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Access to Higher Education by the Luck of the Draw

Author(s): Peter StoneSource: Comparative Education Review, Vol. 57, No. 3, Special Issue on Fair Access to HigherEducation (August 2013), pp. 577-599Published by: The University of Chicago Presson behalf of the Comparative and InternationalEducation SocietyStable URL: http://www.jstor.org/stable/10.1086/670663.

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letter to the editor went so far as to claim that the proposal to have a lotteryfor oversubscribed courses conjures up a dystopian world in which we humans

have programmed computers to make decisions that profoundly affect thelives of young people, but the programme we have written is based on neitherlogic nor a meritocracy (Hackett 2011).1 Hyland has encountered this sus-picion of lotteries before. In 1999, she had participated in the Commissionon the Points System, which was convened to evaluate the Irish HEA ad-missions process. That commission also considered a proposal involving lot-teries in the admissions process but rejected it after finding very little supportfor this proposal by those who contributed to the consultative process.2

Despite this antipathy, lotteries are no strangers to educational admissionsarrangements around the world. This is primarily true at the primary andsecondary levels,3 but there are also clear examples at the tertiary level. InEngland, for example, Leeds Metropolitan University and Huddersfield Uni-

versity randomly select qualified applicants to their much-demanded physio-therapy courses (Curtis 2004). Queen Mary College identifies which of itsapplicants meet its entry requirements, then selects randomly a subset ofthese applicants for interviews (Fuller 2003). Since 1977, the Netherlandshas employed a similar system to admit students to medical, veterinary, andother professional schools. Unlike the English lottery examples, however, theDutch lottery awards higher admission chances to applicants with higherexamination scores (Goudappel 1999). On top of all this, the Irish admissionssystem already makes limited use of lotteries. Applicants are admitted to thecourses to which they have applied based upon points accumulated throughthe Irish Leaving Certificate examination; if a tie must be broken betweenstudents with an equal number of points, a lottery is used.

But in all these instances, lotteries have faced much the same kind ofreaction that greeted Hylands proposal. A British government commissiononce examined the Queen Mary system with an eye to extending its use, butthe idea went nowhere due to resistance of this type (Owen and Halpin 2003;

Admissions to Higher Education Steering Group 2004). And the Dutch pro-fessional school lotteries have repeatedly drawn criticism, especially in 1996,

when a particularly well-qualified student was denied entry. The result was agovernment investigation that reaffirmed the system with minor changes(Drenth 1999; Goudappel 1999).

Given this history of lottery use in educational admissions processes, itis not surprising that scholars have devoted attention to the topic. Sometimes,

1 The letters author apparently has no objections to a computer program making decisions onthe basis of logic or a meritocracy, and so the invocation of computers making decisions seems tobe merely a red herring.

2 Hyland (2011, 22 n. 81); and see Commission on the Points System (1999), Heffernan (2011),and Murray (2011).

3 Stone (2008) provides numerous examples from primary and secondary schools around the world.

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Comparative Education Review 579

ADMISSIONS LOTTERIES

they have done so as part of more general studies of lottery use.4 Sometimes,they have done so as part of more general studies of university education(Wolff 1992; Kennedy 2004). Some have considered the appropriateness oflotteries for primary and secondary school admissions (Saunders 2008; Stone2008). Some have focused specifically on the use of lotteries in admissionsto universities and other higher education institutions (Hofstee [1990] 2011;Boyle 1998; 2010, pt. 2). And some have taken these ideas out of academia,engaging in spirited polemics for or against admission to higher educationinstitutions by the luck of the draw.5

This article defends a theory of fairness and applies it to the problem ofadmission to higher education. This theory holds that a fair (i.e., equi-probable)6 lottery is an appropriate tiebreaker between applicants with

equally strong claims to admission. But use of this conclusion requires an-swering two critically important questions: First, what gives an applicant aclaim to admission? Second, under what circumstances can ties be expectedto arise between applicants? This article argues that merit, an admittedlycontentious standard, generates claims to admission to higher education. Itfurther contends that in properly designed admissions procedures, there willbe routine use of lotteries to break ties. Lotteries may be controversial, butthis controversy should not obscure how essential lotteries are to ensuringfairness in admissions.

I shall first lay out the demands fairness places upon allocative processes.Along the way, I note that fairness may conflict with the general welfare. Ithen apply the demands of fairness to higher education admissions processes.This application requires an account of what gives applicants claims to suchadmissionan account, I argue, that involves the nature of merit. Next, Ishow that there are fairness-related reasons for recognizing limits to ourability to distinguish between claims. These limits provide reasons for ac-cepting regular use of fair lotteries in higher education admissions. I concludeby reconsidering the Irish case in light of the considerations raised here.

Before proceeding, I should note that the word fair is ambiguous inthis context. On the one hand, one can speak of a fair lottery, one gen-erating each of its outcomes with equal probability. On the other hand, onecan ask whether it would be fair to allocate a particular good (e.g., admissionto higher education) via lottery. These two uses of fair need not coincide;it is perfectly coherent to say that it is often unfair to use a fair lottery. Inother works, I have followed Lewis Kornhauser and Lawrence Sager ([1988]2011, 134) by using the word just in place of the second meaning of fair

4 Elster (1989), Duxbury (1999), Goodwin (2005), and Stone (2011b).5

Jump (1988), Matloff (1995), Schwartz (2005a, 2005c, 2009), Karabel (2007), and Zwick (2007).6 Hyland (2011) also expresses support for incorporating weighted lotteriesi.e., lotteries thatfavor some applicants over others. And as noted above, weighted lotteries have been and are still beingused in such a capacity, notably in the Netherlands. I briefly touch on their use in the concludingsection of this article.



