PaperlayerView exact revision on arXiv

Source-linked AI summary

Personalized Recommendations Without Inducing Congestion: Mitigating Disparities in the NYC High School Match

Erica Chiang, Kenny Peng, Rebecca Lichtenstein, Brielle McDaniel, Kristen O'Neil, Deja Thomas, Lianna Wright, Jon Kleinberg, Eva Tardos, Nikhil Garg

arXiv:2610.08275v1cs.CYecon.GNq-fin.EC

TL;DR

In capacity-constrained markets, recommendations can create competition that undermines predicted match chances and disproportionately affects applicants with fewer options. This paper develops a congestion-aware method for allocating recommendations and deploys it in the NYC high school match. In the randomized trial, treatment applicants were 57% more likely to rank a recommended program than controls were to rank a program they would have been recommended.

  • Problem

    In matching markets, recommendations can steer many participants toward the same capacity-limited programs, making predicted match chances endogenous and potentially worsening disparities.

    Source: §1 · pp. 1, 3

  • Method

    The paper uses a bilevel approach that sets nudge capacities to satisfy congestion constraints, then optimizes recommendation allocations within those capacities.

    Source: §1 · p. 3, §3.3 · p. 8

  • Results

    57% more likely to apply to a recommended program (p=0.011), treatment applicants were than controls who applied to a program they would have been recommended.

    Source: §7 · p. 23

  • Takeaways & Limitations

    Recommendation systems in capacity-constrained markets should be designed to account for system-wide congestion effects, which can exacerbate disparities.

    Source: §7 · p. 23

    Demand-side recommendations cannot be scaled indefinitely while preserving offer likelihoods, and the supply of seats at high-performing schools limits potential increases in matches.

    Source: §7 · p. 23

Abstract

from arXiv · show

Algorithmic recommendations can help participants navigate large matching markets. For example, recommendations for school and college choices may reduce information frictions and disparities in access to high-performing programs. At scale, however, recommenders in capacity-constrained settings can be self-defeating: if they steer too many users toward the same items, then even users who were originally predicted to have a high chance of matching to an item may not, due to increased competition. In this paper, we formalize this phenomenon of recommendation-induced congestion; motivated by the NYC high school match, we show that naive recommendations can cause sharp decreases in program acceptance rates, most affecting applicants with the fewest nearby options. Next, we propose and theoretically analyze a congestion-aware, bilevel optimize-and-simulate approach to allocate recommendations and improve match outcomes safely, in equilibrium. Finally, we deploy this approach in the 2025-26 admissions cycle of the NYC high school match, aiming to reduce disparities by highlighting personalized lists of nearby, high-performing programs where an applicant has a high predicted offer likelihood. In a randomized controlled trial, we find that 16.4% of treatment applicants ranked a recommended program, versus 10.5% of control applicants who ranked a program they would have been recommended (57% relative increase; $p$=0.011); 5.6% of treatment applicants matched to such a program, versus 3.3% of control applicants (71% relative increase; $p$=0.071); further, no treatment applicant was rejected from a recommended program. Our findings suggest that recommenders should be analyzed and designed as market-shaping interventions.

1 Introduction

In capacity-constrained markets, recommendations can change competition and undermine predicted match chances, with congestion risks falling unevenly. The paper develops and deploys a congestion-aware approach in the NYC high school match, where a randomized trial found increased ranking of recommended programs.

1 Introduction

  • NYC informational interventions have used shared lists of nearby, high-performing programs, but these either limit choices to broadly accessible programs or risk steering students toward programs where they may be rejected.Personalized offer-likelihood predictions enable guidance tailored to where an applicant is likely to be admitted.Source: §1 · p. 2

This work

  • The NYCPS deployment recommended nearby, high-performing programs with High predicted offer likelihoods to applicants from middle schools that historically sent few students to such schools.Preserving offer likelihood estimates under widespread adoption was a non-negotiable design constraint for NYCPS partners.Source: §1 · p. 3

Characterization of recommendation-induced congestion

  • Naively recommending each program to all eligible students can induce congestion at scale, disproportionately affecting applicants with less ex ante access to high-performing programs.The paper attributes this disparity to geographic correlation in access to programs applicants are eligible for.Source: §1 · pp. 2–3

Method for safe recommendations in equilibrium

  • The proposed bilevel method caps program-level nudges using historical data, then optimizes allocations within those capacities to preserve acceptance rates while targeting desirable matches.Under natural assumptions, the method approximately maximizes expected desirable matches while preserving acceptance rates.Source: §1 · p. 3

