Grade Caps Fail the Game Theory Exam | Opinion | The Harvard Crimson

5 min read Original article ↗

A pair of hikers comes across a grizzly bear. One quickly switches into running shoes — and the other asks, “What are you doing? You can’t outrun a bear!” The first responds: “I don’t have to outrun the bear — I just have to outrun you!”

The current proposal to address grade inflation by capping A grades creates the same incentive structure: what matters is not how well a student performs, but whether they can “outrun” the student sitting next to them.

As a scholar of marketplace and incentive design, I am especially attentive to how rules reshape behavior. I recently co-authored a paper bringing this research lens to the grading debate. The implications for Harvard are clear: the proposal is unlikely to restore informative grading — and it is likely to introduce new distortions.

Capping courses at approximately 20 percent A grades would reduce the number of A’s awarded and make an A-minus or below the norm. A cap has the virtue of clarity: it establishes a bright-line rule and may relieve some instructors of social pressure to inflate.

However, under a grade cap — or any forced curve — what determines your grade is not just how well you perform, but how well you perform relative to your classmates. It’s the hiker and bear story: students must ask not only whether they can achieve extraordinary distinction in a course, but whether they can achieve distinction more extraordinary than that of the students around them.

I have seen this play out firsthand in my teaching at Harvard Business School, which uses a fixed curve in most courses. I have historically taught an especially difficult MBA elective that draws many of the School’s top students. In a typical year, there isn’t enough of the top grade — a “I” in HBS parlance — to go around. As a result, some students who would otherwise earn top marks miss out on honors simply because they took a course filled with other high-performers.

Under the new proposal, in a course like Math 55, which had about 20 students when I took it, more than half would be upper-bounded at an A-minus even if all performed with distinction in one of Harvard’s most demanding courses. And this isn’t limited to math — for example, as Crimson Editorial editor Kai I. Russell noted, capping A’s would bias against non-native speakers in foreign language courses.

A grade cap systematically penalizes ambitious students for surrounding themselves with strong classmates.

Perverse course-shopping incentives ensue as a result. A student who is prepared for an advanced course but concerned about landing in the bottom 80 percent may choose to drop down preemptively — seeking out a pond where they are a relatively bigger fish. As strong students move into lower-level courses, competition for A grades increases there while harder courses continue to shrink — reducing their A allocation further and driving more students away.

These effects compound if, as the current grading proposal suggests, we evaluate students for honors and other recognitions according to average percentile rank, which can magnify otherwise small performance differences: The tenth-strongest undergraduate out of ten enrolled in a graduate-level elective would be marked as being at the 0th percentile rank despite performing at an advanced doctoral level.

The proposal suggests that faculty could opt into satisfactory/unsatisfactory grading to avoid these distortions, but at the cost of excluding those courses from students’ aggregate rankings. If sat/unsat becomes widespread for advanced courses, it would put them at a disadvantage: Non-letter grades are often perceived as weaker, and concentrations frequently cap how many may count for credit.

Moreover, with such courses excluded from grade point averages, we would end up with a system that evaluates students primarily on introductory and general education courses rather than advanced work in their fields. GPA prizes risk becoming a contest for who best avoided letter-graded classes with other top students throughout their time at the College.

These distortions undermine the very objective of reform: to create meaningful signals of student achievement. And they disproportionately harm students who take classes that push the boundaries of their abilities.

The best of the best students typically challenge themselves in this way, and if our grading systematically punishes them, those students might think twice about coming to Harvard at all.

As Joshua S. Gans and I explain in our paper, a grade compresses two dimensions — student ability and course difficulty — into a single signal. Without information about a course’s difficulty, it’s hard to identify whether a student who performs well is strong or if instead the course (or its grading scale) is easy.

Grade caps exacerbate this problem because they leave no leeway for a harder course to give higher grades on the margin in a more demanding environment.

There are better approaches. One option is to report information about course difficulty and grade distributions on transcripts (Dean Amanda Claybaugh’s grading report proposed a version of this). Grades also become more informative when they are finer measurements of quality — for example, using a full numerical scale rather than coarse letter categories.

Even better would be to apply statistical methods. Using data across overlapping enrollments, it is possible to infer students’ relative performance in a way that accounts for differences in how competitive a given classroom is — similar to the way the Elo chess ranking system accounts for the difficulty of a given matchup.

Creating meaningful grade signals is a problem of statistics and incentive design, and we should use the scientific rigor at our disposal to find the optimal solution. As we do so, we must recognize that we are playing a game in a market and we are setting the rules of the game.

The current proposal would set rules that push students to outrun one another rather than to outsmart bears. We should not rush to give grade caps an A they do not deserve.

Scott Duke Kominers ’09 is the Sarofim-Rock Professor of Business Administration at Harvard Business School and a Faculty Affiliate of the Harvard Department of Economics.