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(Stone 2011b, 24). Fairness is not precisely the same as justice, although thedistinction between the two is debated.7 But the topic of this symposium isfairness, and so my terminology will reflect this. I shall normally use the termfair in the second sense; whenever I have in mind fairness-as-equiprobability,I shall indicate this fact.

Fairness

Fairness may be at stake whenever a society must allocate a scarce socialgood. I say may because fairness does not arise unless agents have claimsto the good in question. It is difficult to specify precisely what it means tohave a claim to a good. But at the very least, it means having some sort of

right to the good (cf. Raz 1986; Kornhauser and Sager [1988] 2011, 135;Waldron 1993, 204). When an agent has a claim to a good, there is a reasonto give the good to herbut a reason of a special sort. The reason is thatthere exists a duty owed to the claimant herself. Where no such duty exists,there is no claim; in that case, it might be wrong to deny the agent thegoodperhaps there exist other reasons why she should get itbut it wouldnot be unfair (Broome [199091] 2011, 22325).8

The distribution of some social goods may not generate claims. This willparticularly be the case if the goods do not directly benefit the agent in aspecial way. Imagine, for example, that a government decided to distributenew catalytic converters to automobiles in an effort to reduce air pollution(Stone 2011b, 67). If each converter marginally improved air quality withoutin the process helping (or harming) the owner of the car to which it wasattached, then no car owner would have a claim on a converter. The gov-ernment would be free to allocate the converters unconstrained by the de-mands of fairness; it could focus completely upon maximizing total socialbenefit, for example.9

7 Briefly, some argue that fairness is strictly a relative concept; it is not so much concerned with

what people get as it is with what some people get relative to what other people get. Justice, on theother hand, deals with what people get both absolutely and relatively. But the line is rarely drawn veryclearly, and even those who focus upon the relative nature of fairness (e.g., Broome [199091] 2011)rarely do so with complete consistency. They typically resist, for example, the suggestion that a systemthat simply destroyed goods without distributing them to anyone would be perfectly fair, even thoughany possible complaint would have to be absolute and not relative in nature. I have in mind this moreexpansive understanding of fairness throughout this article.

8 Kornhauser and Sager consider the possibility that agents may have no direct claims to a goodand yet still have fairness-related claims to equal treatment regarding the allocation of the good ([1988]2011, 14445). Neither beggar X nor beggar Y may have any claim to my money, but (so the argumentgoes) it would still be unfair for me to give money to X without also giving it to Y (the example is fromEstlund 2008, 67). The plausibility of this example, however, seems to derive from the possibility thatbeggars may have some (weak or controversial) claims to our help. Where agents clearly have no claims

at all, fairness-related demands do not seem to apply. I shall not consider this possibility further here(see Stone 2011b, 6768).9 Of course, some citizens might demand the converters anyway. (Perhaps they simply like the idea

of doing their part to help the environment.) If there is no reason to believe that a converter is owedto any of these people, then declining to respect these demands is in no way unfair. The mere fact that



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Suppose, however, that the converters provided a substantive benefit tothe owners of the cars to which they were attached. Perhaps the air qualitygains resulted in perceptible health benefits for the drivers of the healthiercars. The allocative process might then give rise to claims on the part ofparticular people for converters on their cars. If that happens, the demandsof fairness might conflict with other considerations. In particular, the allo-cation that best respects claims might differ from the allocation that maxi-mizes aggregate social welfare. If so, then the best allocative procedure might

well reflect a compromise between the demands of fairness and the demandsof other values (Broome [199091] 2011, 22122).

But what does fairness demand? I have said that its demands arise when-ever people possess claims to the good being allocated. These demands will

vary depending upon the circumstances. Because the topic of this article isadmission to higher education, I assume that the following statements holdtrue of the allocative situation (cf. Stone 2011b, 50):

1. The good is lumpy. It cannot be neatly divided between claimants.2. The good is homogeneous. One unit of the good is as good as any

other.3. The claims are homogeneous. Each claimant has a claim to one and

only one unit of the good.

4. The claims, while homogenous, may vary in strength. One claimant mayhave a stronger claim to the good than another.

When these conditions are met, fairness requires the allocator to rank orderthe claimants in accordance with the strength of their respective claims.Those with the strongest claims should get the good first, then those withthe second-strongest, and so on until the good has been completely allocated.Should there arise a situation in which (1) there are a number of people

with equally strong claims to the good, and (2) this number is larger thanthe number of units of the good remaining, and (3) nobody is left with anunsatisfied stronger claim, then fairness requires that a fair (equiprobable)lottery be used to decide which of this number gets the good.

On my account, then, fairness demands that claim strength, and onlyclaim strength, govern the distribution of goods. This requires allocatinggoods to those with the strongest unsatisfied claims, with a fair (equiprobable)lottery being used when there are fewer units of the good to allocate thanthere are agents with equally strong unsatisfied claims. Competing consid-erations (such as overall welfare) may demand deviations from this practice,but if this takes place, then fairness is being sacrificed for the sake of some-

thing else. Elsewhere, I have referred to this allocative practice as the Just

someone wants something does not by itself produce a demand to which the public owes attention(Scanlon 1975).



