Aiding applicants: Leveling the playing field within the immediate acceptance mechanism

In school choice problems, the widely used manipulable Immediate Acceptance mechanism (IA) disadvantages unsophisticated applicants, but may ex-ante Pareto dominate any strategy-proof alternative. In these cases, it may be preferable to aid applicants within IA, rather than to abandon it. In a laboratory experiment, we first document a substantial gap in strategy choices and outcomes between subjects of higher and lower cognitive ability under IA. We then test whether disclosing information on past applications levels the playing field. The treatment is effective in partially reducing the gap between applicants of above- and below-median cognitive ability and in curbing ability segregation across schools, but may leave the least able applicants further behind

fairness comparisons of matching rules

This thesis consists of three studies in matching theory and market design. Its main focus is to compare matching rules according to normative criteria, primarily fairness, when objects have priorities over agents. In the first study we analyze one-to-one matching and prove that in general we cannot find a strategy-proof and Pareto-efficient mechanism which stands out uniquely in terms of fairness when using fundamental criteria for profile-by-profile comparison. In particular, despite suggestions to the contrary in the literature, the Top Trading Cycles (TTC) mechanism is not more fair than all other mechanisms in this class. We also show that while the TTC is not dominated, if the priority profile is strongly cyclic then there is not much scope for TTC to dominate other matching rules in this class. In the second study, which focuses on many-to-on matching, I provide a direct proof that Ergin's cycle (Ergin, 2002) is stronger than Kesten's cycle (Kesten, 2006), due to different scarcity conditions for the quotas on objects. I also prove that when there is a Kesten cycle there is no strategy-proof and Pareto-efficient mechanism which uniquely stands out in terms of the fairness criteria. Moreover, I use simulations to show that as the number of Kesten cycles increases, there are more fairness violations and fewer preference profiles at which the TTC mechanism is fair. The third study compares three competing many-to-one matching mechanisms that are strategy-proof and Pareto-efficient but not fair, namely the TTC, Equitable Top Trading Cycles (ETTC) and Clinch and Trade (CT) mechanisms. Although one would expect that ETTC and CT are more fair than the TTC, I demonstrate the opposite for specific preference profiles and compare the aggregate number of fairness violations using simulations. I find that ETTC tends to have fewer priority violations in the aggregate than the other two mechanisms across both different quota distributions and varying correlations of preferences. Finally, I show that all three mechanisms become more efficient when the commonly most preferred object has the highest quota, and demonstrate that the more unequal the quota distribution, the more fair and efficient the three mechanisms become

