences for "the eco- nomically disadvantaged." Applying the preferences may favor members of ethnic minorities, but only per accidens, and not them alone. We might add the caveat that admissions preferences for any minority, ethnic or economic, will probably not change the pattern of different economic rewards for identical effort. Education may usher more minority members into occupations previously dominated by the majority, but the labor market will doubtless effect a pattern of rewards within the minority citizenry closely resembling the pattern of rewards within the majority. If differences in rewards are undeserved for the former subset, so they would seem to be for the latter.

Once finished with the task of interdicting denials of impartial consideration, affirmative action has left the realm of procedural justice for the arena of distributive policy. Curiously enough, if the polity adopts policies according to which it will distribute the privilege of admission so as to achieve worthy goals, it is not fatuous to propose quotas as methods of distribution. These rubrics may avail here for what we may now see as a deeper reason why they disrupt things elsewhere: quotas are allocations. Distributive grounds may be mustered for them but when disguised as mechanisms of procedural fairness, they appear to override outcomes of fair procedures. This clarifica- tion notwithstanding, redistributive policies of the kind described herein may find no easy avenue for recognition by courts or by a majority of the public. Many will insist, with ample support in the law, that admission is deserved. For a state institution, the "equal protection" clause of the Fourteenth Amendment, of late a weapon against quotas and reverse discrimination, may preclude or at least constrain the use of admissions as a system of distribution. It may then fall to private institutions, long bastions of privilege, to assume the lead in affirmative action initiatives for less advantaged groups, initiatives that




educational leaders generally support. Assuming stable enrollment, private colleges would thereby become more inclusive as to minority groups and more exclusive as to majority applicants. How substantial would be the societal impact of such policies is unclear. Private institutions in the aggregate enroll fewer students than do public institutions in the aggregate. Private institutions may find reason to press for lenient interpretation of "equal protection" lest they shoulder a disproportion- ate share of society's responsibility to educate more minority students.

The future battleground of affirmative action may not be a procedural terrain. The case for measures to enhance the academic development of underperforming students is a case for distributions. The question of how, if it chooses them, the polity may justify preferences for minority applicants to an extent that pedagogical prime is exceeded has led in the foregoing analysis to two grounds, both distributive. First, subordinating the significance of desert, the structure of society in the long run may be accorded higher priority than the suit- ability for admission of any individual candidate. Second, any distribution of work's rewards skewed with respect to a minority may be regarded as an injustice that must be redressed by the lesser injustice of reverse discrimination in educational admissions. The first will be a considerable venture for a society that, since Hobbes and the Puri- tans, has prized individualism. Some may consider the second dispatched by any equilibrium of supply and demand in a labor market. My suggestion is that, if the scale of minority admissions is to surpass the reach of procedural protections, these defenses may be indispensable.

Harvard University

Received December 23, 1996

NOTES

1. Michael Walzer, Spheres of Justice (New York: Basic Books, 1983), p. 149.

2. This may also be expressed by what James S. Fishkin calls a "principle of merit" that enjoins procedural fairness in the evaluation of qualifications for positions. See his Justice, Equal Opportunity, and the Family (New Haven, CT: Yale University Press, 1983), pp. 22-30.

3. Walzer locates this view in the Athenians' policies about civil service, in Luther's priesthood of all believers, in Rousseau's vision of schools in which citizens take turns serving as teachers, in the Jacksonian notion of rotation in office, and in Lenin's notion that everyone is in some sense a bureaucrat {op. cit., p. 133).



1 3 8 PUBLIC AFFAIRS QUARTERLY

4. John Rawls holds that "freedom of movement" in jobs and careers is a constitutional essential (Political Liberalism [New York: Columbia University Press, 1993], pp. 228-230).

5. E. g., Regents of the University of California v. Bakke, 438 U. S. 265 (1978). 6. Strictly speaking, it is selection rather than admission with which we are

concerned inasmuch as "admission" denotes a system that grants a place to everyone who meets a given standard. This distinction is made by Jon Elster in Local Justice (New York: Russell Sage Foundation, 1992), pp. 24-25, 45. It explains the aptness of the phrase "selective admission."

7. Hopwood v. Texas, 21 F. 3d 603 (5th Cir. 1996), cert, denied, 1 16 S. Ct. 2581 (1996).

8. Robert M. Rosensweig, letter to the editor, The Chronicle of Higher Education, May 17, 1996, p. B4; Robert Atwell, quoted in The Chronicle of Higher Education, June 14, 1996, p. A36.

9. A penetrating presentation of these deficiencies is provided by Fishkin in op. cit., pp. 97-102, 104.

10. Sometimes inducements are predicated on perceived national exigencies, as in the post-Sputnik emphasis on training scientists and engineers or the allocation of funds to academic medical centers so as to induce the training of more generalists and fewer specialists. Norman Daniels in Just Health Care (Cambridge: Cambridge University Press, 1985), pp. 1 19-124, offers an argument that the polity's allocation of resources with a view to inducing some careers and disfavoring others is not unjust as to aspirants to the disfavored careers.

11. Fishkin (op. cit., pp. 155-157) criticizes Rawls for failure to reconcile the conflict between the family and equal opportunity, but overlooks the indirect strategy of the difference principle.

12. Ibid, pp. 32-35. 13. John Rawls, Λ Theory of Justice (Cambridge, MA: Harvard University

Press, 1971), p. 73. In this passage Rawls speaks of what he calls "liberal equality," a position less demanding than his own, but one that enjoins fair equality of opportunity.