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Lottery Rule (Stone 2011b, 53; see also Stone 2009a, 2009c) and defendedit, especially the part relating to lotteries. Space limitations prohibit me fromrepeating this defense here, although its intuitive appeal is, hopefully, ob-

vious.10 I shall assume the validity of this account and will turn now to ex-ploring its implications for higher education admissions.

Claims to Higher Education Admission

In order to apply the theory of fairness articulated here to the problemof higher education admissions, one must first answer two questions: First,

who has a claim to higher education and why? Second, does the problemof distinguishing among claims regularly lead to ties between some claims

ties that would appropriately be broken through fair lotteries?

11

The firstquestion is tackled here; the second question is addressed in the followingsection.12

What gives rise to a claim to higher education? The intuitive answer ismerit.13 But merit is not a simple or uncontroversial criterion. Most casualobservers of university admissions would agree that students who demonstratemore abilitythrough standardized examinations such as the Irish LeavingCertificate examination or the US SAT Reasoning Test, for examplepossessmore merit than students who demonstrate less. But there are two competing

ways to understand why this should be so.

One of these ways is backward-looking. Students who have done betterat primary and secondary school have earned their places at higher educationinstitutions through hard work, intelligence, and so forth. On this reading,merit is closely related to desert (i.e., the quality of deserving something),and the competition for admission to higher education is analogous to amarathon. This idea has much intuitive appeal, and it surely lies at the heart

10 I have relied heavily upon the work of John Broome ([199091] 2011) in developing my ownaccount of the demands of fairness. Broome, however, resists what I have called the Just Lottery Rule.Instead, he argues that when there are more claimants than goods to allocate, fairness demands the

use of a weighted lottery, with those possessing stronger claims receiving the good with higher probabilitythan those with weaker claims. Broomes conclusion regarding lotteries, however, does not follow straight-forwardly from the account of fairness he develops. Moreover, his defense of weighted lotteries generatessome highly counterintuitive implications (see Wasserman [1996] 2011). I discuss Broomes case for

weighted lotteries in more depth in Stone (2010).11 There are other fairness-related questions one could raise regarding features of the social struc-

ture that impact how the higher education admissions system functions. One could argue, for example,that it is unfair that students from disadvantaged backgrounds have diminished opportunities to acquire

valid claims. This would be similar to the critique of formal equality of opportunity developed by BernardWilliams (1962). While this argument is definitely relevant to a full consideration of fairness in highereducation, I cannot consider it further here.

12 One can ask similar questions regarding the processes of admission to primary and secondaryschools. As noted above, lotteries have indeed been used to ensure fairness in these processes. But one

would not expect the same admissions system to work across all these contexts, because the answers tothese fairness-related questions will be different for primary schools, secondary schools, and highereducation.

13Merit and need are the factors most often mentioned when ordinary people consider the just

distribution of social goods (Miller 1979).



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of the resistance many parents show to reform of higher education admissionsprocesses; their children have earned their places under the old system,and changing the rules on them would be like changing the finish line aftera marathon has already been run.

Another way to understand merit is forward-looking. Students who havedemonstrated ability are thereby providing evidence that, if given the op-portunity, they will achieve the most in a higher education institution and

will thereby go on to make the most of such an education for the rest oftheir lives. On this reading, merit is closely related to future contribution.Importantly, this understanding of merit makes the measurement process

very unlike a marathon. It is more like the hiring process for a fitness in-structor. Being in good shape, as evidenced by the ability to win a marathon,

surely counts as an important part of the qualifications for such a job. Butnobody would think that winning a marathon gives one an entitlement tosuch a job, even relative to those beaten in the marathon. There may beother relevant qualifications that influence success as a fitness instructorand even with regard to physical ability, there are other, perfectly legitimate

ways of demonstrating that one is in good shape.14

These same factors will, on this understanding of merit, be at work inthe higher education admissions process. It is quite possible, for example,that certain methods for measuring how successful a student will be at a

higher education institution will work better for some students than forothers. Examinations might accurately gauge how well white and affluentstudents will perform but not how well students of different ethnicities and/or social classes will do. If this were the case, there would be nothing strangeabout using different measurement methods for different kinds of studentsby treating a particular score on a standardized examination differently fordifferent kinds of students.15 This would be a strange way to conduct a mar-athon but not at all a strange way of measuring what is surely a very complex

variablethe impact higher education will have on the life of a student and

how much the student will be able to do with access to it.I shall focus here upon the latter, forward-looking understanding of merit.

More must be said about it if we are to understand how it works and thepossible complexities it raises. For merit cannot simply be reduced to thecontribution or utility to society that a student will generate if admitted touniversity. I have sharply distinguished between fairness and the general good.Social contribution is a story about the latter, not the former. If the higher

14 To use Rawlss terminology, the marathon constitutes a case of pure procedural justice, ac-cording to which the procedure produces the correct allocation by definition when properly used. In

contrast, the application procedure for the fitness instructor is a case of imperfect procedural justice,that is, the procedure is a good-but-not-perfect instrument for producing an independently definablecorrect allocation (Rawls 1999).

15Guinier and Sturm (2001) consider this possibility and other problems with narrow understand-

ings of merit.



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education admissions process was merely a utilitarian exercise, then fairnesswould simply not arise as a separate consideration. Applicants would then

be analogous to the cars in need of new catalytic converters considered inthe previous section. They would merely be vehicles for advancing the generalgood; no applicants could claim any special reason why she, rather thansomeone else, should be such a vehicle.