Deployment and RCT of personalized recommendations

  • 16.4% of 444 treatment applicants ranked a nudged program versus 10.5% of 822 controls ranking a program they would have been nudged to (57% increase; p=0.011).5.6% of treatment applicants matched to a nudged program versus 3.3% of controls (71% relative increase; p=0.071); no treatment applicant was rejected from a nudged program.Source: §1 · p. 3

1 Introduction

  • The authors argue that capacity-constrained recommendation systems should account for system-wide effects, including in labor and dating markets.The framework is motivated by the NYC school placement deployment but is also relevant to other capacity-constrained settings.Source: §1 · p. 3

2 Related work

Prior school-choice interventions provide information and recommendations, while related work studies matching, congestion, and equilibrium-aware design. This paper develops, deploys, and evaluates recommendations that explicitly account for congestion under hard capacity and offer-likelihood constraints.

Informational interventions for school choice

  • Prior informational interventions have shared school information or offered personalized search and recommendation, but the authors note that, to their knowledge, none directly controlled recommendation-induced congestion.The cited NYC offer-likelihood tool warns applicants who do not apply to any High-likelihood program, targeting failure to match rather than undermatching.Source: §2 · p. 4
  • Personalized offer likelihoods let the deployment include more competitive programs: over half of its recommendations were oversubscribed the previous year and would have been excluded from a non-personalized intervention limited to broadly accessible programs.Source: §2 · p. 4

Recommendation in equilibrium

  • Prior recommendation research addresses scarcity through exposure balancing, assortment optimization, incentive changes, or congestion modeling, while this work builds on that literature with recommendations under hard capacity and offer-likelihood constraints.Source: §2 · pp. 4–5
  • Congestion-aware recommender deployments and ex-post congestion analyses span dating, volunteer matching, employment, and school choice, with some studies reporting diminished gains or negative downstream effects at scale.Source: §2 · p. 5

Related work

  • Related work identifies recommendation-induced congestion with algorithmic monoculture and performative prediction, where recommendations based on offer likelihoods can change those likelihoods.Source: §2 · p. 5

3 Safe Recommendation in capacity-constrained settings

This section treats recommendations as interventions that can shift demand and congest capacity-constrained programs, and develops a bilevel approach for safely allocating nudges while preserving offer likelihoods. The method seeks to maximize desirable matches, including under student-varying utilities, and is deployed conservatively given uncertainty in simulated behavior and congestion.

3 Safe Recommendation in capacity-constrained settings

  • The intervention aims to increase matches in an exogenously specified desirable set by nudging students toward programs they otherwise would not have applied to, while accounting for capacity-driven changes in acceptance rates.Source: §3 · p. 5

3.1 Motivation: consequences of recommendation-induced congestion

  • Under naive nudging, adoption sharply lowers acceptance rates even for applicants initially given at least 99% offer likelihood; congestion is greatest where applicants have fewer alternatives.Simulations also show that applicants with less ex ante access have the lowest match rates to nudged programs.Source: §3.1 · p. 6

3.2 Model and Problem Definition

  • The model chooses nudges only for desirable student-program pairs and seeks to increase desirable matches while requiring acceptance rates for high-likelihood applicants to meet a threshold at eligible programs.In implementation, the congestion constraint is enforced among high-likelihood applicants because estimates for small adopting subsets can be noisy; the threshold is 0.8 in simulations and 0.95 in deployment.Source: §3.2 · p. 7

3.3 Methodological Approach and Theoretical Results

  • The bilevel method derives program-level nudge capacities from historical data, then allocates nudges at deployment; under stated adoption and monotonicity assumptions, it gives an L-approximation while satisfying safety constraints.The guarantee concerns a lower bound on the objective among safe capacities and feasible allocations under those capacities.Source: §3.3 · pp. 8–9

3.3.1 Allocating nudges subject to nudge capacities.

  • CNA uses an increasing, strictly discretely concave objective to distribute nudges more broadly, and under the adoption assumption it maximizes a lower bound on matches among feasible allocations.The resulting allocation has prefix-maximal coverage: it maximizes the number of applicants receiving at least one nudge, then at least two, and so on.Source: §3.3.1 · p. 10

