# Scariness and Self-Selection: A Shopping-Week Meditation

nb: For those outside of the Harvard ecosystem, "shopping week" is the first week of classes, during which all courses are open to drop-ins. It's only at the end of shopping week that we submit study cards and are assigned final schedules.

One of the things that inevitably happens during shopping week is that classes are overfull. Since almost all students shop weakly more courses than they end up taking, even classes with correctly-sized rooms end up crowded, short on chairs, and/or with students sitting on the floor.

I've noticed that this problem is remarkably bad in upper-level CS / Math / Stat courses (it might also be bad everywhere else; I just don't have enough data to say). Once you get past the intro-programming and intro-theory sequences, concentrators have almost-infinite freedom in selecting technical electives in the department, so there's a lot of comparison-shopping going around.

To make it worse, a phenomenon I'll dub "window-shopping" is particularly egregious in the CS department -- in-the-know concentrators will show up for the first two lectures of a well-liked professor's class just to hear funny one-liners, even if they know they won't be taking the course that semester.

What this means is that it's not uncommon for the attendance at the first lecture of the semester in a 100- or 200-level class to be 150-200% of the actual enrollment the professor and the College had planned for.

I shopped five courses this shopping week, and in four of them, the professor remarked on such over-attendance.

In two, the professor made a half-joke along the lines of "Well, this is obviously too many people to fit in the room, so we'll have to scare some people off until we fit."

In the third, the professor simply said "Well, this is too many people to give everyone enough time to talk; we'll run a lottery tonight to get down to a better size."

In the fourth, the professor said "Wow, this is more people than I expected. I guess we'll have to get a bigger room and change around some of our plans!"

One other course I ended up taking didn't meet at all during shopping week, since it admitted by written application only.

It's worth meditating on the difference of atmosphere these approaches predictably create.

### (1)

One way of balancing course sizes is a market-inspired model: If all students want to learn [X], but have different levels of interest/commitment, then you can turn up the intensity of the class until it better-serves the (appropriate) number of students who remain. They get a higher-level, better-focused class, and the other students -- who presumably have other interests they are equally passionate about -- can sign up for those classes.

In the end, everyone ends up studying the things they most want to study, with the other people who most want to study it, at the highest level that's suitable for all of them. This assumes that courses can, in general, be made "harder" in ways that benefit the committed student rather than merely padding their hours with busywork, but for most courses with real content, this isn't an impossibility.

Another way of balancing course sizes is by fair or weighted lottery. Among all applicants, the professor selects (probably randomly, but potentially with some preference for favored characteristics such as seniority or in-concentration status) some subset of students to accept. They get a representative cross-section of all interested students (perhaps up to some useful bias), and all students have a shot at the most-desired classes.

On the other hand, there is little way for a student who is unusually interested in a course -- who presumably would benefit more by taking it -- to signal this fact. A related mechanism is to have students submit applications which are selected based on some criteria, but this can be incredibly time-consuming for classes past a certain size, as well as for students in aggregate as more and more courses require unique effort to apply.

A third response to oversubscription is to simply accept more students. No one is left out of a course, and -- at least as importantly -- no one is left in a course they don't want because they couldn't get into another.

But expanding the course isn't always possible, and even when it is, the students themselves may suffer. Some of the best high-level courses I've taken have been discussion-oriented, but average opportunity to contribute diminishes as $O(1/n)$ in the number of students, and in practice, large groups are almost always dominated by a core of the loudest students...which tends in my experience to grow smaller as the class size grows.

So what's wrong with the market mechanism, again? (i.e. Make the class more hardcore until only the most committed students remain.)

### (2a)

In two words: selection bias.

In three: self-selection bias.

In the supply-and-demand equilibrium of class 'hardcoreness', you don't actually select for the students who are best suited to the class -- you select for the students who believe they are best suited for the class. In some cases, this works well -- some people have a well-calibrated sense of their own abilities, and may in fact be well-positioned to judge if they'll be able to jump into a class without an unconventional background or less prior experience.