But, of course, applicants are more than just vehicles for advancing thegeneral good. Each would-be higher education student has a life to lead.Education makes a significant intrinsic contribution to the quality of thestudents life. It also makes a significant extrinsic contribution, of course;education often leads to more opportunities for money, status, and the like.But, typically, the intrinsic contribution is the largest single moral contri-bution made by higher education admission.16 It is precisely because of thisfact that higher education admission gives rise to considerations of fairnessat all. A student has a claim to admission based upon the intrinsic contri-bution that higher education would make to her life. A student who wouldgain more from admission has a stronger claim than does a student who

would gain less.17

How, then, does fairness relate to the advancement of the general goodhere? If higher education admission makes a significant intrinsic contributionto a students life, then this will be, in the normal range of cases, becausethe student has already demonstrated achievement in her desired course ofstudy. As a result, she can be expected to contribute a great deal to societyat the same time as she obtains the benefit. In other words, the presumptionshould be that in higher education admission, fairness and the general goodcoincide: the advancement of one leads to the advancement of the other.

This presumption may, however, fail to hold under certain circumstances.For example, the composition of the admitted group itself might contributeto the general good. Proponents of diversity, for example, argue that thepresence of historically underrepresented populations (e.g., women, racialminorities, ethnic minorities) in higher education institutions improves theability of those institutions to fulfill their mission; the education offered atsuch institutions, in other words, gets better in the presence of diversity. Thisargument might conceivably justify admitting less-meritorious members ofunderrepresented groups ahead of more-meritorious members of overrep-

16There are certainly exceptions to this claim. In a war-torn society, for example, the contributions

of a surgeon to the general well-being would dwarf the contribution that the surgeons career makesto his own life.

17 Daniels compares claims to health care with claims to education. Both of these goods display

the combination of their unequal distributionand theirgreat strategic importance, which puts these needsin a separate category from those basic needs we can expect people to purchase from their fair incomeshares, like food and shelter (Daniels 1985, 4647). With education, as with health care, it is theintrinsic contribution that stands out regarding fairness. It is much less clear (though arguable) thatextrinsic contributions are similarly fairness-related.



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resented groups. This would constitute a sacrifice of fairness in the interestof broader social welfare.18

Distinguishing among Claims

Assume, then, that one applicant has a stronger claim to higher educationadmission than another if and only if the former demonstrates greater ability(through prior achievement, etc.) than the latter. This demonstration ofability will ordinarily provide evidence of the contribution that higher edu-cation attendance will make to that applicants life; it will also ordinarilyprovide evidence of the contribution to the general welfare that the student

will make after completing higher education. Then the demands of fairness

are relatively straightforward. The student with the strongest claimthat is,the student who demonstrates the most abilityshould be admitted first,then the student with the second-strongest claim, and so on. If a point isreached at which there are a number of students demonstrating equal levelsof ability, and it is possible to admit some but not all of them, a fair lotteryought to be used to admit students from this number.

Typically, those who deny the appropriateness of lottery use do not doso because they reject the account of fairness offered here.19 Rather, they donot believe that the conditions for lottery use will ever hold in practice; theydeny, in other words, that ties will ever obtain except in a few fringe cases.In effect, then, proponents and opponents of fair lotteries in higher edu-cation admissions are disputing an empirical question: how often will ties begenerated in a well-functioning and fair university admissions system?

To answer this question, one must recognize that distinguishing amongclaims requires effort. People do not wear their claims on their sleeves, afterall, and when claims yield significant social benefits, the incentive to mis-represent or inflate claims can be very strong. And so the decision on howmuch effort to put into examining claims is a critical one. It is also not adichotomous one: there are many more options available than Make no

effort to distinguish between claims or Continue examining claims untilthere is no possibility that further distinctions will be found. No one seriouslyadvocates the former, regarding higher education admissions or any other

18 Dworkin (1985) denies that fairness (i.e., admission according to merit) and the general goodcan come apart in this manner. This is because he defines a meritorious applicant as one who, ifadmitted, would make a large contribution to society. But this definition denies the commonsensedistinction between being a good doctor and being a doctor who benefits society. There is no reasonto think that the two must coincide; many of the most talented doctors in the United States spend theircareers performing breast implants and tummy tucks. There is good reason to deny admission to would-be plastic surgeons so as to let in more would-be pediatricians. But that is simply an argument for

allowing social contributions to override claims of merit. It is a mistake to act, as Dworkin does, asthough only one value is relevant when admissions to higher education are being allocated.19 There are those who deny wholesale the connection between lotteries and the fair allocation

of goods (e.g., Wolfle [1970] 2011). But these denials misunderstand the contribution that lottery usemakes to fairness. I respond to these denials in Stone (2011b, 8485).



