scholarly journals Heterogeneous Beliefs and School Choice Mechanisms

2020 ◽  
Vol 110 (5) ◽  
pp. 1274-1315 ◽  
Author(s):  
Adam J. Kapor ◽  
Christopher A. Neilson ◽  
Seth D. Zimmerman
Keyword(s):  
School Choice ◽  
Rational Expectations ◽  
Choice Behavior ◽  
Heterogeneous Beliefs ◽  
Welfare Costs ◽  
Subjective Beliefs ◽  
Opposite Conclusion ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

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)

scholarly journals Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

2019 ◽  
Vol 109 (4) ◽  
pp. 1486-1529 ◽  
Author(s):  
Gabrielle Fack ◽  
Julien Grenet ◽  
Yinghua He
Keyword(s):  
School Choice ◽  
Test Scores ◽  
Real Life ◽  
Truth Telling ◽  
Student Preferences ◽  
Ex Post ◽  
Is Strategy ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Novel Approaches

We propose novel approaches to estimating student preferences with data from matching mechanisms, especially the Gale-Shapley deferred acceptance. Even if the mechanism is strategy-proof, assuming that students truthfully rank schools in applications may be restrictive. We show that when students are ranked strictly by some ex ante known priority index (e.g., test scores), stability is a plausible and weaker assumption, implying that every student is matched with her favorite school/college among those she qualifies for ex post. The methods are illustrated in simulations and applied to school choice in Paris. We discuss when each approach is more appropriate in real-life settings. (JEL D11, D12, D82, I23)

scholarly journals Controlled School Choice with Soft Bounds and Overlapping Types

2017 ◽  
Vol 58 ◽  
pp. 153-184 ◽  
Author(s):  
Ryoji Kurata ◽  
Naoto Hamada ◽  
Atsushi Iwasaki ◽  
Makoto Yokoo
Keyword(s):  
School Choice ◽  
Stable Matching ◽  
Extended Model ◽  
The Public ◽  
Distributional Constraints ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Stability Definition ◽  
Model Computer ◽  
Straightforward Extension

School choice programs are implemented to give students/parents an opportunity to choose the public school the students attend. Controlled school choice programs need to provide choices for students/parents while maintaining distributional constraints on the composition of students, typically in terms of socioeconomic status. Previous works show that setting soft-bounds, which flexibly change the priorities of students based on their types, is more appropriate than setting hard-bounds, which strictly limit the number of accepted students for each type. We consider a case where soft-bounds are imposed and one student can belong to multiple types, e.g., “financially-distressed” and “minority” types. We first show that when we apply a model that is a straightforward extension of an existing model for disjoint types, there is a chance that no stable matching exists. Thus we propose an alternative model and an alternative stability definition, where a school has reserved seats for each type. We show that a stable matching is guaranteed to exist in this model and develop a mechanism called Deferred Acceptance for Overlapping Types (DA-OT). The DA-OT mechanism is strategy-proof and obtains the student-optimal matching within all stable matchings. Furthermore, we introduce an extended model that can handle both type-specific ceilings and floors and propose a extended mechanism DA-OT* to handle the extended model. Computer simulation results illustrate that DA-OT outperforms an artificial cap mechanism where we set a hard-bound for each type in each school. DA-OT* can achieve stability in the extended model without sacrificing students’ welfare.

Optimal Priority-Based Allocation Mechanisms

2021 ◽  
Author(s):  
Peng Shi
Keyword(s):  
Elementary School ◽  
School Choice ◽  
Revenue Management ◽  
Choice Behavior ◽  
Planning Problem ◽  
Market Models ◽  
Special Cases ◽  
Choice Sets ◽  
Deferred Acceptance ◽  
Student Welfare

This paper develops a tractable methodology for designing an optimal priority system for assigning agents to heterogeneous items while accounting for agents’ choice behavior. The space of mechanisms being optimized includes deferred acceptance and top trading cycles as special cases. In contrast to previous literature, I treat the inputs to these mechanisms, namely the priority distribution of agents and quotas of items, as parameters to be optimized. The methodology is based on analyzing large market models of one-sided matching using techniques from revenue management and solving a certain assortment planning problem whose objective is social welfare. I apply the methodology to school choice and show that restricting choices may be beneficial to student welfare. Moreover, I compute optimized choice sets and priorities for elementary school choice in Boston. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Mistaken Play in the Deferred Acceptance Algorithm: Implications for Positive Assortative Matching

