On Selectivity

There's natural (almost foregone) conclusion that a university's acceptance rate is inversely proportional to its quality: low acceptance rate represents high quality, and vice versa. The other day, I realized that this metric is much more easily manipulated than I had previously thought.

Here's an illuminating example. In a town of 1,000 students, there are two universities: Coin Toss College and the School of Scores. Each student must apply to exactly one college, and all applicants would prefer to attend the School of Scores. The School of Scores takes the top 100 applicants by score. Coin Toss College takes 200 applicants: 190 by score, and then 10 more entirely at random.

By all measures, SoS is the more selective school. It is more desirable than its competition, and has fewer spots to fill. Our intuition would lead us to expect that it'll have a lower acceptance rate. But consider the situation from the perspective of an individual student, and a strange result emerges. Any student who scored above the 10th percentile (the top ~100 testers) will apply to SoS. The remaining 900 will apply to CTC. 190 will get in by score, and 710 hope to win one of the 10 wild card slots. This puts SoS's acceptance rate near 100%, and CTC's acceptance rate at ~25%. Surprisingly, SoS has an acceptance rate four times higher than CTC, despite the fact that SoS admits half as many students and is strictly preferable to CTC!

Self-selection is responsible for this strange phenomenon. The SoS applicant pool heavily self-selects: kids who won't get in know this, and don't apply. In contrast, CTC's admissions process leaves little room for self-selection. Its unpredictable nature gives all applicants a chance, so they all apply.

From this example, we can see that uncertainty in admissions processes hinders self-selection, which drives up applicant pool size and drives down acceptance rate. By increasing uncertainty (as CTC's admissions scheme does), you can dramatically decrease your admission rate, and implicitly present your school as more desirable than it is.

What else can we do to manipulate our admissions rate? Since we probably don't want to decrease the number of incoming students, we need to increase the number of applicants. Normal applicants decide where to apply using some calculation like this:

$$\frac{\textrm{(how much I like the school)} * \textrm{(perceived chance of admission)}}{\textrm{work required to apply}}$$

Injecting uncertainty works because it increases an applicant's perceived chance of admission. Test taker rank #865 has ~0% chance of admission at SoS, but has a lottery ticket at CTC, so she applies to CTC.

(We're already trying to make prospective applicants like the school as much as possible.)

Our final option is decrease the work required to apply by making filling out an application as easy as possible. If I think I have a 5% chance of getting into Northeastern, I'll apply if it costs me three clicks, but not if it requires me to write five essays. This is intuitively obvious; less work to do an application equals more applicants. Unfortunately, this is also a double edged sword, since fewer essays implies a greater reliance on scores, which decreases uncertainty and may discourage applicants. Since it's dubious whether most applicants consider this final point, it probably doesn't matter much in practice.

Here's a formula. If you're a college admissions department trying to clamp down your acceptance rate, inject uncertainty into the admissions process. Ask essay questions that demand weird and unusual responses. Publish no statistics about scores. Make the details of your admissions process as opaque and magical as possible. Make answers to questions about process unnecessarily vague. Don't require applicants to have taken any specific high school classes. Make all standardized tests optional.

Simultaneously, make it as easy to apply as possible to apply. Use the common application, so applicants don't spend any time on administrative overhead. Make your required essays, if any, few in number and short in length.

Respecting your applicants

Decreasing acceptance rate increases the number of rejected applicants, and correspondingly the amount of time wasted applying to your university. By clearly stating reasonable requirements for admission to your university, you save everyone time, and earn the respect of your applicants.

If you don't accept anyone with an ACT less than X, say so. If you don't accept applicants who took art in high school, say so. People often mistake this for colleges trashing people who got ACTs less than X or took art or whatever. Although it might seem harsh, colleges are doing these applicants a favor. Instead of wasting their time applying to your university, they'll spend more time on applications to schools where they might get in and have a great undergraduate experience.

The most recent and flagrant example of this is UChicago dropping their requirement for standardized tests.

"We wanted to [make sure] that everybody, anybody could aspire to a place like UChicago."

I read this as "we want to make sure that applicants whose time would be better spent applying elsewhere still waste their time so we can drive down our acceptance rate." It feels disgustingly predatory. I'll won't be holding my breath to know how many applicants are admitted without scores in the 2019 cycle.

This is also one of the reasons I respect MIT's admissions department (bias alert!). First, they don't inject artificial uncertainty. Want to know what the admissions process looks like? What goes through admissions officers' heads as they read your application? What the admit rates by score are, even if they're ugly (spoiler: they are)? What the difference between early and regular admission is, really? It's all online, spread across thousands of blogs and comments. Second, their application is shamelessly (and inconveniently) entirely separate from the Common App, which dramatically increases the amount of work required to apply. Both of these factors likely drive their acceptance rate up. To be frank, I'm surprised it's as low as it is.