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processes themselves are equivalent. Imagine the difference between a pro-cess that breaks ties between claimants using a fair lottery and a process thatbreaks ties between claimants by admitting white candidates ahead of non-

white ones, or male candidates ahead of female ones. The latter processesemploy bad reasonsreasons completely unrelated to claim strengthindiscriminating between claimants. The former process distinguishes betweenclaimants on the basis of no reasons at all. A lottery distinguishes betweenclaimants without reference to reasons; it thereby ensures that reasons un-related to fairness never taint the process.21

This point is crucial to the defense of random allocation. If there wereno downside to trying to distinguish among claims, then it would seem thatany process, no matter how crude, that offered a chance of success would

be worth a try. And, indeed, this is the case when the general good alone,and not fairness, is at stake. As Willem K. B. Hofstee points out, sloppychoicereliance upon an unreliable procedure with some chance of iden-tifying the superior optionis normally preferable to random selection([1990] 2011, 203). But sloppy choice is far less acceptable when fairness isinvolved. This is because the sloppy procedure might track unacceptable,non-fairness-related factors, such as race, gender, or class. One must believeones instruments are measuring claim strength, and not something else,before treating one claim as stronger than another. If one treats claims as

equalby selecting between them by lotterywhen they are not equal, onecommits an act of unfairness. But if one treats claims as unequalby de-clining to select between them by lottery and employing instead some alter-native procedurewhen they are equal, one introduces non-fairness-basedreasons into the allocative process and thereby commits another act of un-fairness.

Critics of lottery use often fail to acknowledge this fact. They act as thoughall non-claim-tracking allocative processes are on a par.22 And so, they ask,

21There is a sense, of course, in which even an allocation made randomly can be said to be made

according to reasons: in answer to the question, Why did you admit applicant X and not applicant Y?the admissions officials reasoned response would be, Because Xs number was drawn in the lottery, andnot Ys. But this reason makes reference only to the workings of allocation procedure itself, not to anyfeature of the applicants. It is a second-order reasona reason governing the reasoning processand nota first-order reason (see Sunstein and Ullmann-Margalit 1999). Fairness, on my account, requires theexclusion of only first-order reasons; to exclude second-order reasons would be to exclude any means of

justifying one allocation procedure over another. See Stone (2011b, 9293) on this point.22 Even proponents of lottery use can make this mistake. Jump, for example, suggests that the

only fair way to choose a freshman class from among too many qualified applicants is by some type ofrandom selection. One way would be to have the qualified applicants draw lots. Another would be toaccept candidates when their credentials are complete and they are judged qualified, until the class isfull. A third . . . would be to put every qualified applicant on the waiting list and admit the ones whorespond first (1988, A52). Jumps second and third proposals are variants of First come, first served,

a procedure often conflated with random selection (see Stone 2011b, chap. 5.3). Unfortunately, suchproposals reward students who are quick on the draw, best able to apply fast and respond fast whentheir applications are successful. Wealthier students with more resources will typically have an advantagein this area, so reliance upon such a procedure is not equivalent to a lottery. It predictably rewards afactor unrelated to claim strength.



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where is the harm in at least trying to distinguish between claims? Thisargument was on display in an exchange in 2005 in the Chronicle of HigherEducation. The exchange took place between the psychologist Barry Schwartz,who advocates higher education admissions via lottery, and a number ofuniversity officials collectively very critical of lottery use.23 Willis J. Stetson Jr.,dean of admissions at the University of Pennsylvania, argued that it simply

wouldnt make sense to ignore the knowledge driving our current system,for one introducing arbitrary and capricious standards (Stetson 2005). RobinG. Mamlet, dean of admissions and financial aid at Stanford University, as-serted that reform is needed, but while college admissions may be perceivedby many to be a crapshoot, no one gains if we actually turn it into one(Mamlet 2005). Both Stetson and Mamlet overlook the fact that not all

crapshoots are alike, and neither are all arbitrary and capricious standards.The obvious difference between a race-based tiebreaker and a random tie-breaker should be enough to establish the point.24

Mamlet further offers the following observation: Ive been a dean atseveral selective colleges, and Ive repeatedly met people who ask me why

Johnny or Molly did not get in. Often there is no obvious reason other thanthe reality of space constraints. Does that prove Mr. Schwartzs point? I dontthink so. There is always a good reason why Nick or Sarah did get in (2005).This observation, while possibly true, distorts the point of the original ques-

tion. If there are good reasons for admitting Nick or Sarah, but no goodreasons for denying admission to Johnny or Molly, the fairness of the ad-missions process is not yet proved. How the tie between Nick, Sarah, Johnny,and Molly is broken matters greatlythis is the crux of the issue, not spaceper se. Schwartz recognizes this point: It may be true, he writes elsewhere,when the systems are working as they should, that people deserve what theyget. But the converse of this claim is certainly not true: people dont alwaysget what they deserve. There just arent enough rungs on the top of lifesladders for everyone to fit. Contra Mamlet and Stetson, Schwartz recognizesthat college admission is already a crap shoot, and our failure to acknowledgethis is a collective exercise in self-deception (Schwartz 2009). This self-de-ception is inherently undesirableit is good to know what you are doingand also has undesirable effects. One of the most important of these effectsis the failure to achieve fairness and the intrusion of arbitrary factors un-related to merit into the admissions process.25

23 Mamlet (2005), Schwartz (2005a, 2005c), Stetson (2005), Thiboutot (2005).24 OHear (2007) similarly overlooks the possibility that all arbitrary allocative processes are not

on a par. See Stone (2009b).25 Schwartz also recognizes the following additional benefit to ending this self-deception: If tal-

ented and hard working people are forced to confront the element of chance in lifes outcomes whenthey (or their kids) fail to get into the best college, they may be more inclined to acknowledge therole of luck in shaping the lives of the people around them. And this acknowledgment may make thema good deal more empathic toward others, and a good deal more committed to creating more room,for themselves and others, at the top (2009). Parents who cannot, thanks to the acknowledged random



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None of this is to deny, as critics of lotteries often seem to think, thatsome scrutiny of claims is desirable.26 At minimum, there is the need todistinguish those with some claim to the good from those with none. Butonce this distinction is made, how finely grained any subsequent distinctionsought to be is an open question. In other words, there is no calculus forpredetermining the amount of scrutiny that will be required to ascertain therelative strengths of claims. But recognizing this fact is fully compatible withthe argument that too much scrutiny of claims can lead to unfairness. Letus consider one way that such a problem could arise.