3.3.2 Computing nudge capacities for congestion constraints.

  • NudgeCapComputation returns safe capacities that are coordinatewise greatest among safe vectors bounded by the supplied upper bounds.Under the monotonicity assumption, the algorithm terminates after a bounded number of oracle calls.Source: §3.3.2 · p. 11

3.4 Implementing our method in practice

  • For practice, the authors use 2024-25 application profiles, simulate adoption by adding one randomly selected nudged program with fixed probability, and simulate matching with deferred acceptance.Because the implemented oracle is stochastic, capacity updates use empirical congestion estimates; computing capacities for 56 eligible programs took approximately 24 hours.Source: §3.4 · pp. 11–12

3.5 Model and Methods Discussion

  • The definition of desirable matches reflects normative choices about programs, target schools, offer likelihood, and distance; the method is agnostic to those choices, and stakeholders chose to nudge only desirable pairs.Source: §3.5 · pp. 12–13
  • Counterfactual simulation and adoption assumptions can misestimate nudge capacities and congestion, so deployment is limited to programs with reconstructable admissions rankings and is conservative.The model assumes non-nudged students do not change their behavior; future models could incorporate spillovers and other behavioral changes.Source: §3.5 · p. 13
  • The method optimizes total desirable matches; with student-varying utilities, the greedy solution still optimizes even if solutions are no longer prefix-maximal.Utilities could vary with heterogeneous adoption rates or student importance weights.Source: §3.5 · p. 13

4 Design decisions and empirical context on the NYC HS match

The study uses 2024–25 NYC high school match data to design an intervention for students at middle schools that historically sent few students to high-performing high schools. It defines high-performing schools, eligible programs, target middle schools, and student eligibility using performance, admissions-likelihood, and travel criteria.

Data and scope

  • Historical analysis used 72,197 students from the 2024–25 cycle; deployment was for 2025–26 and excluded the nine Specialized High Schools.Those schools run a parallel admissions process.Source: §4 · p. 13

High-performing schools

  • A high-performing high school had to meet thresholds for graduation, college and career readiness, and safety and school climate.The thresholds were graduation rate ≥95%, readiness rating ≥60, and safety and school climate rating ≥3.0.Source: §4 · p. 13

Eligible programs

  • Potential nudge-eligible programs were at high-performing schools and had offer-likelihood estimates; simulations included 56 programs, while deployment included 15 programs across 12 schools and 9 districts.Deployment programs were reduced after superintendent approvals and for a conservative rollout; the set included no Bronx or Staten Island programs.Source: §4 · pp. 13–14

Target middle schools

  • Target middle schools sent less than 15% of students to high-performing high schools, averaged across the 2023–24 and 2024–25 cycles.The simulation set had 240 schools; deployment had 218, and 83% of their students were FRL-eligible versus 73% overall.Source: §4 · p. 14

Student eligibility

  • Students were eligible for a program-specific nudge if their school sent less than 2% of students to that program, they had a High offer likelihood, and the program was within 45 minutes of home.The definition also required attendance at a target middle school; travel time was estimated using subway, bus, and walking.Source: §4 · p. 14

Eligible students

  • About 11,500 students were nudge-eligible for at least one program; 88% were FRL-eligible, compared with 73% of students overall and 83% at target middle schools.The estimate used 2024–25 data and zip code as a proxy for census tract.Source: §4 · p. 14

5 Results: Congestion in simulation

In simulations of the NYC high school match, nudge capacities reduced congestion and improved match outcomes, with particularly large gains for students with limited access to eligible programs. Balanced Capacitated allocation increased matches to nudged programs while approximately preserving their total number.

5.1 Empirical setup

  • The simulations used 2024-25 cycle data, 56 potential nudge-eligible programs, varying adoption rates, and compared Naive, Capacitated, and Balanced Capacitated allocations.The latter two enforced capacities; Balanced Capacitated used a concave utility objective, while Capacitated maximized the total number of nudges.Source: §5 · p. 14, §5.1 · pp. 14–15