Essays on matching and preference aggregation

Cette thèse est une collection de trois articles dont deux portent sur le problème d’appariement et un sur le problème d’agrégation des préférences. Les deux premiers chapitres portent sur le problème d’affectation des élèves ou étudiants dans des écoles ou universités. Dans ce problème, le mécanisme d’acceptation différée de Gale et Shapley dans sa version où les étudiants proposent et le mécanisme connu sous le nom de mécanisme de Boston sont beaucoup utilisés dans plusieurs circonscriptions éducatives aux Etats-Unis et partout dans le monde. Le mécanisme de Boston est sujet à des manipulations. Le mécanisme d’acceptation différée pour sa part n’est pas manipulable mais il n’est pas efficace au sens de Pareto. L’objectif des deux premiers chapitres est de trouver des mécanismes pouvant améliorer le bien-être des étudiants par rapport au mécanisme d’acceptation différée ou réduire le dégré de vulnérabilité à la manipulation par rapport au mécanisme de Boston. Dans le Chapitre 1, nous étudions un jeux inspiré du système d’admission précoce aux Etats-Unis. C’est un système d’admission dans les collèges par lequel un étudiant peut recevoir une décision d’admission avant la phase générale. Mais il y a des exigences. Chaque étudiant est requis de soumettre son application à un seul collège et de s’engager à s’inscrire s’il était admis. Nous étudions un jeu séquentiel dans lequel chaque étudiant soumet une application et à la suite les collèges décident de leurs admissions dont les étudiants acceptent. Nous avons montré que selon une notion appropriée d’équilibre parfait en sous-jeux, les résultats de ce mécanisme sont plus efficaces que celui du mécanisme d’acceptation différée. vi Dans le Chapitre 2, nous étudions un mécanisme centralisé d’admissions dans les universités françaises que le gouvernement a mis en place en 2009 pour mieux orienter les étudiants dans les établissements universitaires. Pour faire face aux écoles dont les places sont insuffisantes par rapport à la demande, le système défini des priorités qui repartissent les étudiants en grandes classes d’équivalence. Mais le système repose sur les préférences exprimées pour départager les ex-aequos. Nous avons prouvé que l’application du mécanisme d’acceptation différée avec étudiant proposant aprés avoir briser les ex-aequos est raisonable. Nous appelons ce mécanisme mécanisme français. Nous avons montré que le mécanisme français réduit la vulnérabilité à la manipulation par rapport au mécanisme de Boston et améliore le bien-être des étudiants par rapport au mécanisme standard d’acceptation différée où les ex-aequos sont brisés de façon aléatoire. Dans le Chapitre 3, nous introduisons une classe de règles pour combiner les préférences individuelles en un ordre collectif. Le problème d’agrégation des préférences survient lorsque les membres d’une faculté cherchent une stratégie pour offrir une position sans savoir quel candidat va accepter l’offre. Il est courant de classer les candidats puis donner l’offre suivant cet ordre. Nous avons introuduit une classe de règles appélée règles de dictature sérielle augmentée dont chacune est paramétrée par une liste d’agents (avec répétition) et une règle de vote par comité. Pour chaque profile de préférences, le premier choix de l’agent en tête de la liste devient le premier choix collectif. Le choix du deuxème agent sur la liste, parmi les candidats restants, devient le deuxième choix collectif. Et ainsi de suite jusqu’à ce qu’il reste deux candidats auquel cas le comité vote pour classer ces derniers. Ces règles sont succinctement caractérisées par la non-manipulabilité et la neutralité sous l’extension lexicographique des préférences. Nous avons montré aussi que ces règles sont non-manipulables sous une variété d’extensions raisonable des préférences. Mots-clés : Appariement, mécanisme d’acceptation différée, mécanisme de Boston, mécanisme français, agrégation des préférences, règle non-manipulable, règle de dictature sérielle augmentée.This thesis is a collection of two papers on matching and one paper on preference aggregation. The first two chapters are concerned with the problem of assigning students to schools. For this problem, the student proposing version of Gale and Shapley’s deferred acceptance mechanism and a mechanism known as Boston mechanism are widely used in many school districts in U.S and around the world. The Boston mechanism is prone to manipulation. The deferred acceptance mechanism is not manipulable ; however, it is not Pareto efficient. The first two chapters of this thesis deal with the problem of either improving the welfare of students over deferred acceptance or reducing the degree of manipulation under Boston. In Chapter 1, we study a decentralized matching game inspired from the early decision system in the U.S : It is a college admission system in which students can receive admission decisions before the general application period. But there are two requirements. First, each student is required to apply to one college. Second, each student commits to attend the college upon admitted. We propose a game in which students sequentially make one application each and colleges ultimately make admission decisions to which students commit to accept. We show that up to a relevant refinement of subgame perfect equilibrium notion, the expected outcomes of this mechanism are more efficient than that of deferred acceptance mechanism. In Chapter 2, we study a centralized university admission mechanism that the French government has implemented in 2009 to better match students to viii university schools. To deal with oversubscribed schools, the system defined priorities that partition students into very coarse equivalence classes but relies on student reported preferences to further resolve ties.We show that applying student-proposing deferred acceptance mechanism after breaking ties is a reasonable procedure. We refer to this mechanism as French mechanism. We show that this mechanism is less manipulable than the Boston mechanism and more efficient than the standard deferred acceptance in which ties are broken randomly. In Chapter 3, we introduce a class of rules called augmented serial rules for combining individual preferences into a collective ordering. The aggregation problem appears when faculty members want to devise a strategy for offering an open position without knowing whether any given applicant will ultimately accept an offer. It is a commonplace to order the applicants and make offers accordingly. Each of these augmented serial rules is parametrized by a list of agents (with possible repetition) and a committee voting rule. For a given preference profile, the collective ordering is determined as follows : The first agent’s most preferred alternative becomes the top-ranked alternative in the collective ordering, the second agent’s most preferred alternative (among those remaining) becomes the second-ranked alternative and so on until two alternatives remain, which are ranked by the committee voting rule. The main result establishes that these rules are succinctly characterized by neutrality and strategy-proofness under the lexicographic extension. Additional results show that these rules are strategy-proof under a variety of other reasonable preference extensions

Theoretical Studies On The Design of School Choice Mechanism

This thesis consists of three papers on market design which address broadly applicable questions on the design of school choice mechanisms, refugee placement, assignment in entry-level labour markets and similar matching rules.In the first paper a new family of rules is introduced for many-to-one matching problems, the Preference Rank Partitioned (PRP) rules. PRP rules are Student-Proposing Deferred Acceptance rules where the schools use a choice function based on the students' preference orderings in addition to the schools' strict priority orderings. Each PRP rule uses a choice function which is a function of a fixed partition of both student preference ranks and school priority ranks: the choice function first seeks to select students based on the priority classes and then based on the preference classes. The strict priorities are only used for tie-breaking. PRP rules include many well-known matching rules and some interesting new rules, and we analyze them in this unified framework. In the second paper we study a new class of matching rules, called Deferred Acceptance with Improvement Trading Cycles (DA-ITC), which start with the DA, and if the DA outcome is not Pareto-efficient then there is an iterated improvement trading cycle phase which allows for Pareto-improvements until a Pareto-efficient outcome is reached. We first revisit EADAM (Kesten, 2010) and show that a simple algorithm which retraces cycles in the DA procedure in a backward order of the rejections is equivalent to the EADAM rule. The new class of DA-ITC rules contains the EADAM and DA-TTC as its two extreme members and exhibits some of their desirable properties. In the third paper we focus on matching problems where stability need not be satisfied if the violation of priorities is "small," such as when a small priority difference is considered insignificant or when one is willing to consent but only if the priority reversal is small. Based on the degree of stability which specifies what is considered a small priority gap, we define two families of matching rules, the k-Consent rules and the k-DA rules, and explore their attributes