2017 ◽  
Vol 107 (5) ◽  
pp. 225-229 ◽  
Author(s):  
Alex Rees-Jones
Keyword(s):  
Recent Literature ◽  
Welfare Effects ◽  
Assortative Matching ◽  
Welfare Evaluation ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

Recent literature has documented failures of truthful preference reporting in the strategy-proof deferred acceptance algorithm. I consider the implications of these strategic mistakes for a common welfare consideration: the ability of the mechanism to sort the best students to the best schools. I find that these mistakes have the potential to significantly help or significantly hinder sorting. Through this channel, the presence of mistaken play may have widely varying welfare effects. I discuss related considerations in the welfare evaluation of mistaken play in the deferred acceptance algorithm and the implications for “nudges” that correct these mistakes.

Resolving Conflicting Preferences in School Choice: The “Boston Mechanism” Reconsidered

2011 ◽  
Vol 101 (1) ◽  
pp. 399-410 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Yeon-Koo Che ◽  
Yosuke Yasuda
Keyword(s):  
School Choice ◽  
Ordinal Preferences ◽  
Boston Mechanism ◽  
Ex Ante ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Good Schools

Despite its widespread use, the Boston mechanism has been criticized for its poor incentive and welfare performances compared to the Gale-Shapley deferred acceptance algorithm (DA). By contrast, when students have the same ordinal preferences and schools have no priorities, we find that the Boston mechanism Pareto dominates the DA in ex ante welfare, that it may not harm but rather benefit participants who may not strategize well, and that, in the presence of school priorities, the Boston mechanism also tends to facilitate greater access than the DA to good schools for those lacking priorities at those schools. (JEL D82, I21, I28)

scholarly journals What's the Matter with Tie-Breaking? Improving Efficiency in School Choice

2008 ◽  
Vol 98 (3) ◽  
pp. 669-689 ◽  
Author(s):  
Aytek Erdil ◽  
Haluk Ergin
Keyword(s):  
United States ◽  
School Choice ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The United States ◽  
Stable Mechanism ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Stable Improvement

In several school choice districts in the United States, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken in some exogenous way. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. Our main finding is a polynomial-time algorithm for the computation of a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. We also investigate the strategic properties of the student-optimal stable mechanism. (JEL C78, D82, I21)

scholarly journals School choice with asymmetric information: Priority design and the curse of acceptance

2020 ◽  
Vol 15 (3) ◽  
pp. 1095-1133
Author(s):  
Andrew Kloosterman ◽  
Peter Troyan
Keyword(s):  
Asymmetric Information ◽  
School Choice ◽  
Choice Models ◽  
Current Debate ◽  
Interdependent Preferences ◽  
Equilibrium Strategies ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Positive Results

We generalize standard school choice models to allow for interdependent preferences and differentially informed students. We show that, in general, the commonly used deferred acceptance mechanism is no longer strategy‐proof, the outcome is not stable, and may make less informed students worse off. We attribute these results to a curse of acceptance. However, we also show that if priorities are designed appropriately, positive results are recovered: equilibrium strategies are simple, the outcome is stable, and less informed students are protected from the curse of acceptance. Our results have implications for the current debate over priority design in school choice.

scholarly journals The Review of Methods for Assignment of Elective Courses at Universities

2019 ◽  
Vol 57 (4) ◽  
pp. 511-526
Author(s):  
Dejan Trifunović
Keyword(s):  
Business School ◽  
Competitive Equilibrium ◽  
Price Mechanism ◽  
Ex Post ◽  
Elective Courses ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
Serial Dictatorship

AbstractIn this paper we present a review of matching algorithms that are used for matching students with elective courses at universities. This is an example of a market where price mechanism cannot be used to determine the equilibrium allocation. In the Random Serial Dictatorship students select courses based on their position in a random queue. This mechanism is not ex post Pareto-efficient and its drawback is overcome in the Probabilistic Serial Assignment, although this mechanism is not strategy-proof. In the auction mechanism, students’ bids for courses do not represent their true preferences, since bids depend on their beliefs about the popularity of courses. The efficient allocation is obtained when Deferred Acceptance Algorithm is used - where the priority of students is determined based on their bids. Harvard draft mechanism is based on changing the order of students in the random queue from one round to another and this mechanism is not strategy-proof; however, it is, by all means, better for students than Random Serial Dictatorship. The Wharton Business School mechanism is based on the calculation of approximate competitive equilibrium.

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