5.2 Results

  • Naive allocation put High offer likelihood students below the 80% acceptance-rate target at 7 of 56 programs with 20% adoption and 15 of 56 with 50% adoption.Nudge capacities kept program-level acceptance rates above the targeted threshold.Source: §5.2 · p. 15
  • Nudge capacities increased match rates among nudged students across the city and addressed geographic disparities seen under Naive allocation.Source: §5.2 · p. 15
  • With Balanced Capacitated allocation, match rates rose from 51.6% to 76.2% for students with 1 inventory program and from 91.3% to 95.8% for those with 5+ inventory programs.Gains were particularly large for students with limited access to nudge-eligible programs.Source: §5.2 · p. 15
  • At 20% adoption, Balanced Capacitated allocation produced more matches to nudge-eligible programs than Naive allocation while approximately preserving total matches to nudged programs.The authors attribute this to constrained nudges steering applicants toward programs they are more likely to enter in equilibrium.Source: §5.2 · p. 15
  • Balanced Capacitated allocation shifted nudges toward Bronx Latin-only eligible zip codes, which had 25 matches versus 9 under Capacitated, while other zip codes' matches to other nudged programs rose from 517 to 611.In the simulation, 630 students lived in zip codes with no access to another nudge-eligible program.Source: §5.2 · p. 16, Figure 4 · p. 16

6 Deployment and Randomized Controlled Trial

In the 2025–26 NYC high school match, NYCPS deployed personalized program recommendations in a randomized trial and examined their effects and potential for scale-up. The section reports greater ranking of recommended programs, models a larger safe reach, and finds that historical capacities do not provide exact guarantees under market shifts.

6.1 Experiment design

  • NYCPS emailed personalized program recommendations, with capacities targeting at least 95% acceptance among High-likelihood applicants at up to 40% adoption.The capacity policy was chosen conservatively to account for uncertainty about adoption.Source: §6 · pp. 16–17, §6.1 · p. 18, §6.3 · p. 21

6 Deployment and Randomized Controlled Trial

  • At 20% adoption, capacity enforcement raised match rates, while Balanced Capacitated still produced more desirable matches than Naive despite fewer nudges.Source: Table 1 · p. 17

6.1 Experiment design

  • The RCT randomized middle schools to 0%, 50%, or 100% treatment; control applicants’ hypothetical nudges came from a parallel optimization with treatment and control groups swapped.Applicants were randomized within schools according to assigned intensity; the parallel control optimization addressed the lack of a clear individual counterfactual when allocations depend on group composition.Source: §6.1 · pp. 17–18

6.2 Experiment results

  • 16.4% of treatment applicants ranked a recommended program versus 10.5% of controls, and 5.6% versus 3.3% matched; no treatment applicant was rejected from a recommended program.The primary experimental results are shown in Figure 5.Source: §6.2 · p. 19, Figure 5 · p. 20
  • Treatment raised recommended-program ranking by 6.5 percentage points (SE=2.6pp, p=0.013); the 2.7-percentage-point increase in matches was suggestive (SE=1.6pp, p=0.103).Source: §6.2 · p. 20
  • 19.8% of treatment students clicked tracked links, and 28.4% of clickers ranked a nudged program; survey responses cited interest-area mismatch and extracurricular preferences as reasons for not adding recommendations.Survey responses were descriptive and subject to potential selection bias.Source: §6.2 · pp. 20–21

6.3 Scale-up and robustness: What are the limits of student-side interventions?

  • At 100% adoption, simulations estimated 873 desirable matches among 4,982 nudge-eligible students using the 15 deployed programs, compared with 42 such matches in 2024–25.Source: §6.3 · p. 21
  • The prior-year simulator’s match accuracy fell from 98.2% for 2024–25 to 88.6% for 2025–26; capacities correlated across years (R=0.945), but four programs fell to zero, so historical capacities offer no exact guarantees.The mean absolute capacity difference was 48, against an average 2025 capacity of 144.Source: §6.3 · p. 22

7 Conclusion

The conclusion reports increased applications to recommended programs and suggestive evidence of increased matches, while emphasizing that recommendations can reshape market outcomes and disparities. It also identifies limits of demand-side interventions and situates the work among research on public-service algorithms, deployment, and market interference.

