Simulation of Academic Performance and Prestige Dynamics

The problem

The Double Degree in Physics and Electronic Engineering at UPV/EHU has had a limited number of places since 2011. Its cut-off grade rose year after year, the press reported it, and the reporting raised it further, until the degree attracted the highest-scoring school leavers in the system. Teachers on the degree describe a paradox: the entry grades keep rising while the mean grades inside the degree drift down. One hypothesis is that prestige selects for students motivated by status rather than vocation, who cope worse with a hard curriculum. The question is whether removing the limit on places would reverse the trend, and it is a question about a feedback loop between a ranking and the population that the ranking sorts. That loop is a well-studied object in the physics of social systems.

Basis paper

A. Clauset, S. Arbesman and D. B. Larremore, “Systematic inequality and hierarchy in faculty hiring networks”, Science Advances 1, e1400005 (2015), doi:10.1126/sciadv.1400005. Open access; the hiring networks for computer science, business and history are released with the paper.

The authors build the network of who hires whose graduates, extract a prestige ranking from it with a minimum-violation ordering, and show that the hierarchy is far steeper than merit alone would produce and that prestige propagates downward almost exclusively. It is the cleanest quantitative demonstration that prestige is a self-reinforcing variable, which is exactly what the double-degree hypothesis assumes.

Second reading: T. Bol, M. de Vaan and A. van de Rijt, “The Matthew effect in science funding”, PNAS 115, 4887 (2018), a natural experiment showing how an early advantage compounds.

The path

1. Study. Networks and rankings (adjacency matrices, directed graphs, ranking by minimum violations, PageRank as a comparison); cumulative advantage and the Matthew effect; the basics of agent-based modelling and how to validate a stochastic simulation; the public statistics of university admissions in the Basque Country, where the yearly cut-off grades are published.

2. Reproduce. Load the released hiring networks with networkx, implement the minimum-violation ranking, and reproduce the paper’s core figures: the fraction of hires that move down the hierarchy, the shape of the prestige distribution, and the comparison with a merit-only null model. Matching the published numbers is the checkpoint.

3. Find the gaps and go beyond.

• Build an agent-based model of the double degree: a yearly cohort of applicants with a grade and a motivation; a fixed number of places; a cut-off grade that becomes public; a prestige signal that shifts next year’s applicant pool; a performance rule inside the degree that depends on motivation and on a resilience variable with its own fluctuations.
• Calibrate the applicant side against the published cut-off series 2011 to 2026 and test the model’s central prediction: what happens to mean performance if the limit on places is removed.
• Explore the model as a dynamical system: is there a stable prestige equilibrium, a runaway, or oscillations? Where are the transitions in parameter space?
• Compare with the Clauset et al. mechanism: can the same feedback that steepens faculty hierarchies steepen a single degree’s applicant pool?

What you need

Statistical physics and probability from the degree; Python with NumPy, pandas, networkx and Matplotlib. No laboratory work. Suitable for one student; a second could take the data side (admissions statistics) while the first builds the model.