Do institutions -- and their professors -- have a right to choose?

Alternate title: An auction theory of entrance exams!

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In a thoughtful post, Arunn Narasimhan of IIT-M lays out two possibilities for selecting students (look at this and this for some more background).

While the first mechanism selects students based on high cut-off in each of the three subjects of the exam, the second uses just the aggregate marks. The first method could de-select those -- let's call them specialist stars -- who excel in one subject, but don't meet the cut-off in one or both of the other subjects. A corollary is that the second method may put some -- let's call them all-rounders -- at a disadvantage.

Sidebar

Clearly, at the top end of the achievement spectrum, the difference between two procedures has a very high probability of being small; you cannot be among the top 500 (or, even 1000) unless you score exceedingly well in all the three subjects. But as you go down to ranks beyond 1000, the differences are likely to mount. The Telegraph's story about JEE-2006 shows that this is indeed the case: the number of discrepancies between the two procedures was only nine in the top 1000 ranks, and it increases to 54, 125, 255 and 354 for the next four sets of 1000 ranks each.

To me, the real surprise is the 35 percent difference by the time you come to 5000th rank. Remember, this position falls in the top 0.5 percentile of the pool of higher secondary (Pre-University or Plus Two) students in the science stream! In this exalted regime, this represents a huge divergence between the all-rounders and specialist stars.

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Arunn points out that it is difficult to select one of the two procedures over the other (JEE-2006 went for the all-rounders, while JEE-2007 went for star specialists. But, as I said, the difference is not much at the top end of the spectrum). I don't see why a choice has to be made between these two procedures. Why not select students using both? Since all-rounders and specialist stars bring different sets of aptitudes and attitudes to the table, isn't it a good thing for the IITs?

I would say yes, but only if something else is also taken care of. That something is this: if you select specialist stars, you should find some way by which they get to study fields that play to their strengths. What good does it do to the institution (or, even the student) if someone who excels in math (but scores poorly in the other two subjects) if he/she cannot find a place in computer science, or does not choose mathematics because of parental pressure? Similarly, is it desirable for a chemistry star to skip studying chemistry, chemical engineering and metallurgical engineering, and choose electrical or mechanical engineering?

Let me state categorically again: I am not arguing for a Big Brother who'll 'guide' students to areas that he thinks is right for them. My argument is that institutions -- and their individual departments (and their professors!) -- also have a right to be choosy about the kind of students they want to teach; their exercise of this right need not infringe on the right of individual students to choose what they want to do.

Thus, for example, a computer science department may want a student body that has more than a few specialist math stars (irrespective of how well they did in their physics and chemistry exams). Similarly, a chemical engineering department may want a few chemistry whizkids even though they may not have done all that well in the other two.

If we accept this line of thinking, we still have to address the issue of matching students to specific departments in specific institutions. Currently, the IITs rank students, who then take their turn at choosing an institution-department combination, with professors being mere spectators. Is there an alternative that respects the rights of professors as well as those of the students?

Sidebar

Rahul has argued (see this post and this comment) for dispensing with the idea of assigning a student to to a specific department at an IIT (which is currently being done through a ranking mechanism). Students will then take a common set of courses during the first one or two years, at the end of which they can be assigned to a department; this step will have the backing of the 'revealed competence' of the students (through their grades in the relevant subjects). Let me say that I like Rahul's point about giving students a year or two to explore the intellectual territory before they specialize.

But, in this post, I want to explore a different possibility that allows students to join a specific department in an IIT.

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Let me take a stab at this question:

1. Let each student get a numerical score (normalized to, say, 1000) in each JEE subject . In principle, every student taking the exam may be given this score; but the IITs may want to not embarrass those with negative marks!

2. Each department in every IIT announces, before the exam, its preferred weights for individual subjects. For example, a chemical engineering department might choose (0.25, 0.3, 0.55) as weights for (math, physics, chemistry), while a computer science department may use (0.5, 0.3 and 0.2). Heck, another CS department at another IIT may even go for (0.6, 0.4, 0.0)!

3. While the scores may be sent to as many students as the IITs choose, only those in the top X percentile (say, X = 5) in any of the subjects are invited to give their preferences for specific institution-department combinations. This is best done through a website.

4. For each department, a list of all eligible students is prepared, in the decreasing order of their composite scores. Similarly, each student may be eligible for multiple fields of studies in different places.

5. Students are assigned to their top-most choice for which they are eligible.

Such a procedure would not have been possible in the 1980s (for example) when students' choices were processed manually. It can be contemplated now only because the technology for doing it is available. After all, fancy auctions are being used (and some IIT professors are probably designing even fancier ones!) for matching advertisers with search phrases at Google and other online firms; what we are talking about here is essentially an auction -- involving IIT seats as the object of desire and JEE marks as the currency -- that aims to maximize the 'outcome' for the interested parties.

Let me be the first to admit that what I have suggested is probably not the most perfect way matching students to institutions; the procedure I outlined above may not be air-tight, and there may be other mechanisms that achieve the same goal in a more elegant way.

But, what cannot be denied is that individual departments have a right to select their students who, in their opinion (and collective wisdom), will benefit the most from the education they impart. If this right is conceded, I think it's difficult to justify the JEE's current format with its undifferentiated ranking that selects specialist stars but places them in sub-optimal settings.