Existing computational models of admissions markets tend to fall at one of two extremes: Either they envision a centralized admissions process in which the school board runs an algorithm that says which students go where, or a decentralized process in which colleges compete for the best students. But the Korean college admissions process cannot be adequately described in either of these terms.
The Korean admissions process is decentralized in the sense that students ultimately can choose which college to attend from the subset to which they are admitted. However, the application procedure is facilitated by the government, which enforces a limit on how many schools each student can apply to (currently six) and requires a certain distribution of applications across three tiers of selectivity. This means that the Ivy League sweep is theoretically impossible in Korea.
In addition, the government assigns each college a quota, meaning the maximum number of students it can “recruit” in each academic major. In smaller universities, the quota for a given program may be as small as a single-digit number. To ensure that no college exceeds its quota, students are admitted over the course of several rounds of acceptances, with different scoring criteria and cutoffs in each round. Because colleges are not allowed to use empty seats in one major to admit extra students in another, this creates endless possibilities for strategic application. As an applicant, if you can identify an underdemanded program at your target school, you will be guaranteed admission in the final round as long as you meet the minimum application requirements. And, as many have probably heard, a signature feature of the Korean admissions process is a big test called the Suneung or CSAT. Whereas American universities have begun to discount standardized test scores, a typical Korean university determines about 80 percent of applicants’ composite score using the Suneung; the remainder comes from high school grades, an interview, and/or an admissions test specific to the program the student is applying to. It is from this weighted average that the college defines its final ordering of the applicants and sets its score cutoff. As a result, students’ admissions probabilities are highly correlated across universities.
The argument for this design is twofold: First, it is cost-efficient, because it caps the total number of applications and therefore reduces the number of applications that each college has to read. (However, we ought to question the amount of reading actually involved, since very few universities require anything as textually substantial as the American “college essay.”) Second, it is fair in the sense that it evaluates all students on the same, quantitative metrics.
The most obvious and common argument against the semicentralized admissions procedure used in Korea is that it is actually unfair, because evaluating students in approximately the same way at every college means that winners take all. A student with low test scores but a high degree of motivation does not have the chance to prove herself by actually taking college courses alongside high-achieving peers. You have to get smart by the end of high school, or it’s game over. A related argument says that the Suneung is unfair because wealthy students receive private tutoring in order to increase their score. However, I find these arguments to mistargeted, because (to my knowledge) the high priority colleges give to the Seneung in their admissions decisions is not mandated by the government. In theory, if a college wants to admit students purely on the basis of high school grades or tennis ability, it can, but colleges stick to the Suneung because they like it. It’s a legible (if unreliable) indicator of academic ability, it avoids the appearance of corruptibility, and it’s easy for the college to track year over year as it tweaks its admissions standards in response to market conditions.
However, even if we set aside the Suneung and the attendant debate about fairness, I argue that the Korean admissions process is economically inefficient because of the limits it imposes on students’ application strategies. If an outstanding student from a rural area knows that she can only apply to two schools ranked within the top fifty, she may be inclined to hedge her bets by applying to schools ranked in the thirties and forties rather than wasting an application on (what Americans would call) a “reach” school in the top ten. Because of situations like this, in any admissions process that circumscribes students’ ability to consider a broad range of colleges produces, the outcome is highly sensitive to students’ ability to intuit their rank in the broader distribution of academic talent.
I hypothesize that students who don’t have role models who attended top universities will tend to adopt a minimax strategy, and end up attending a university that’s worse than where they could theoretically get in under an efficient allocation. On the other hand, students who have the financial means to take a gap year can afford to apply to reach schools, and reapply to a more conservative set of schools next year if they don’t get in. With the right computational model, we can attach numbers to these hypotheses; for example, if the number of allowed applications increases from six to seven, we can try to predict the change in the number of students who decide to take a gap year.
Why study the Korean college admissions market from an economic perspective? Anyone familiar with the computational models typically used to study admissions markets should have raised an eyebrow at the monolithic notion of better and worse schools implied by the previous two paragraphs. In fact, the very thing that makes the classical school-choice problem interesting is the possibility that students have diverse preferences (based on individual variations in geography, academic interest, family alumni, and so on). Thus, in the canonical problem, there is not necessarily a global ordering of better and worse schools. Nor is there a global ordering of students, like the one that arises when all universities grade students based on standardized test scores. Korea is exceptional on both of these points. Most schools rank students in a similar way, and because of the high degree of vertical differentiation, most students have a similar preference order over the 300ish universities in the market.
Loosely speaking, when the preference orders are more or less random, the set of possible stable assignments is relatively large, and we can start to “play” with other distributional goals, like trying to obtain gender parity at each university while preserving overall stability. This is what a lot of current papers in stable assignment are doing now. However, in a stylized Korean admissions market in which most students have a similar preference order over the schools and all schools assess students in the same way, there is only one stable assignment (as I can show mathematically). Although we don’t get to play with distributional goals, because the stable assignment is unique, we can examine it in greater detail, and compute comparative statics such as the marginal effect of a change in student population on the selectivity of each university.
Another reason to take a closer look at correlated admissions procedures like the one used in Korea is that such market designs are common around the world, not just in Asia, but also in many European countries and in local school-choice markets in places like New York City. It’s cool, if you know how to program, that we have a simple algorithm for computing stable assignments in arbitrary discrete admissions markets given lists of student and school preferences. But by narrowing our focus to the case of correlated admissions, we can make more ambitious quantitative predictions about the long-run behavior of the market, including, hopefully, computing the efficiency cost of admissions quotas and limits on the number of applications each student has.