Students in the Maastricht University exchange program provide an ordered list of their six most-preferred schools. Despite this, because their preferences matched many other students’ preferences and/or they were far back in the queues, 47 of the 357 participating students have not yet been placed.
Is there any way to do a better job of matching? Does the path-breaking work of Alvin Roth (more here) give any guidelines to improving the efficiency of this complicated matching scheme? One possibility is a two-stage process, asking students who are unplaced after Round 1 to list their preferences over the remaining available list of unfilled places. One could even iterate additional rounds until all students are placed. Both students and those foreign universities that are not attracting enough Maastricht students would be better off. But can one do better than this simple addition to the matching process?
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Andreas,
I don’t understand your objection to the “rank 10 schools instead of 6.” Yes, in the limit, this would extend to listing all schools, which would be very costly–which is why it’s not what is suggested.
There is a cost-benefit trade-off in the number of schools students rank. The costs are more time spent investigating and listing schools; the benefits are reducing the number of unmatched students.
If there’s a high number of unmatched students, then there’s a decent chance that expanding the number of ranking slots by some small amount would pass a cost-benefit test.
All students who did not find a university after the first round are put on a waiting list, and can still go. Their options are decreased immensely, and that is why most students try to get their first 6 options according to their assumed possibilities.
I’ve heard that this semester more students want to go abroad than usual, which could have caused the problem.
Sounds like a stable marriage problem – hospitals in the US use it to place residents. It’s based on a ranking by both the hospitals and the residents. http://en.wikipedia.org/wiki/Stable_marriage_problem#Similar_problems
This seems to be an instance of the “Stable marriage problem” (http://en.wikipedia.org/wiki/Stable_marriage_problem), which is solved by the Gale-Shapley algorithm. Some variant of this is already used to match medical students to residency programs, which is almost identical to the problem with exchange students.
I agree with Andreas that extending the list from 6 to a slightly higher value is not a theoretically interesting solution. It would, perhaps, solve the question simply without additional inefficiency in resource expenditure by the office in charge.
Perhaps not all student ranked spots need to be filled. I am unclear if under the current rules all 6 spots need to be ranked by the student. Perhaps not attending should also be an option? Buenos Aires or bust?
I think the best idea would be to QUIT WORRYING so much.
It’s an exchange term in which students want to absorb the culture around them and meet lots of new people. It should be during this exchange term that students take electives or classes they are very interested in rather than boring requirements.
In my experience with exchange students we spend so much time worrying about picking the right place, not realizing that if we go someplace else it’ll turn out very well. Students read about them and talk to others, but the experience is unique to each person, never being exactly what you expected.
I feel students should order their top 20 schools, if #1 doesn’t accept, go to #2, then #3, until they are eventually placed.
This is not a new problem.
I presume for the system to work, students are obligated to attend the program to which they are matched. If this is the case, I don’t believe that increasing the size of the rank list will solve the problem. There needs to be a second round for unmatched students.
Or there could be something like the residency match scramble for those graduating medical students who fail to match into a residency program.
As there were 396 places and only 357 students, this a problem of incomplete information. The only information available is the allocation of the previous year. So students who are high ranked, choose medium ranked universities as their save choices. Medium ranked students choose low ranked universities as save choices. So in the end there is a gap some where. This gap is due to incomplete information. Students should know what is left for them. Student #1 starts choosing from the 396 places. Student #2 than can choose from the remaining 395 places and so on, until each student received an allocation. That is a very fair method and it would finish the gambling, which each student has to encounter. I assume that this allocation can be done by a clever software, or by meetings in the university.