7 Conclusion

  • Simultaneous adoption can sharply and heterogeneously reduce acceptance rates, while recommendation systems can create system-wide externalities and disparities.The conclusion argues that recommenders should be designed with congestion in mind.Source: §7 · pp. 22–23
  • 57% more likely to apply to a recommended program (p=0.011) and 71% more likely to match to one (p=0.071), showing shifted application behavior and suggestive match changes.The paper describes this as its first field deployment of a recommendation system to control congestion in a centralized school matching platform.Source: §7 · p. 23
  • Recommendations should incorporate match probabilities in equilibrium; congestion can disproportionately affect applicants with few existing opportunities, and constraint choices encode policy priorities.The paper also prioritizes preserving offer likelihoods for High-likelihood students while allowing displacement of lower-likelihood applicants; the congestion constraint can be adapted to other policy goals.Source: §7 · p. 23, Discussion and Limitations · p. 23
  • Demand-side interventions cannot scale indefinitely while preserving offer likelihoods, and limited high-performing-school seats constrain potential match gains.Larger changes may require supply-side interventions, such as increasing the supply of seats in high-performing schools.Source: §7 · p. 23
  • Offer-likelihood predictions shown to all applicants may change behavior and shift the congestion anticipated when recommendations are designed.The authors identify this as a reason for conservative intervention design and suggest jointly designing predictions and recommendations.Source: Discussion and Limitations · p. 23
  • The framework assumes homogeneous nudge adoption, uses batch recommendations, and relies on accurate match simulation; richer personalization and real-time stochastic settings require further work and validation.The authors warn that extensions could add complexity and require checks against de-prioritizing disadvantaged students or amplifying prediction error.Source: Discussion and Limitations · pp. 23–24
  • Because true applicant preferences are unobserved and school-quality measures are incomplete, matching to a nudged program does not necessarily imply an individual welfare gain.The paper notes that program interest area matters to families and that its measures omit quality measures such as causal value-add.Source: Discussion and Limitations · p. 24

A Additional related work

  • The paper situates its deployment among public-service algorithm applications and interference research, distinguishing intervention design from work on randomization and estimator debiasing.It also uses match simulations to characterize interference and optimize recommendations, then runs scale-up analyses to bound it.Source: A Additional related work · p. 31

B.1 Coverage and proof of Theorem 3.2

Theorem B.1 characterizes concave-optimal nudge allocations by prefix-maximal coverage. Its proof models feasible allocations as a matroid problem, allowing a greedy construction to maximize coverage priorities in order.

B.1 Coverage and proof of Theorem 3.2

  • Coverage at level k counts students receiving at least k nudges, and lexicographic maximum coverage prioritizes these counts from the first level onward.The first priority is maximizing students with at least one nudge, then those with at least two, and so on.Source: §B.1 · pp. 31–32
  • Under increasing, strictly discretely concave u, an allocation optimizes CNA(C,u) if and only if it has prefix-maximal coverage.Prefix-maximal coverage implies lexicographically maximizing the numbers of students receiving at least 1, 2, and subsequent nudges.Source: §B.1 · p. 32
  • Feasible nudge allocations correspond to integral flows in a layered network, with student-copy, eligible-pair, and program nodes encoding allocation constraints.Program-to-sink capacities enforce nudge caps, while pair nodes prevent nudging a student to the same program twice.Source: §B.1 · pp. 32–34
  • The matchable sets of student-copy nodes form a gammoid matroid, so feasible nudge allocations inherit the independence structure needed for greedy optimization.A standard matroid result supplies the gammoid property.Source: §B.1 · p. 34
  • Strict discrete concavity makes marginal weights decrease by nudge level, so matroid greedy optimization processes first nudges before later nudges.This yields prefix-maximal coverage and therefore lexicographic maximum coverage.Source: §B.1 · p. 35

B.1.1 Intuition for Theorem B.1.

Theorem B.2 shows that concave nudge allocation attains maximum coverage, with an alternating-path exchange giving an intuitive proof. The exchange covers an additional student without lowering the concave objective.

B.1.1 Intuition for Theorem B.1.

  • A concave-optimal allocation covers at least as many students as any allocation maximizing the total number of nudges; strict diminishing returns from the first to second nudge makes every optimizer maximize coverage.The exchange argument reallocates a nudge from a student with at least two nudges to an uncovered student.Source: §B.1.1 · pp. 36, 39
  • Discrete concavity ensures the path exchange does not decrease the objective, and strict diminishing returns between the first and second nudge makes the increase strict.The endpoint with at least two nudges loses one, while the previously uncovered endpoint gains its first.Source: §B.1.1 · pp. 36, 39
  • An alternating path from an uncovered student to a student with at least two nudges can be flipped to increase coverage by one while preserving program caps.Internal students retain their nudge counts, while the endpoints gain and lose one nudge respectively.Source: Figure 7 · p. 37, §B.1.1 · p. 38
  • The proof compares a concave-optimal allocation with a full-utilization allocation attaining maximum coverage, then uses alternating paths to find a coverage-improving exchange.The symmetric difference of the allocations decomposes into alternating paths and cycles.Source: §B.1.1 · p. 37

B.1.2 Proof of Theorem 3.2.

