scholarly journals Minimally unstable Pareto improvements over deferred acceptance

2021 ◽  
Vol 16 (4) ◽  
pp. 1249-1279
Author(s):  
Battal Dogan ◽  
Lars Ehlers
Keyword(s):  
School Choice ◽  
Pareto Improvement ◽  
Blocking Pair ◽  
Deferred Acceptance ◽  
Pareto Improvements ◽  
The Stability

We investigate efficient and minimally unstable Pareto improvements over the deferred acceptance (DA) mechanism—a popular school choice mechanism that is stable but not efficient. We show that there is no Pareto improvement over the DA mechanism that 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.

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 Persistent Distortionary Policies with Asymmetric Information

2006 ◽  
Vol 96 (1) ◽  
pp. 387-393 ◽  
Author(s):  
Matthew F Mitchell ◽  
Andrea Moro
Keyword(s):  
Asymmetric Information ◽  
Efficient Method ◽  
Pareto Frontier ◽  
Pareto Improvement ◽  
Lump Sum ◽  
Standard Textbook ◽  
Pareto Improvements

Why are distortionary policies used when seemingly Pareto improvements exist? According to a standard textbook argument, a Pareto improvement can be obtained by eliminating the distortions, compensating the losers with a lump sum transfer, and redistributing the gains that are left over. We relax the assumption that winners know the losses suffered by the losers and show that the informationally efficient method of compensating losers may involve the use of seemingly inefficient (but informationally efficient) distortionary policies. The risk of overcompensating losers may make distortions informationally efficient, as there are points on the Pareto frontier where distortions are used.

scholarly journals The Hidden Advantage of Delegation: Pareto Improvements in a Gift Exchange Game

2012 ◽  
Vol 102 (5) ◽  
pp. 2358-2379 ◽  
Author(s):  
Gary Charness ◽  
Ramón Cobo-Reyes ◽  
Natalia Jiménez ◽  
Juan A Lacomba ◽  
Francisco Lagos
Keyword(s):  
Positive Reaction ◽  
Strong Evidence ◽  
Gift Exchange ◽  
Pareto Improvement ◽  
Pareto Improvements

This paper analyzes the effect on performance and earnings of delegating the wage choice to employees. Our results show that such delegation significantly increases effort levels. Moreover, we observe a Pareto improvement, as the earnings of both employers and employees increase when employers delegate than when they do not. Interestingly, we also find that the employees' performance under delegation is higher than under nondelegation, even for similar wages. While there is strong evidence that behavior reflects strategic considerations, this result also holds for one-shot interactions. A possible nonstrategic motivation explaining the positive reaction to delegation is a sense of enhanced responsibility. (JEL J31, J33, J41)

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 (Il)legal Assignments in School Choice

2019 ◽  
Vol 87 (4) ◽  
pp. 1837-1875 ◽  
Author(s):  
Lars Ehlers ◽  
Thayer Morrill
Keyword(s):  
Public School ◽  
School Choice ◽  
Stability Criterion ◽  
Rural Hospitals ◽  
Choice Functions ◽  
Public School Choice ◽  
Blocking Pair

Abstract In public school choice, students with strict preferences are assigned to schools. Schools are endowed with priorities over students. Incorporating constraints from different applications, priorities are often modelled as choice functions over sets of students. It has been argued that the most desirable criterion for an assignment is stability; there should not exist any blocking pair: no student shall prefer some school to her assigned school and have higher priority than some student who got into that school or the school has an empty seat. We propose a blocking notion where in addition it must be possible to assign the student to her preferred school. We then define the following stability criterion for a set of assignments: a set of assignments is legal if and only if any assignment outside the set is blocked with some assignment in the set and no two assignments inside the set block each other. We show that under very basic conditions on priorities, there always exists a unique legal set of assignments, and that this set has a structure common to the set of stable assignments: (i) it is a lattice and (ii) it satisfies the rural hospitals theorem. The student-optimal legal assignment is efficient and provides a solution for the conflict between stability and efficiency.

scholarly journals Expanding “Choice” in School Choice

2015 ◽  
Vol 7 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Yeon-Koo Che ◽  
Yosuke Yasuda
Keyword(s):  
Public Schools ◽  
School Choice ◽  
Ex Ante ◽  
Deferred Acceptance ◽  
School Preferences

Gale-Shapley's deferred acceptance (henceforth DA) mechanism has emerged as a prominent candidate for placing students to public schools. While DA has desirable fairness and incentive properties, it limits the applicants' abilities to communicate their preference intensities, which entails ex ante inefficiency when ties at school preferences are broken randomly. We propose a variant of deferred acceptance mechanism that allows students to influence how they are treated in ties. It inherits much of the desirable properties of DA but performs better in ex ante efficiency. (JEL D82, H75, I21, I28)

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.

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