When the Bus Routes Decide the School: Santos et al. (2024) on Transit as a Lever Against School Segregation
santos_2024_school_segregation.md · 1,664 words · 7 min read
When the Bus Routes Decide the School: Santos et al. (2024) on Transit as a Lever Against School Segregation
A three-layer agent-based model in which the policy variable is not the matching rule but the transportation network itself — and an RL planner learns which edges to upgrade.
The research question
Most modern democracies have moved away from explicit school zoning toward some flavor of "free choice": households rank schools, schools fill seats by capacity, and a centralized rule resolves conflicts. The hope, in the Netherlands as in many U.S. urban districts, is that decoupling enrollment from residential boundaries should weaken the link between neighborhood demography and school demography. In practice, free-choice systems often segregate just as sharply as the zoned systems they replaced. Schools end up sorted by ethnicity and socioeconomic status, even though no rule says they have to.
Michailidis, Tasnim, Ghebreab, and Santos (JAAMAS 2024) ask why, and — more importantly — what a planner can do about it without touching the matching algorithm. Their answer focuses on a quietly powerful intermediate variable: the transportation network. A school is "close" to a household only insofar as a tram line, a bus, or a bicycle route makes it close. When transit infrastructure differentially advantages some residential blocks over others, the geometry of "free" choice is anything but free. Households trade off commute time against composition preferences, and that trade-off is parametrized by edges in a graph the planner controls. Reshape the graph, and you reshape the equilibrium.
This is the mechanism-design twist of the paper. Most school-choice work treats the matching algorithm as the lever — Boston versus deferred acceptance, lotteries versus priorities, capacities versus quotas. Santos and colleagues take that algorithm as fixed and shift attention to the substrate underneath it. The infrastructure layer becomes the design variable.
Method: a three-layer ABM
The model is built as three coupled graphs. The first is a residence graph, in which nodes are residential cells of a city and edges are physical adjacencies. Each cell is endowed with a population of households, partitioned into demographic groups (ethnic or SES strata). In the synthetic experiments these groups are placed using a stochastic block model that biases corner cells toward one group and central cells toward the other, producing realistic residential clustering without hand-tuning. In the Amsterdam validation, real cell-level demographics are used.
The second is a transit graph layered on top of the residence graph. Its edges encode commute time between cells, weighted by the speed and frequency of available lines. Adding a tram line is an edge insertion or a weight reduction; redirecting a route is a topology change. The transit graph is the policy lever the planner manipulates.
The third is the school layer: a set of fixed-location schools with hard capacities. In Amsterdam, this is the OSVO list of 47 secondary schools with their published seat counts. Schools have endogenous compositions — they are whatever the matching produces — but their capacities and locations are exogenous.
Households make choices over schools using a bilinear utility that trades off two terms. The first is travel time along the cheapest path through the transit graph. The second is demographic composition: a preference for schools whose composition matches the household's group, or, in some specifications, a preference for balance. The utility takes the rough form
U(school s | household h) = -α · travel_time(c_h, s)
+ β · composition_match(s, group_h)
+ ε
with idiosyncratic noise. Households submit preference orderings; allocation is a deferred-acceptance-style assignment that places each student at the closest school with available capacity, falling through to next-preferred schools when overflow occurs. Because households cannot observe the equilibrium composition of each school ex ante, the model iterates: an initial allocation produces beliefs about composition, those beliefs feed the next round of utility evaluation, and the process settles. The output is a school-level demographic mix, summarized by the standard dissimilarity index.
Method: the planner as designer
The substantive contribution sits at the second level of the model. A planner agent observes the equilibrium that the household ABM produces and chooses interventions on the transit graph in order to drive the dissimilarity index down. The action space is the catalogue of admissible network edits: add a new line between two cells, increase the frequency on an existing edge, redirect a route. The reward is the post-intervention dissimilarity, often combined with a constraint that average commute time should not rise.
The authors compare two families of planners. The first is a battery of heuristic baselines: random edge upgrades, betweenness-centrality targeting, group-based centrality measures that prioritize edges whose accessibility currently favors over-represented groups. These are plausible policy strategies a real transit authority might consider. The second is a reinforcement-learning policy that learns, by interacting with the simulated city, which edits compound to shift the equilibrium. The RL agent treats the network design problem as a Markov decision process: state is the current network plus the current school composition, action is the next edge edit, reward is the change in dissimilarity.
The mechanism-design framing is unusual and worth stating plainly. The matching rule itself — closest-with-capacity, deferred-acceptance-flavored — never moves. What moves is the metric the matching rule reads. Two households submitting identical preferences over the same school list will be assigned differently if the underlying transit network puts a different school within their reach. The planner exploits exactly this lever.