Theorem 3.2 establishes an L-approximation guarantee for the match objective when the allocation is safe and maximizes the concave objective. The argument links coverage to expected adoption and then to desirable matches.

B.1.2 Proof of Theorem 3.2.

  • For a safe allocation maximizing CNA(C,u) with increasing, strictly discretely concave u, the match objective is at least an L-approximation among feasible allocations.The proof uses the coverage property to maximize expected adoption, then the offer-likelihood guarantee to lower-bound desirable matches.Source: §B.1.2 · p. 39

B.2 Proof of algorithm guarantees (Theorem 3.3)

Theorem 3.3 guarantees that the capacity procedure returns the greatest safe nudge-capacity vector under its assumptions. A comparison with non-personalized recommendations shows much higher simulated rejection rates for that approach than for the proposed allocations.

B.2 Proof of algorithm guarantees (Theorem 3.3)

  • NudgeCapComputation terminates with safe capacities that are coordinatewise at least as large as any other safe vector bounded by the given upper bounds.The returned vector is the unique coordinatewise greatest safe vector.Source: §B.2 · p. 39
  • The capacity updates rely on monotonicity: increasing other programs’ capacities cannot increase congestion at a given program.The proof uses this property to establish that the iterative update preserves the greatest-safe-vector guarantee.Source: §B.2 · p. 40

C.1 Non-personalized recommendations

  • Restricting non-personalized recommendations to programs with open capacity would have limited scale: only 28 of 56 high-performing programs had open capacity, and only 4 of 56 had High likelihood for at least half of target-middle-school students.These figures describe the 2025 admissions cycle.Source: §C.1 · pp. 40–41
  • With 20% adoption, 41 of 56 high-performing programs rejected over half of nudged applicants under non-personalized recommendations, versus 5 of 56 under Naive allocation and 0 of 56 under Balanced Capacitated allocation.The simulation compares nudging all students at target middle schools to nearby high-performing programs against the two personalized allocation methods.Source: §C.1 · p. 41

C.2 Displacement effects

The displacement analysis tests whether 20% adoption under Balanced Capacitated allocation preserves offer-likelihood calibration while reallocating matches. The accompanying figures and table describe how allocation and capacity assumptions affect program access.

C.2 Displacement effects

  • Medium offer acceptance fell from 63.8% to 49.0%, while Low offer acceptance fell from 8.36% to 5.60%; calibration largely held, with two programs below 1% for Medium students.Among 53 programs assigning Medium likelihood, 46 were calibrated without nudges; the overall reallocation aligned with the authors’ objectives despite some displacement.Source: §C.2 · p. 41
  • Among displaced students, 13.0% attended target middle schools; 75.7% were FRL-eligible, versus 86.1% of students newly matching to these programs.The authors say displacement increases target-middle-school representation at nudge-eligible schools, particularly among students with High offer likelihoods.Source: §C.2 · p. 41

C.3 Other tables and figures

  • At 50% adoption, enforcing nudge capacities improved match rates with minimal effect on total students matched to nudged and nudge-eligible programs.The table reports simulation results at 50% student adoption.Source: Table 2 · p. 42
  • Balanced allocation shifted Bronx Latin matches toward students in zip codes without access to other programs; the figure marks nudge-eligible programs and shows the geographic distribution.A separate figure maps schools and students by zip code, while another defines inventory as the number of high-performing programs for which students are nudge-eligible.Source: Figure 8 · p. 42, Figure 9 · p. 42, Figure 10 · p. 43
  • Setting nudge capacities too high or too low trades off High-offer-likelihood acceptance rates against total intervention effectiveness, measured as matches to nudged programs.The figure characterizes this tradeoff by sweeping assumed and true adoption rates.Source: Figure 11 · p. 43

D.1 Details on NYC High School Match

  • The NYC match uses ranked program applications and student-proposing deferred acceptance; all students can access offer-likelihood estimates, while the intervention highlights selected programs.The estimates depend on a student’s lottery number and are shown after an application is started.Source: §D.1 · p. 44

D.2 Data

The data section describes the school, feeder-pattern, student, and match-simulator inputs used to design and evaluate the intervention. Balance checks found no systematic assignment imbalance in the tested covariates.