Essays on the Economics of Education and Market Design

This dissertation consists of three essays on the economics of education and market design. The first two chapters are united in their attention on school choice issues. Chapter 1 considers a specific application, whereas chapter 2 focuses on a matching mechanism widely used in multiple applications. Both chapters 1 and 3 explore equity concerns in education but through very different lenses (affirmative action vs. educational investment) and very different settings (the United States vs. Vietnam). Chapter 1 addresses the diversity issue that is especially prevalent in elite schools that select students based on exams. Whereas previous studies only consider the direct impact on elite schools, I quantify the effects of two widely-discussed affirmative action plans on both elite and regular schools in New York City. I find that the two plans have quite different effects. First, there is a trade-off between improving diversity and maintaining student quality in elite schools as measured by state test scores in middle school. Despite taking into account the socioeconomic status of students' neighborhoods, the Chicago plan gives rise mostly to reshuffling within elite schools. Thus, both the overall racial composition and quality of incoming students are largely preserved as in the status quo. In contrast, the Top 7% plan, which would accept into the elite sector students in the top 7% by academic performance of each public middle school, causes considerable flows of students between the elite and regular sectors. The elite sector experiences a substantial increase in the proportions of Black and Hispanic students, along with a decrease in average student quality. Analyzing the difference between the outcomes of these two policies provides some insight into how the two objectives—diversity and peer quality in elite schools—might be better balanced in general. The second difference between the plans arises because they transform the distribution of diversity across schools in different ways. The Chicago plan reduces the differences among schools within the elite sector, while the Top 7% plan reduces the gap in diversity between the two sectors even as it increases within-sector dispersion. Both plans result in considerable changes in school assignments in the regular school sector, thus affecting the average student quality in these schools. Chapter 2, joint work with Guillaume Haeringer and Silvio Ravaioli, uses a lab experiment to study learning dynamics when participants receive feedback in centralized matching mechanisms. Our design allows for two types of learning: to coordinate within the same environment as well as to understand the underlying mechanisms. We provide additional evidence to previous work that the majority of the deviations from truth-telling, the dominant strategy in the Deferred Acceptance mechanism, are those that do not affect payoffs. Furthermore, by explicitly analyzing learning, we can confirm that at least some of the participants learn about the optimality of truth-telling, and their departures from it happen primarily when they face the same environment being repeated. Finally, we find that when learning to coordinate, agents tend to retain their previous strategy when the payoff from this strategy is high. This is suggestive evidence of reinforcement learning. Chapter 3 documents the pattern of educational investments for high school students across different demographics and their effects on performance on the college entrance exam and in college. Survey data from Vietnam shows that high school students from higher-income households have higher education expenditure and participation in extra classes (both at the extensive and intensive margin). Minority and rural students invest less than their non-minority and urban counterparts even after controlling for income. Out of these investments, only extra classes during the school year education expenditure other than that on extra classes are effective in increasing college entrance exam scores. In terms of college performance, a higher entrance exam score leads to a slightly higher grade point average at graduation, controlling for academic department fixed effects and investments in high school. Neither education expenditure or participation in extra classes in high school show any significant effects on college performance, except that already captured in the entrance exam scores. I record multiple gender differences. Female high school students tend to receive more investments. Even though they perform slightly worse on the entrance exam than their male peers with the same investments, they perform better in college, given the same entrance exam scores

The Secure Boston Mechanism

It is well known in the school assignment literature that it is impossible for a strategyproof mechanism to Pareto improve the assignment made be the Deferred Acceptance algorithm (DA). However, we show that it is possible for an algorithm to Pareto dominate DA in equilibrium. We do this by introduce a new algorithm, the Secure Boston Mechanism (sBM), that is a hybrid between the Boston Mechanism (BM) and DA. Our algorithm protects students that are initially guaranteed a school a but otherwise adjusts priorities at a based on how students rank a. We demonstrate that sBM always has an equilibrium that weakly dominates the DA assignment. We show that in equilibria that survive iterated elimination of dominated strategies that no student receives a school worse than a school she receives in a fair assignment. Finally, we show that whenever DA is inefficient, there exists a larger economy in which DA makes the same assignment but an equilibrium of sBM makes the Pareto dominating reassignment