For any given level of claim scrutiny, there is some danger that the dis-tinctions drawn will track non-fairness-based considerations, thereby intro-ducing unfairness into the allocative process. A professional assessment that

a female candidate has marginally less talent than a male one, for example,can easily serve as a veil for simple sexism.27 This danger must be set againstthe benefit that such scrutiny offersthe ability to recognize genuine dis-tinctions in claim strength. Failure to attempt such recognition is also unfair.

And so these two dangers must be balanced against each other. This is equiv-alent to the need in statistical inference to avoid both Type I error (identifyinga connection between two variables where none exists) and Type II error(failing to identify a connection where one actually exists). And just as theonly way (other things being equal) to decrease the chance of avoiding Type

I error is to increase the chance of incurring Type II error, so the only way(other things being equal) to increase the chance of identifying real dis-tinctions between claims is to increase the chance of drawing unwarranteddistinctions between similar claims.28 For low levels of scrutiny, the balanceof risks clearly favors increased effort; there are clear distinctions betweenclaims to be made, with minimal risk of arbitrary factors intruding themselves.For higher levels of scrutiny, the balance shifts in the other direction, untilthe undetected distinctions between claims become small enough to be easilyconflated with arbitrary social factors unrelated to fairness. At that point, theprocess of evaluating claims becomes one of, in John Allen Pauloss mem-orable phrase, measuring bacteria with a yardstick (Paulos 2000), and fur-ther scrutiny would only serve to introduce unfairness.

Of course, at this level of generality, it is impossible to identify the rightlevel of claim scrutiny. The story told thus far is, in principle, fully compatible

with the assertion that higher education authorities are capable of making

element in the admissions process, guarantee their children spots at the top universities have everyincentive to maximize the number of spots at such universities and to ensure that those failing to attainthese spots can still pursue their life dreams. Others have noted the potentially desirable incentiveeffects generated by lotteries; see Goodwin (2005), and Stone (2011b, chap. 6).

26 Schwartz (2005a) believes that some of his critics miss this point.27 For an example demonstrating this, see the concluding section in Gladwell (2005, 24554).28 Obviously, other things may not be equal. A larger data set may allow a statistician to reduce

the chances of both Type I and Type II error. A new examination process may facilitate finer-graineddistinctions regarding merit without thereby increasing the number of spurious distinctions drawn.



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extremely finely grained distinctions between claimants, allowing them to sayconfidently that (for example) they can identify clearly the applicant with

the 1524th-strongest claim and rank her ahead of the applicant with the1525th-strongest claim. But one should be at least a little suspicious of anysuch assertion. (None of Schwartzs critics assert this, and Mamlet at leastappears to deny it.) This is particularly the case given the lack of unambig-uous, intersubjectively valid measures of claim strength, at least beyond acertain level of claim measurement. A rough cut between candidates can beachieved using some sort of standardized examination process. Some suchmeasures do seem to have a significant degree of validity in predicting studentsuccess in higher education. In the Irish context, for example, the evidencesuggests that the mathematics results and, to a lesser extent, the Englishresults on Leaving Certificate examinations are reliable predictors of aca-demic performance at the postsecondary level (Hyland 2011).29 But suchrough measures generate frequent ties, thereby frustrating those desiringmore precise measures of claim strength.

Moving beyond such standardized processes necessarily requires subjec-tive and ambiguous measures of claim strength. In particular, it requiresconsiderable use of judgment on the part of administrators. Judgment, as Idiscuss in other work (Stone 2011a), involves an agent deciding between anumber of options. The agents goal is to identify which of these optionshas the strongest reasons in favor of selecting it but without identifying thereasons themselves. Rather, the agent relies on an internal feeling (going

with ones gut) that the agent believes accurately tracks reasons. As JamesJump notes in his defense of lotteries, judgment inevitably enters the highereducation admissions process because the objective measurements com-monly used to predict success in college . . . are of little use in making closedistinctions among superior students who apply to selective institutions. Theirgrades and test scores predict success for all of them[;] . . . without objectiveinformation with which to make fine distinctions, the committee is free to

decide arbitrarily (Jump 1988, A52).Judgment can prove valuable in many contexts (Gladwell 2005; Giger-

enzer 2007), but it also has many limitations. Precisely because the reasonsbeing tracked by the act of judgmentif anyare unknown at the time ofdecision, it is difficult to distinguish a successful act of judgment from anact of prejudice or bias. Put another way, judgment may be tracking some-thing, but it may not be tracking the right thing. Reliance upon judgmentthus depends upon some external check that repeated acts of judgment areaccurately tracking what they purport to be tracking. If a decision maker

goes with his gut, there must be some evidence that his gut is not leading

29The evidence is much less clear regarding the American SAT Reasoning Test (Hyland 2011, 19

n. 76), which helps explain the continued controversy over its use.



