Finding a Way to Develop Better Algorithms
For a better ‘matching’ in our society
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Professor Koh Young-woo of the Department of Economics and Finance is an expert in the field of microeconomic theory, market design and mechanism design. His main research interest is relevant to studies of matching and auction theory. His recent paper, “Decentralized College Admissions” researched on decentralized college admissions with uncertain student preferences. Since schools strategically target students when students’ preferences of schools are unknown, a matching between colleges and students is often inefficient and unfair.
“When colleges admit students every new year, they strategically accept some students who are possibly overlooked by other colleges, or competitors. When that happens, highly ranked students, who are better qualified in their scores, essays, or interviews perhaps, may receive fewer admissions or have a higher chance of receiving no admissions than those students who are ranked below,” explained Koh.
In the paper, there are two colleges, each with its limited capacity of students they can admit, and a unit mass of students. Colleges make admission decisions based on two attributes of a student: a score that is common to all colleges, and a ‘fit’ that is college specific (essays, exams, or extra-curricular activities). Colleges rank students according to their scores and fits but they have no way to observe students’ preferences, which causes uncertainty. While such uncertainty leads to unfair outcomes, it also shows inefficient equilibrium as some colleges leave their seats unfilled although there are unmatched students who could have been welcomed by other colleges.
“Thus, strategic targeting and biased admissions make the outcome also unfair in other dimensions. It creates what is called ‘justified envy’, when a mass of students are unable to enroll in their preferred schools because the schools are taking students who are ranked below them,” said Koh. To cope with such congestion, colleges employ additional measures like restricting the number of applications students can apply to or admitting students in sequence by putting them on the waiting list. However, it is hard to say that these additional measures eliminate aforementioned undesirable outcomes. Even when colleges make their waiting lists, it is hard to determine or expect which students will enroll as time is limited for the students to make their choices.
The solution to this problem could be to centralize the matching through ‘deferred acceptance’. Deferred acceptance can be seen when students apply to high schools. It was actually devised and used in New York. Students report their preference orders to the clearing house, which then the information is used to simulate the following algorithm: at the first round, students apply to their most preferred schools, and the schools tentatively admit favorable students up to their capacities and reject the rest. The rejected students then apply to their second choice, and the schools reject lower-ranked students below their capacities. This process is repeated until no further applications are made. “More students are satisfied by this method, as more students and schools can find a better match for one another,” said Koh.
Unfortunately, it is hard to expect a centralized admission in colleges as there are different qualifications schools want from students unlike high schools. Different and complex admissions are less likely to be perfectly merged into a single algorithm. “Thus, more research and studies have to be followed to develop a better algorithm to reduce unfairness, and to increase efficiency and effectiveness of the matches,” added Koh.
“I think new ways of matching in many other circumstances like donating organs and allocating teachers in public schools can improve the outcomes better,” asserted Koh. “While the resources are limited and there are more people who want it, we can better utilize resources just by allocating with more efficiency, leaving more people satisfied as a result.”
Yun Ji-hyun firstname.lastname@example.org
Photos by Choi Min-ju
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