D.2 Data

  • School-level graduation, college and career readiness, and safety metrics identified high-performing programs, with every program at a school assigned the same performance measures.The metrics came from the 2023-24 school year; a historical check found that 91% of programs at schools with graduation rates above 95% had program-level rates of at least 90%.Source: §D.2 · p. 44
  • Feeder-pattern data from 2023-24 and 2024-25 characterized middle-school enrollment at high schools; student records included preferences, outcomes, location, lottery numbers, and offer likelihoods.The data cover both General Education and Students with Disabilities, which share the match process but have separate seat groups.Source: §D.2 · p. 44
  • The system used 2024-25 application data for development and deployment in 2025-26; zip codes substituted for census tracts in 2024-25 simulations, and a deferred-acceptance simulator modeled that cycle.The historical data included 72,197 students; program offer-likelihood predictions were unavailable where admissions used qualitative or human-graded information.Source: §D.2 · pp. 44–45

D.3 Balance checks

  • Balance-test p-values were approximately uniform, consistent with valid randomization; regressions additionally controlled for borough and school-size strata.The figure reports balance tests for all students at target middle schools and for nudge-eligible students at those schools.Source: §D.3 · p. 45, Figure 12 · p. 45

D.5 Pre-registration compliance

  • The intervention followed the pre-registration except that Batch 2 excluded continuing middle schools, follow-up emails went only to Batch 1, and planned text messages were not sent.The same Batch 2 exclusion rule applied to treatment and control students.Source: §D.5 · p. 50

D.6 Additional Experimental Results

These additional analyses examine application-list changes, alternative outcomes, spillovers, and treatment-effect heterogeneity. Several findings are qualified by limited power, small samples, or the email-engagement measure.

Regression robustness checks

  • Robustness results preserved significance findings except for ranking a nudged program in the top three without stratum fixed effects, which had p=0.111 with OLS.The pre-registration specified logistic regression for the primary outcome; the robustness check used linear probability models.Source: §D.6 · p. 51

Additional outcome specifications

  • Effects on ranking any nudge-eligible program were not consistently significant across specifications, and effects on ranking a nudged program first or its rank position were not significant.The authors describe application changes for nudged programs as additive, translating to similar percentage-point increases in nudge-eligible programs.Source: §D.6 · p. 51

Exploratory spillover analysis

  • Untreated students in 50% treatment-intensity schools had higher application rates to nudged programs than students in 0% schools, but residual imbalance or noise could explain the pattern.The estimate relies on between-school variation and relatively few untreated students in partially treated schools.Source: §D.6 · p. 51

Local Average Treatment Effects

  • Click-defined email engagement classified 19.8% of treatment students as compliers, but readers who did not click violate the exclusion restriction, likely overstating LATE estimates.The authors report these estimates for preregistration consistency but do not rely on them.Source: §D.6 · p. 51, Table 12 · p. 54

Heterogeneous treatment effects

  • The study found no evidence of heterogeneous treatment effects or link-clicking behavior across examined subgroups, but it was underpowered to detect such differences.Treated applicants averaged 0.502 link clicks and clicked links for 18.2% of their nudged programs.Source: §D.6 · pp. 51–52

Additional application-list analysis

  • Only 10 of 444 treatment applicants and 18 of 822 control applicants had saved programs before the email; none of the 10 treatment applicants added a nudged program.The authors note that this small, potentially biased group limits what can be learned about revisions to existing saved lists.Source: §D.6 · p. 52

D.7 Additional survey results

The additional survey analyses found no evidence of treatment effects on reported familiarity or recognition, while open-ended responses suggested varied information needs. The scale-up figure compares nudge capacities across years.

D.7 Additional survey results

  • The survey found no evidence of treatment effects on self-reported familiarity with nearby high-performing programs or recognition of sampled programs.There were 42 treatment and 61 control respondents; the authors caution that the small sample makes other survey results descriptive.Source: §D.7 · p. 57
  • Among families explaining why they did not apply to a sampled program, common reasons were its academic focus or distance; advice requests included more information and admissions guidance.Only 2 of 25 families answered the open-ended question about their perception of the email, so the authors draw no conclusive insights from it.Source: §D.7 · p. 57

D.8 Scale-up analyses

  • The capacity comparison uses 2024-25 and 2025-26 application data under two simulated adoption rates; orange dots mark programs limited by eligible-student inventory rather than congestion.The figure presents a year-to-year comparison of nudge capacities.Source: Figure 14 · p. 60
Loading 2610.08275v1…