School Choice Mechanisms Research Articles

Minimally Unstable Pareto Improvements over Deferred Acceptance

We investigate efficient and minimally unstable Pareto improvements over the deferred acceptance (DA) mechanism — a popular school choice mechanism which is stable but not efficient. We show that there is no Pareto improvement over the DA mechanism which is minimally unstable among efficient assignments when the stability comparison is based on counting the number of blocking pairs. Our main result characterizes the priority profiles for which there exists a Pareto improvement over the DA assignment that is minimally unstable among efficient assignments. We further consider an alternative natural stability comparison based on the set of blocking students who are involved in at least one blocking pair, show that the impossibilities remain, and characterize the possibility domain of priority profiles.

Inefficiency-Manipulability Tradeoff in the Parallel Mechanism

Most school choice and other matching mechanisms are based on deferred acceptance (DA) for its incentive properties. However, non-strategyproof mechanisms can dominate DA in welfare because manipulation in preference rankings can reflect the intensities of underlying cardinal preferences. In this work, we use the parallel mechanism of Chen and Kesten, which interpolates between Boston mechanism and DA, to quantify this tradeoff. While it is previously known that mechanisms that are closer to Boston mechanism are more manipulable, we show that they are also more efficient in student welfare if school priorities are weak. Our theoretical results show the inefficiency-manipulability tradeoff in the worst case, while our simulation results show the same tradeoff in the typical case.

Affirmative action under common school priorities: The top trading cycles mechanism case

In school choice, there are two types of extensively used affirmative action policies based on majority quotas and minority reserves, respectively. This paper investigates the responsiveness of the top trading cycles school choice mechanism to these two types of affirmative action policies when all schools have the same priority order over students. Under the common school priority (within student type) condition, we show that the top trading cycles mechanism is minimally responsive to the minority reserves type of affirmative action policy, while a stronger majority quotas type of affirmative action policy may yield a Pareto inferior assignment for the minority.

Chinese college admissions and school choice reforms: An experimental study

Since 2001, many Chinese provinces have transitioned from a “sequential” to a “parallel” school choice or college admissions mechanism. Inspired by this natural experiment, we evaluate the sequential (immediate acceptance, IA), parallel (PA), and deferred acceptance (DA) mechanisms in the laboratory. We find that participants are most likely to reveal their preferences truthfully under DA, followed by PA and then DA. While stability comparisons also follow the same order, efficiency comparisons vary across environments. Regardless of the metrics, the performance of PA is robustly sandwiched between IA and DA. Furthermore, 53% of our subjects adopt an insurance strategy under PA, making them at least as well off as what they could guarantee themselves under IA. These results help explain the recent reforms in Chinese school choice and college admissions.

On Becoming a District of Choice: Implications for Equity Along the United States-Mexico Border.

Despite the popularity of open enrollment as a school choice mechanism, there is little research on how principals behave in a district-run competitive setting. This study adds to our understanding of how open enrollment policies affect the role of the principal as well as educational equity by examining the roles and behaviors of school principals in an unregulated marketplace of schools. This study uses an explanatory sequential mixed methods approach. We first analyze school-level transfer data for school year 2014-2015 and demographic data in order to examine trends such as poverty concentration as well as to identify "winners," "losers," and "nonplayers" in the open enrollment marketplace. Since principals are heavily involved in recruitment, student screening, and selection of specialized programs, we interviewed 12 principals to better understand their role in the competitive settings. We find that some schools have emerged as "winners" in this marketplace, attracting large numbers of transfers without losing many students, while other principals and schools struggle to overcome a negative perception and find a market niche to attract students. Our quantitative analysis indicates a relatively small relationship between open enrollment and increased segregation in the district. District oversight seems to have prevented worsening segregation. However, many principals seek more control on the screening process raising equity concerns if formal regulations are not provided. These findings have implications for school and district leaders navigating open enrollment plans as a means to increase enrollments and encourage innovation while also maintaining equity.

Transparency and Fairness in School Choice Mechanisms

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justified envy may not be a sucient condition of fairness.

Transparency and Fairness in School Choice Mechanisms

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justified envy may not be a sufficient condition of fairness.

Creating Educational Destruction: A Critical Exploration of Central Neoliberal Concepts and Their Transformative Effects on Public Education

Individualism and competition are central neoliberal concepts that have profoundly altered the U.S. public education system. This article draws on poststructuralist theory and advances the argument that these concepts have produced problematic policies and deeply flawed school choice mechanisms such as charter schools and school vouchers. I also explore how educational activists contested neoliberal ideology and reshaped reality as they defeated a neoliberal education policy in North Carolina.

High School Admission Reform in China: A Welfare Analysis

In recent years, China has experienced a trend of changing from the Boston mechanism (BM) to the Chinese parallel mechanism for high school and college admissions. Using a unique data set from the high-school-assignment system in China that combines survey data eliciting students' school preferences with administrative data that cover students' school choices and admission records under both mechanisms, this paper compares the welfare performance of BM, the Chinese parallel mechanism, and the Deferred Acceptance (DA) mechanism. We find a non-monotonic relationship between the manipulability and efficiency of school choice mechanisms: DA yields significantly higher welfare than the Chinese parallel mechanism and BM, but BM yields higher welfare than Chinese parallel mechanism although not significantly. We also find that switching from BM to Chinese parallel mechanism hurts students regardless of their socioeconomic status. Students put schools they prefer more on all of their ranks under Chinese parallel mechanism than BM, and only students who are admitted by one of their first two choices benefit from the mechanism change.