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him astray.30 This is especially true when fairness is at stake; the claimantswho lose out are entitled to demand evidence that they possessed weakerclaims than the winners (Stone 2009c). But such evidence is rarely forth-coming in the higher education admissions context.31 To be sure, adminis-trators routinely receive evidence that the students they admit perform well.But they rarely receive evidence regarding how well the rejected students

would have performed. They are constantly at risk of running afoul of theconfirmation bias identified by psychologists (Schwartz 2005c).32 It is there-fore easy for them to forget that it is not enough to admit students who havegood reason to be there; it is also important to ensure that they reject (only)students who have less good reason to be there. If the rejected students havereasons for being there that are just as good as the reasons for admitted

students being there, and no lottery is used, then a serious unfairness isbeing committed.

It is for this reason that Schwartz believes that higher education admis-sions processes are governed by what Detlof von Winterfeldt and Ward Ed-

wards called the principle of the flat maximum, which asserts that in manysituations involving uncertaintyand college choice is certainly such a sit-uation, from the perspectives of both applicants and institutionsthe likelyoutcomes of many choices are effectively equivalent. Or, to put it perhapsmore accurately, the degree of uncertainty makes it impossible to know which

excellent school (or student) will be better than which other excellent school(or student). Said another way, there are many right choices (Schwartz2005c). This principle implies that in higher education admissions, there willbe a large group of applicants with claims so similar that the differencesamong claims within this group are smaller than the measuring error gen-erated by the best measuring instruments available. Efforts to distinguish

within this group are therefore counterproductive. They are more likely togenerate unfairness (by wrongfully distinguishing among candidates withequal claims) than they are to generate fairness (by rightfully distinguishingamong candidates with unequal claims).33

30 Schwartz (2005c) relies upon the important work surveyed in Dawes et al. (1989), which dem-onstrates that clinical judgment (judgment as I have defined it) is often significantly outperformedby actuarial judgment (reliance upon a few objective indicative factors). Standardized measurementprocesses, of course, can be overused and abused, just like all political instruments. See Harcourt (2007)on this point.

31 Karabel (2007) advocates the selection of a small subset of each university class (say, 510 percent)randomly. This subset (which would remain unaware of how it was selected) would serve as a controlgroup. If the judgment-dependent processes employed by universities are truly effective, then thoseadmitted via these processes should routinely outperform the control group. If they do not, then theseprocesses should be replaced.

32 Compare Jumps contention: a good universitys admissions office has the luxury of knowing

it will choose a superb freshman class, no matter how it decides (1988, A52). Obviously, this argumentapplies more to elite higher education institutions than to less prestigious institutions.33 Schwartz further believes that higher education admissions officers are prone to make this

mistake because they are committed to maximizing, as opposed to satisficing. The former involveslooking for the best candidates; the latter involves finding good enough candidates. Schwartz develops



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Resistance to this idea, I suspect, accounts for much of the popularresistance to the expanded use of lotteries in higher education admissions.People, as Jon Elster once noted, want to have reasons for what they do(1989, 116). This is particularly true in political decision making; if oneperson receives a good and another does not, people want there to be reasonsfor that difference. And so the designers of admission processes go to greatlengths to pretend that nobody gets admitted or denied without good reason.This may involve treating measurement instruments (such as standardizedtests) as far more precise than they are; it may involve relying upon plausible-sounding but specious measures of merit (such as interviews); and, aboveall, it may involve expending massive resources for marginal-to-insignificantmeasurement gains. As noted above, Elster dubs this failure to recognize the

limits of reason hyperrationality. Avoiding hyperrationality, I contend, is acritical part of ensuring fairness in higher education admissions.

Conclusion

In the argument made in this article, fairness in admission to highereducation is both theoretically simple and practically complex. Applicantsshould be admitted in accordance with the strength of their claims to ad-mission, where those claims depend upon individual merit. Ties betweenequally meritorious applicants should, if necessary, be broken randomly. Fair-ness demands this much. Deviations from this system can potentially be

justified by reference to overall social good, whenever this good conflictswith fairness. And, of course, the demands imposed by fairness will be morestrenuous the more selective the higher education institution in question.Thus, fairness imposes the most severe demands upon elite institutions.

This is the simple part. The complexity arises in applying this theory toreal admissions processes. This will involve a number of critical factors thatdetermine when, and to what extent, reliance upon a fair lottery makes sense.The factors include how closely claim strength (the intrinsic contribution

higher education makes to an individuals life) and the general good (thecontribution educated individuals make to the well-being of society) trackeach other; how precise the best instruments available for distinguishingclaims are; and what distribution of claims is to be found within the popu-lationin particular, the number of people with claims that are either equiv-alent in strength or nearly so.

This complexity reveals itself if one considers the topic with which thisarticle beganIrelands higher education admissions system. Let us return,then, to A ine Hylands proposal to expand that systems use of lotteries. The

his view of this satisficing-maximizing distinctiona distinction commonly drawn in the literature onbounded rationalityin his book The Paradox of Choice(Schwartz 2005b, chap. 4). I do not believe thatthis distinction correctly captures what is at stake between rival approaches to higher education ad-missions, but space limitations prohibit further consideration of the topic here.



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present system relies heavily upon the Irish Leaving Certificate examination,which secondary students take before completing their studies. The conven-tional wisdom is that this examination tracks ability faithfully but not perfectly.Hyland accepts this conventional wisdom; while expressing concern that sec-ondary schools are teaching to the exam in undesirable ways, she alsoadmits that successive studies carried out since the introduction of the pointssystem indicate that the Leaving Certificate continues to be a reliable pre-dictor of student performance in higher education (Hyland 2011, 15). Ifability and merit are highly correlated, my article suggests, then it is reason-able to continue using the Leaving Certificate examination as the basis forhigher education admission, at least until some more accurate merit-trackinginstrument can be devised.