14. Walzer, op. cit., p. 210. 15. Rawls adopts this stance (A Theory of Justice, pp. 101, 106-107, 158) even

though his theory concerns only the basic structure of society, and, while it constrains associations like universities, may be unsuitable within them (Political Liberalism, p. 261).

'6. Political Liberalism, pp. 182-183, 185-188. 17. A. K. Sen, "Equality of What?" in S. McMurrin, ed., Tanner Lectures on

Human Values, I (Cambridge: Cambridge University Press, 1980), pp. 213-220; "Well-Being and Freedom" and "Freedom and Agency," Journal of Philosophy 82 (1985), pp. 185-221; "Justice: Means Versus Freedoms," Philosophy and Public Affairs 19 (1990), pp. 111-121; and Inequality Reexamined (Cambridge, MA: Harvard University Press, 1992). A capability set comprises all n- tuples of measures of human functionings that a person can achieve by deploying the




person' s capacities to use goods upon whatever fixed quantity of goods comes that person's way. Each η-tuple of the capability set is the result of spreading that fixed quantity in such fashion as the person chooses, or is constrained by exigencies to choose, among the respective functionings. It is a considerable question what functionings merit recognition.

18. Kenneth J. Arrow, "Some Ordinalist-Utilitarian Notes on Rawls's Theory of Justice," Journal of Philosophy 70 (1973), pp. 245-263, esp. 251-254.

19. Robert Nozick, Anarchy, Statey and Utopia (New York: Basic Books, 1974), pp. 235, 238.

20. Ibid., pp. 152-153, 173.

21. In the phrasing of his fair equality of opportunity principle, which says that "social and economic inequalities . . . must be attached to offices and positions open to all under conditions of fair equality of opportunity," Rawls might appear to say that every social and economic inequality must be attached to some office or position. In such case "office or position" would sweep so broadly as perhaps to include every "relevant social position." To the contrary, Rawls elsewhere makes clear that his opportunity principle only pertains to such inequalities as happen to be attached to offices and positions (Political Liberalism, p. 6). "Office or position" remains confined to jobs and authority, to "organizations that make use of differences in authority and responsibility, or chains of command" and to "political and economic institutions" (A Theory of Justice, p. 61; Political Liberalism, p. 181). This is also the only sensible reading of the difference principle, which requires that any inequalities benefit the least advantaged. Rawls assumes a fairly close correlation between income and wealth, on the one hand, and power and authority, on the other (A Theory of Justice, p. 97). But inequalities to which the difference principle pertains are inequalities in relative levels of income and wealth - "starting places" in the social structure - regardless whether they are associated with offices and positions (ibid., pp. 96, 99).

22. In addition to favoring such familiar characteristics as race and religion, a college might also give preference to candidates who are disabled, suffer some economic disadvantage, or reside near the campus and wish to save expenses by living at home. Elster explains in op. cit., p. 43, that the latter criteria are used for admission to German institutions of higher education.

23. Walzer, op. cit., p. 131.

24. So Walzer argues at ibid., p. 144.

25. A Theory of Justice, pp. 87, 101, 107, 158.

26. This will only be a partial ordering unless it is known how every applicant compares to every other.

27. Ibid., pp. 104,310-315.

28. Nozick, op. cit., pp 159, 213-227.

29. The admissions process is properly assimilated to voting in an election that presents three or more candidates because in both cases there is constructed a preference relation. The functional equivalent of a voter is an admissions decision-maker or a conceptual engine generating a qualification-based relation.




30. If each qualification-based relation is "single-peaked" and the number of relations is odd, the paradox is avoided. This result, Black's theorem, was generalized by A. K. Sen in Collective Choice and Social Welfare (San Francisco, CA: Holden Day, 1970), pp. 166-172. An example of single-peakedness is an election in which voters prefer or disfavor candidates strictly in the order in which they indisputedly fall on a single scale of classification from far right to far left.

31. Kenneth J. Arrow, Social Choice and Individual Values, 2nd ed. (New Haven, CT: Yale University Press, 1963).

32. Allan Gibbard, "Manipulation of Voting Schemes: A General Result," Econométrica 41 (1973), pp. 587-601.

33. Collective Choice and Social Welfare, pp. 14, 16, 28, and 52. Given a weak relation R on Γ, let Ρ be the irreflexive strict relation (read by economists as a relation of strict "preference") formed by excluding from R every pair <x, y> where jc/v, / is an indifference relation defined by saying that xly if and only if xRy and yRx. This entails that whereas in general under a weak relation a set can have more than one greatest member only if the greatest members are equal, under R distinct alternatives can all be "best" if there is no preference between them. R is said to be acyclical if and only if for all *y,jc2, . . . xn in Γ, if x,Pxr x2Px3, . . . *Λ.;*'» then XjRxn. As Sen says (p. 47), "If xt is preferred to xY x2 to x3, and so on, until

xn, then ancyclicity requires that *7 be regarded as at least as good as xH" 34. Ibid., p. 48.

3 5 . Larry S . Temkin "A Continuum Argument for Intransiti vity ," Philosophy and Public Affairs 25 (1996), pp. 175-210. Robert Dahl claims in A Preface to Democratic Theory (Chicago: University of Chicago Press, 1956), p. 42n., that transitivity is "irrational in a great many types of collective choices."

36. Walzer invokes the distinction to deny that an office is deserved (op. cit., pp. 135-139); here we may apply it to admissions.

37. Thomas Nagel, "Equal Treatment and Compensatory Discrimination," Philosophy and Public Affairs 2 (1973), pp. 349-363.

38. Fishkin, op. cit., pp. 89, 103.



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Affirmative Action in Higher Education as Redistribution