Competing for Priorities in School Choice

We present a model in which students can influence their priority in a school choice mechanism through a first-stage costly effort game. We show that efficiency improvements to the mechanism can lead to net efficiency losses if they come at the price of increased allocative inequalities, which in turn increase competition in the effort stage. We apply these results to the deferred and immediate acceptance mechanisms (DA and IA) and show that, even when DA is more allocatively efficient than IA, IA may remain more efficient overall because it features less inequalities between students with high and low priorities.

Heterogeneous Beliefs and School Choice Mechanisms

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)

Family networks and school choice

This paper uses variation in school assignments generated by Mexico City's public high school choice mechanism to document a strong causal influence of older siblings on their younger siblings' school choice behavior. The effects of older sibling admission on the probabilities of choosing both the sibling's school and distinct but observably similar schools are large and positive, even when siblings are too far apart in age to attend school together. The evidence is more consistent with information transmission and path dependence channels than cost, convenience, sibling competition, or parental pressure. Sibling-induced changes in stated preferences affect admissions outcomes, including assignment to elite schools. The results imply significant externalities from policies such as affirmative action that alter the distribution of school assignments, as well as providing insight into the role of family networks in decision-making regarding educational investments.

Outcome equivalence in school choice with reciprocal preferences

We show that modifications of the Boston school choice mechanism, the student proposing deferred acceptance algorithm and the top trading cycles algorithm where the colleges’ priorities are adjusted according to students’ preferences in a “first preferences first” manner generate the same outcome. This outcome coincides with the BM outcome under original priorities. As a result, the question which of the three algorithms is chosen becomes immaterial.

Identifying the Harm of Manipulable School-Choice Mechanisms

An important but under-explored issue in student assignment procedures is heterogeneity in the level of strategic sophistication among students. Our work provides the first direct measure of which students rank schools following their true preference order (sincere students) and which rank schools by manipulating their true preferences (sophisticated students). We present evidence that our proxy for sophistication captures systematic differences among students. Our results demonstrate that sophisticated students are 9.6 percentage points more likely to be assigned to one of their preferred schools. Further, we show that this large difference in assignment probability occurs because sophisticated students systematically avoid over-demanded schools. (JEL D82, H75, I21, I28)

In Search of Advice for Participants in Constrained School Choice

School choice mechanisms are typically constrained, with students allowed to report preferences on a limited number of schools only Under constraints, the deferred acceptance mechanism (DA) is manipulable and it is unclear how students should play in DA. In order to provide advice to participants, we characterize the undominated strategies for the constrained versions of DA and the Boston mechanism (BOS).We show that domination alone allows to exclude more strategies in the constrained DA than in the constrained BOS.To provide additional advice to highly risk averse students, we also characterize undominated maximin strategies in the two mechanisms.We show that constrained DA is {safer} than constrained BOS in the sense that a student always prefers her maximin outcome in the former to her maximin outcome in the latter.

Demand Analysis Using Strategic Reports: An Application to a School Choice Mechanism

Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are non-parametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 82% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report truthfully.

Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations

In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful, and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the permuted lottery deferred acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used deferred acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second-round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare and that reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from New York City high school admissions support our theoretical findings. This paper was accepted by Gad Allon, operations management.

Dynamic Matching in School Choice: Efficient Seat Reassignment after Late Cancellations

In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the Permuted Lottery Deferred Acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used Deferred Acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare, and reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from NYC high school admissions support our theoretical findings.

Strategy-proof school choice mechanisms with minimum quotas and initial endowments

We consider a school choice program where minimum quotas are imposed for each school, i.e., a school must be assigned at least a certain number of students to operate. We require that the obtained matching must respect the initial endowments, i.e., each student must be assigned to a school that is at least as good as her initial endowment school. Although minimum quotas are relevant in school choice programs and strategy-proofness is important to many policymakers, few existing mechanisms simultaneously achieve both. One difficulty is that no strategy-proof mechanism exists that is both efficient and fair under the presence of minimum quotas. Furthermore, existing mechanisms require that all students consider all schools acceptable to obtain a feasible matching that respects minimum quotas. This assumption is unrealistic in a school choice program.We consider the environment where a student considers her initial endowment school acceptable and the initial endowments satisfy all the minimum quotas. We develop two strategy-proof mechanisms. One mechanism, which we call the Top Trading Cycles among Representatives with Supplementary Seats (TTCR-SS), is based on the Top Trading Cycles (TTC) mechanism and is significantly extended to handle the supplementary seats of schools while respecting minimum quotas. TTCR-SS is Pareto efficient. The other mechanism, which we call Priority List-based Deferred Acceptance with Minimum Quotas (PLDA-MQ), is based on the Deferred Acceptance (DA) mechanism. PLDA-MQ is fair, satisfies a concept called Priority List-based (PL-) stability, and obtains the student-optimal matching within all PL-stable matchings. Our simulation results show that our new mechanisms are significantly better than simple extensions of the existing mechanisms.

Choosing schools, choosing selves: exploring the influence of parental identity and biography on the school choice process in Delhi, India

Drawing on qualitative interview data from a group of lower income parents in Delhi, India, this paper focuses on the dynamic relationship between parental choice of a particular school and parents’ own identity construction. The data indicate that choice of school is for some parents a symbolic expression of identity, influenced by family dynamics and parents’ educational biographies. The paper outlines the concept of ‘forging solidarities’ and proposes it as an alternative way of understanding school enrolment decisions that recognises the social significance of such choices for the wider family unit. More generally, as school choice mechanisms in various forms become an increasingly important part of the educational landscape in many countries, the findings draw attention to the sociocultural nature of choice in real-world market settings and the contribution of schooling choices to processes of social and educational segregation.