When navigating the complex landscape of higher education, prospective students and their families often seek reliable metrics to compare colleges. Parchment College Compare offers a unique approach to college rankings, moving beyond traditional metrics to analyze actual student decisions. Instead of relying solely on factors like acceptance rates or endowment sizes, this system is built upon the revealed preferences of students themselves. This article delves into how Parchment College Compare works, providing insight into its data-driven methodology.
The core principle of Parchment College Compare rests on observing student choices when they are admitted to multiple institutions. Imagine a student accepted to both College A and College B. Their ultimate decision to attend one over the other reveals a direct preference. By aggregating thousands of these decisions, a comprehensive picture of college preference emerges.
To quantify these preferences, Parchment College Compare employs a dynamic scoring system. Initially, all colleges are assigned an equal score, reflecting the absence of prior preference knowledge. This starting point is crucial for unbiased comparison. For every student decision, a “matchup” is created between the chosen college and each of the colleges the student was admitted to but did not choose to attend. For instance, a student admitted to three colleges generates two matchups: one comparing the chosen college to the first rejected college, and another comparing it to the second rejected college. The number of matchups per student is always one less than the number of colleges they were admitted to (N-1 matchups for N admissions).
These matchups are then evaluated using an Elo-based system, a methodology originally developed for chess rankings and adapted here to reflect college preferences. This system is expectation-driven, meaning the point adjustments after each matchup are not fixed but depend on the pre-existing scores of the colleges involved. In the initial stages, with all colleges having the same score, victories are largely considered equal. However, as the system processes more data, scores diverge, and the point allocation becomes more nuanced.
Consider the example of Berkeley. As Berkeley is frequently chosen over other institutions, its score will tend to increase rapidly. The Elo system recognizes the significance of victories against highly-ranked colleges. Therefore, when Berkeley is chosen over a college with a similar high score, it gains more points than when chosen over a college with a significantly lower score. Conversely, if a student chooses a lower-ranked college over Berkeley, the lower-ranked college experiences a substantial point increase, while Berkeley’s score decreases, albeit to a lesser extent. This dynamic adjustment ensures that the rankings are responsive to the strength of preference revealed by student choices.
Ultimately, Parchment College Compare ranks colleges based on their accumulated scores. These scores are not merely arbitrary numbers; they are mathematically translated into probabilities of student choice. For example, the system might output that “there is an 84% chance that a student admitted to Berkeley and Texas A&M would choose Berkeley.” This probabilistic interpretation provides a tangible and meaningful summary of student preferences expressed through their enrollment decisions.
To refine the accuracy and stability of these rankings, Parchment College Compare incorporates an advanced statistical technique to address potential path dependency. Path dependency refers to the possibility that the order in which student decisions are processed could influence the final rankings. To mitigate this, the system employs a Monte Carlo simulation approach.
The data is organized by admissions cycle, starting from the oldest available data. Within each admissions cycle, the order of student decisions is randomized. This randomization is repeated thousands of times (e.g., 10,000 iterations). For each iteration, the matchups within that year are processed in a different random order, and the resulting scores are recorded. This process is akin to repeatedly simulating the admissions cycle under slightly different conditions to ensure the rankings are robust and not unduly influenced by chance ordering of data.
These iterated scores from one year then serve as the starting scores for the subsequent admissions cycle. This chronological progression is important because past admissions data informs future rankings. By the time data from a later year is processed, the system has already learned from previous years’ student choices. By randomizing the order of matchups within each admissions cycle and iterating this process over thousands of simulations, Parchment College Compare generates stable and reliable college rankings that genuinely reflect the revealed preferences of students, providing a powerful tool for college comparison.