But on the other hand, impostor syndrome is real, and I'm not certain I could devise a better way to trigger it than "I guess we'll scare some of you off until only the best-suited students remain."

### (2b)

It takes a lot to make me feel like I don't belong in an academic setting. I've got a lot of what Nate Soares calls confidence all the way up, especially in academics.

Maybe the only time that I've felt so out-of-place that I backed away from a course was when I was shopping Introductory Sanskrit last semester. I needed to fulfill a language requirement, and two of my classicist friends convinced me that Sanskrit would be a fun way to do so. (Yes, I have strange friends.)

As we introduced ourselves one at a time, I quickly realized that something like three-quarters of the students were students from the Divinity School, who answered "Why do you want to take this class?" with "My studies involve South Asian religions." as if, you know, obviously.

The professor then took care to stress upon us that Sanskrit was hard, that we would have to work hard to master the language, and that anyone who was not prepared to work hard should study an easier language. "But," he continued, "since most of you have to be here anyway, let us not waste time," and he began the first lesson on vowels.

After that experience, it was abundantly clear to me that I was not prepared to take even Introductory Sanskrit. The next day, I enrolled in Introductory Spanish, and consigned myself to two semesters of dull (but survivable) review of a language I was already more than passingly familiar with.

### (2c)

My experience with Sanskrit was pretty eye-opening to me when I realized that some people feel like that all the time. I still believe that, if I had committed myself to it, I could have learned to read some of the oldest (and, I am told, the most beautiful) religious poetry on Earth.

But I didn't. I thought "Well, if this is going to be this hard, I guess I'll take some other class I'm better suited to instead."

I am, generally, the sort of person who believes that prerequisites are for other people, and that the correct way to take classes is by skipping about one prerequisite at a time, picking up the missing background by osmosis over the semester. But when everyone else in the room introduced themselves as the sorts of people who were used to studying dead languages and the professor told them it was going to be a bumpy ride...it didn't take me long to get off.

And that was even without the implicit threat that it I -- as pretty much the least-qualified person in the room (as far as I could tell) -- didn't excuse myself, the course would just get harder until I did.

If you've never been scared out of an academic environment in your life -- and I was! -- I encourage you to shop the first day of Introductory Sanskrit to feel what it's like.

edit: In the Facebook thread, the two of my friends who did stay in the class chimed in to inform me that actually, most of the Div students there ended being pretty mediocre at Sanskrit, never having studied a classical language before.

But (sorry, Roman) I think this makes my experience an even more appropriate example, since it highlights the fact that scariness and stereotype threat are entirely a function of what message is received, no matter what message is intended. My point is not that the preceptor intended a "culling of the unworthy" or that I was out of place in the class, but that the ultimate effect of his words and the environment I found myself in was to make me uncomfortable enough to back out.

Whether or not Div students are better at Sanskrit has about as much to do with it as whether or not Asian guys are better at computer science. Stereotype threat requires only a perceived difference, not a true one. And so it's incredibly important to remember that harm of this sort is almost always done without intended malice.

### (3)

In Intro Sanskrit, if you accidentally scare off everyone who maybe doubts that they belong, you won't have many undergrads looking to branch out and enrich their lives. In Computer Science, if you accidentally scare off everyone who maybe doubts that they belong, you're likely to scare off a fair number of people from groups traditionally underrepresented in CS.

For now, I am just going to assert that the resulting monoculture is a generally bad thing that we'd like to avoid. Diversity in our classrooms, like diversity in our industry, is generally good for producing new perspectives and ideas, and our field is young enough and open enough that we can use all the new ideas we can get.

Of course, sometimes one does need to communicate to students that a course is going to be difficult, and sometimes one does want a method for selecting for the students who will be most dedicated. But, no matter your goal, there's probably a better way to go about it than simply turning the self-selection dials up to 11. Remember: what one student takes as an offhand joke may give another student serious pause.

So unless you're trying to filter for "unshakeable faith in my own abilities" and "I have no reason whatsoever to believe that I may not belong here", be careful with small words that are received with differential impact.