Headline results
Two stylized findings come out of the experiments. On the synthetic stochastic-block-model city, segregation emerges endogenously: a baseline run lands the dissimilarity index well above the conventional 0.2 threshold for "noticeable" segregation, even though the matching rule is content-blind. The simulation reproduces, in miniature, the empirical pattern that motivates the paper.
On both the synthetic city and the Amsterdam validation, the RL planner outperforms the heuristic baselines. Targeted accessibility increases for under-served groups can lower the dissimilarity index by 10–25% without raising mean commute time, and in some configurations the best targeted upgrades reduce both segregation and average travel time simultaneously. Random edge upgrades, by contrast, leave dissimilarity essentially unchanged. The result is robust across the two environments, suggesting that the shape of the lever — accessibility, not algorithm — is what matters, and that the policy space is large enough to repay learned search rather than rule-of-thumb intuition.
What college-sim already does
The college-sim engine has many of the ingredients needed to engage with this paper, but assembled in a different shape. It models a population of high schools as a structural input to the admissions market: the classic mode includes 20 elite feeders and the pro mode extends to 925 curated schools, each with archetype distributions and a feeder-tier multiplier. That feeder bonus enters admissions decisions explicitly, log-scaled and centered on the pool average, inside the academic-index logit term in computeAdmissionScore() at sim.js:3873. The pipeline effect from a high school to a college is a real, modeled channel — not as rich as a residence-by-cell layer, but it captures the central empirical fact that admissions outcomes inherit information from the high school context.
The high-school neighborhood is also not flat. When a user picks a real school, selectPeerSchools() at sim.js:1593–1872 builds a bespoke competitive cohort by finding the ~25 nearest neighbors in a seven-dimensional feature space — SAT mean, Ivy+ percent, top-50 percent, school-type ordinal, GPA, region distance, and log enrollment — using a weighted Euclidean metric. Distance in that feature space, plus a curated fallback of about 200 schools at EXTENDED_SCHOOLS_FALLBACK in sim.js:1473, defines who shows up as the user's peers in the simulated round.
The crucial structural difference: this is a flat geometric neighborhood, not a network of edges. There is no transit graph, no residential cell, no notion that one school is reachable from another by some upgradeable infrastructure. Two high schools are either close in feature space or they are not, and the planner has nothing to manipulate.
What Santos does that we don't (yet)
Santos and colleagues add two pieces college-sim currently lacks. First, an explicit graph of cells with transit edges, in which physical accessibility is a first-class variable rather than a static covariate. Second, an RL planner over the network design space — an agent that chooses edits to minimize a system-level objective and reads back the equilibrium that emerges.
The most natural college-sim translation of the planner is not a transit planner at all but an RL admissions-policy designer. The college-sim engine already exposes a rich set of institutional dials: hook multipliers for legacy, athlete, donor, first-gen, and Pell; per-college yield protection strength; phantom-applicant scaling; tier-dependent admission thresholds and threshold deltas. Each of these is a knob a real admissions office turns, and each shifts the equilibrium distribution of admitted students by archetype, income, and feeder tier.
A learned policy over those knobs, evaluated against an explicit equity-versus-efficiency objective — for example, the dissimilarity of admitted classes by income bracket against a yield or class-quality target — would be the direct college-sim analog of Santos's transit planner. The matching rule (the six-round decentralized ABM) would stay fixed, just as Santos keeps deferred acceptance fixed; the design variable becomes the parameter vector that institutions actually control. This is on the extensions roadmap as a Tier-2/3 prototype; see cas_abm_extensions_roadmap.html for the planned sequencing relative to the other matching-markets papers.
Run the reproduction yourself
A minimal Node.js reproduction of the synthetic-city experiment lives in this repository at /research2/cas-abm-references/reproductions/03-santos-transit-segregation/README.md. It uses a 6×6 grid of residential cells with two demographic groups, six fixed-location schools at capacity 1200, a deferred-acceptance allocation, and a brute-force enumeration over the 60 grid edges in place of the RL planner. The qualitative result reproduces: the baseline allocation is segregated, the best targeted single-edge upgrade lowers dissimilarity by roughly 16%, and a random edge upgrade does nothing.
Citation
Michailidis, G., Tasnim, M., Ghebreab, S., Santos, F. P. (2024). Tackling School Segregation with Transportation Network Interventions: An Agent-Based Modelling Approach. Autonomous Agents and Multi-Agent Systems 38(2): 42. DOI: 10.1007/s10458-024-09652-x. Code: https://github.com/sias-uva/transport-network-school-choice.