Hyland does not propose abandoning reliance upon the Leaving Certif-icate examination; she does, however, propose restricting reliance upon itby incorporating lotteries into the process. She considers several ways to dothis, including a proposal to set minimum entry requirements for eachcourse. All students who satisfied these requirements would be eligible forrandom selection through a lottery system (Hyland 2011, 22).34 While Hy-land initially offers this proposal as one of a number of possible alternativereforms, at the end of her report she endorses it tentatively[,] . . . as a wayforward in helping to address some of the concerns about transfer from

second to third level education (25).35

Hyland does not explain her rationale for endorsing this proposal. Shedoes, however, make extensive reference to a report by P. J. D. Drenth onthe Dutch weighted lottery system for admission to medical school. (Drenth

wrote this report during the previous review of the Irish higher educationadmissions system.) In that report, Drenth explains that

the weighted lottery model was a compromise between two opposite and hardlyreconcilable points of view. One [stressed] that according to the Dutch legislationeveryone who has completed the VWO with the proper subjects is entitled to startthe academic study of his/her preference. In the undesirable case of more appli-

cants than available places the only fair way to comply with this right is to arrangeadmission by drawing lots. The other view . . . held [that] . . . the maximisation

34As a variant on this proposal, she also suggests a weighted system of random selection, which

would give a higher probability of selection to students with higher points (Hyland 2011, 22). Hylandcites as inspiration here the Dutch experience with weighted lotteries. Nothing, however, about thetheory of fairness sketched here in my article points toward a weighted lottery. My suspicion, which Icannot defend here, is that weighted lotteries represent an attempt to find a compromise betweencompeting values, values including fairness and the general good. Intuitively, such a compromise mayhave some appeal, but its theoretical foundations remain unspecified. If this suspicion is correct, thenselection via fair lottery and selection via weighted lottery are not close cousins.

35 Hyland is not the only one to endorse such a proposal; a recent report by the Irish Universities

Association entertained the idea of admitting to a higher education course all applicants who haveexamination results above a certain threshold, with a lottery used to break ties. This threshold couldbe either substantive, such that all eligible applicants should have a reasonable expectation of com-pleting the course, or minimal, such that even minimally qualified applicants would have a chance(Irish Universities Association 2011, 1619).



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above a threshold. This endorsement seems to demand ignoring detectabledifferences in ability, which according to the first position track differencesin claim strength. Sustaining this position would require endorsing thesecond or third position, both of which are fairly radical and require moresustained argument than Hyland offers.

The first position is the most conservative and thus the easiest to sustain.It also fits well with the account of fairness presented in the present article.But conservative as it is, it still provides a basis for some reliance upon lotteriesin Irelands higher education admissions process. Understanding how re-quires further detail regarding the way that process works. Irish students takea number of examinations at the end of their secondary school studies. Theyreceive numerical grades on each of these examinations. These numerical

grades are converted into letter grades, and these letter grades are translatedinto points. Students are then admitted to the higher education courses for

which they have applied on the basis of the total points they have received.Ties between students with equal point scores are broken randomly.

The presence of randomization in the Irish higher education admissionsprocess has long left many people uneasy. As noted above, Hyland partici-pated in the Commission on the Points System, which reviewed the Irishhigher education admissions process in 1999. This commission also consid-ered the possibility of expanding the use of lotteries. But it noted that not

only was the public opposed to random selection in a general senseobjec-tions were also raised to the present limited system of random selection whichoperates when a number of applicants share the same cutoff point and thereare not enough places for all of them (Commission on the Points System1999, 90). These objections have had an impact on the higher educationadmissions process. In 1992, the system of translating numerical grades intoletter grades was made more fine-grained (by introducing additional lettergrades). Part of the rationale for introducing the more detailed system in1992, the commission noted, was to reduce the number of places in third-

level education which were then being decided on the basis of random se-lection (66). Some proposed reducing reliance upon lotteries even further,by breaking ties between applicants with equal point scores by using thenumerical examination grades (90). The commission rejected this idea.

The argument presented here suggests that the Commission on the PointsSystem was correct to reject efforts to avoid lotteries at all costs. It may beuncomfortable admitting that existing instruments for measuring claimstrength are imperfect and that beyond a point they generate no reliableinformation. But failing to recognize this fact by insisting on the elimination

of all tie breaking is worse than useless; it risks introducing unfairness intothe process. Lotteries guarantee that irrelevant (i.e., unfair) reasons will holdno sway over the tie-breaking process; unreliable and arbitrary tie-breakingdevices cannot do this. Until more precise measurement instruments prove



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their worth, tie breaking via lottery must be accepted as a routine part of afair higher education admissions process, and efforts to eliminate it must beresisted.36

What, then, is the proper place of lotteries in higher education admis-sions? Probably less than Hyland envisions but much more than Irish publicopinion appears ready to tolerate. Fairness in admissions to institutions ofhigher education will, for the foreseeable future, provide ample room forthe use of lotteries, despite the hostility that prolottery proposals invariablyseem to generate. A clearer understanding of what lotteries can do for fairnessis an important first step in the process of overcoming this hostility. Thisarticle has, hopefully, contributed to this clarification process.

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