Respecting priorities versus respecting preferences in school choice: When is there a trade-off?

A classic trade-off that school districts face when deciding which matching algorithm to use is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm (DA) respects priorities but can lead to inefficient allocations. We identify a new condition on school choice markets under which DA is efficient. Our condition generalizes earlier conditions by placing restrictions on how preferences and priorities relate to one another only on the parts that are relevant for the assignment. Whenever there is a unique allocation that respects priorities, our condition captures all the environments for which DA is efficient. We show through stylized examples and simulations that our condition significantly expands the range of known environments for which DA is efficient. We also discuss how our condition sheds light on existing empirical findings

The Mechanism Design Approach to Student Assignment

The mechanism design approach to student assignment involves the theoretical, empirical, and experimental study of systems used to allocate students into schools around the world. Recent practical experience designing systems for student assignment has raised new theoretical questions for the theory of matching and assignment. This article reviews some of this recent literature, highlighting how issues from the field motivated theoretical developments and emphasizing how the dialogue may be a road map for other areas of applied mechanism design. Finally, it concludes with some open questions.National Science Foundation (U.S.

Strategy-proof stochastic assignment

I study strategy-proof assignment mechanisms where the agents reveal their preference rankings over the available objects. A stochastic mechanism returns lotteries over deterministic assignments, and mechanisms are compared according to first-order stochastic dominance. I show that non-wasteful strategy-proof mechanisms are not dominated by strategy-proof mechanisms, however non-wastefulness is highly restrictive when the mechanism involves randomization. Infact, the Random Priority mechanism (i.e.,the Random Serial Dictatorship), and a recently adopted school choice mechanism, Deferred Acceptance with Random Tie-breaking, are wasteful. I find that both these mechanisms are dominated by strategy-proof mechanisms. In general, strategy proof improvement cannot be due to merely reshuffling objects, and therefore must involve assigning more objects

Strategy-Proof Fair School Placement

This paper provides an `escape route' from the efficiency-equity trade-off in the School Choice problem. We achieve our objective by presenting a weak notion of fairness, called τ-fairness, which is always satisfied by some allocation. Then, we propose the adoption of the Student Optimal Compensating Exchange mechanism, a procedure that assigns a τ-fair allocation to each problem. We further identify a condition on students' preferences guaranteeing incentive compatibility of this mechanism

Strategy-proof tie-breaking

We study a general class of priority-based allocation problems with weak priority orders and identify conditions under which there exists a strategy-proof mechanism which always chooses an agent-optimal stable, or constrained efficient, matching. A priority structure for which these two requirements are compatible is called solvable. For the general class of priority-based allocation problems with weak priority orders,we introduce three simple necessary conditions on the priority structure. We show that these conditions completely characterize solvable environments within the class of indifferences at the bottom (IB) environments, where ties occur only at the bottom of the priority structure. This generalizes and unifies previously known results on solvable and unsolvable environments established in school choice, housing markets and house allocation with existing tenants. We show how the previously known solvable cases can be viewed as extreme cases of solvable environments. For sufficiency of our conditions we introduce a version of the agent-proposing deferred acceptance algorithm with exogenous and preference-based tie-breaking

Essays on Market Design

“Market Design […] strives to understand how the design of marketplaces influences the functioning of markets” (Roth 2018, p. 1609). The simple but powerful rationale of market design is to improve markets by actively designing them, guided by economic theory, empirical data, and carefully designed economic experiments. In recent years, economists have been successful in designing a variety of institutions, including spectrum auctions, electricity markets, feedback systems, kidney exchanges, and school choice (Chen et al., 2020). This thesis consists of four chapters, all devoted to different aspects and areas of market design. Another unifying element of this thesis is the methodology. In all chapters, laboratory experiments are conducted, data are analyzed, and the results are linked to real-world applications. Laboratory experimental studies are a particularly useful tool in the context of market design. They are often compared to a wind tunnel, where the performance of existing designs is studied in a simplified environment or even new design ideas are tested in a controlled environment (Chen et al., 2020). The first chapter looks at auction design. We investigate the puzzle behind the popularity of a non-binding soft reserve price in practice. Here, we use the laboratory as a "wind tunnel" to compare the performance of different existing auction designs in a controlled environment. Chapter two focuses on the design of feedback systems. In this chapter, we propose a small but very effective modification to existing feedback withdrawal mechanisms. Therefore, we use the possibility of laboratory experiments to test a new design idea that has not yet been implemented in practice and for which, of course, no field data are available. The third chapter is concerned with the area of school choice. Here, I investigate the value of fairness to participants in school choice markets, which can guide a market designer in choosing an appropriate algorithm. A laboratory experiment allows for the observation and control of student preferences that are typically unobservable in field data. Finally, chapter four focuses on norm information acquisition. When designing real-world institutions, incentives must be aligned with behavior in terms of underlying goals (Bolton and Ockenfels 2012). Therefore, social norms, which are known to be a powerful force influencing behavior, are of great importance for market design. We study how economic agents choose between different types of norm information in a social choice context with uncertainty

Matching with Couples: Stability and Incentives in Large Markets*

Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. We find conditions under which a stable matching exists with high probability in large markets. We present a mechanism that finds a stable matching with high probability, and which makes truth-telling by all participants an approximate equilibrium. We relate these theoretical results to the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.Economic

Essays on Matching Markets

The thesis "Essays on Matching Markets" contributes to the theory and applications of matching theory. The first chapter analyzes the German university admissions system and proposes an alternative admissions procedure that outperforms the currently used mechanism. In particular, the new mechanism provides strong (i.e. dominant strategy) incentives for applicants to reveal their true preferences and achieves a notion of stability that is adapted to the German system. In the second chapter we analyze the school choice problem with indifferences in priority orders. In this context, stability (with respect to student preferences and school priorities) can be understood as a fairness criterion which ensures that no student ever envies another student for a school at which she has higher priority. Since school seats are objects to be allocated among students, it is important to ensure that a constrained efficient allocation is selected, i.e. an allocation that is stable and not (Pareto-) dominated by any other stable matching. A counterexample of Erdil and Ergin (American Economic Review, 2008) shows that there may not exist a non-manipulable and constrained efficient mechanism. We consider the case where students either all have the same priority or all have distinct priorities for a given school. For this important special case we investigate whether the negative result of Erdil and Ergin is the rule or an exception and derive sufficient conditions for the existence of a constrained efficient and (dominant strategy) incentive compatible mechanism. The proof is constructive and shows how preferences of students can (sometimes) be used to prevent any welfare loss from tie-breaking decisions. The third chapter deals with a more general matching model recently introduced by Ostrovsky (American Economic Review, 2008). For this model we analyze the relation between Ostrovsky's chain stability concept, efficiency, and several competing stability concepts. We characterize the largest class of matching models for which chain stable outcomes are guaranteed to be stable and robust to all possible coalitional deviations. Furthermore, we provide two rationales, one based on efficiency and the other based on robustness considerations, for chain stability in the general supply chain model