Sanctioned by its constitution, India is home to the world's most comprehensive affirmative action program, where historically discriminated groups are protected with vertical reservations implemented as “set asides,” and other... more
Sanctioned by its constitution, India is home to the world's most comprehensive affirmative action program, where historically discriminated groups are protected with vertical reservations implemented as “set asides,” and other disadvantaged groups are protected with horizontal reservations implemented as “minimum guarantees.” A mechanism mandated by the Supreme Court in 1995 suffers from important anomalies, triggering countless litigations in India. Foretelling a recent reform correcting the flawed mechanism, we propose the 2SMG mechanism that resolves all anomalies, and characterize it with desiderata reflecting laws of India. Subsequently rediscovered with a high court judgment and enforced in Gujarat, 2SMG is also endorsed by Saurav Yadav v. State of UP (2020), in a Supreme Court ruling that rescinded the flawed mechanism. While not explicitly enforced, 2SMG is indirectly enforced for an important subclass of applications in India, because no other mechanism satisfies the n...
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Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a "double... more
Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a "double coincidence of wants." Developing infrastructure to perform three-way as well as two-way exchanges will have a substantial effect on the number of transplants that can be arranged. Larger than three-way exchanges have less impact on efficiency. In a general model of type-compatible exchanges, the size of the largest exchanges required to achieve efficiency equals the number of types.
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Most transplanted kidneys are from cadavers, but there are also many transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the... more
Most transplanted kidneys are from cadavers, but there are also many transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each patient can receive a kidney from the other donor. Exchanges are also made in which a donor-patient pair makes a donation to someone waiting for a cadaver kidney, in return for the patient in the pair receiving high priority for a compatible cadaver kidney when one becomes available. There are stringent legal/ethical constraints on how exchanges can be conducted. We explore how larger scale exchanges of these kinds can be arranged efficiently and incentive compatibly, within existing constraints. The problem resembles some of the “housing ” problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned si...
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This online appendix includes proofs of all mathematical results in the main text and a documentation appendix for Table 1. THEOREM 1: Suppose each student has a complete rank ordering and k> 1. The old Chicago Public Schools mechanism... more
This online appendix includes proofs of all mathematical results in the main text and a documentation appendix for Table 1. THEOREM 1: Suppose each student has a complete rank ordering and k> 1. The old Chicago Public Schools mechanism (Chi k) is at least as manipulable as any weakly stable mechanism. PROOF: Fix a problem P and let ϕ be an arbitrary mechanism that is weakly stable. Suppose that Chi k is not manipulable for problem P. Claim 1: Any student assigned under Chik (P) receives her top choice. Proof. If not, since each student has a complete rank order list, |I |> Q, k> 1, there must be a student that is assigned to a school s he has not ranked first. Consider the highest composite score student i who is unassigned. Student i can rank school s first and will be assigned a seat there in the first round of Chik mechanism instead of some student who has not ranked school s first. That contradicts Chik is not manipulable for problem P. Claim 2. The set of students who ...
We show that Hatfield and Kojima (2010) inherits a critical ambiguity from its predecessor
School choice plans in many cities grant students higher priority for some (but not all) seats at their neighborhood schools. This paper demonstrates how the precedence order, i.e. the order in which different types of seats are filled by... more
School choice plans in many cities grant students higher priority for some (but not all) seats at their neighborhood schools. This paper demonstrates how the precedence order, i.e. the order in which different types of seats are filled by applicants, has quantitative effects on distributional objectives comparable to priorities in the celebrated deferred acceptance algorithm. While Boston's school choice plan gives priority to neighborhood applicants for half of each school's seats, the intended effect of this policy is lost because of the precedence order. Despite widely held impressions about the importance of neighborhood priority, the outcome of Boston's implementation of a 50-50 school split is nearly identical to a system without neighborhood priority. We formally establish that either increasing the number of neighborhood priority seats or lowering the precedence order positions of neighborhood seats at a school have the same effect: an increase in the number o...
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Narita provided helpful comments. Kominers is grateful for the support of National Science Foundation
Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper,... more
Although a pilot national live-donor kidney exchange program was recently launched in the US, the kidney shortage is increasing faster than ever. A new solution paradigm is able to incorporate compatible pairs in exchange. In this paper, we consider an exchange framework that has both compatible and incompatible pairs, and patients are indifferent over compatible pairs. Only two-way exchanges are permitted because of institutional constraints. We explore the structure of Pareto-efficient matchings in this framework. We show that under Pareto-efficient matchings, the same number of patients receive transplants, and it is possible to construct Pareto-efficient matchings that match the same incompatible pairs while matching the least number of compatible pairs. We extend the celebrated Gallai-Edmonds Decomposition in the combinatorial optimization literature to our new framework. We also conduct comparative static exercises on how this decomposition changes as new compatible pairs join...
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Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such... more
Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resembles models of the “double coincidence of wants, ” and relatively few exchanges have been consummated by decentralized means. As the population of available patient-donor pairs grows, the frequency with which exchanges can be arranged will depend in part on how exchanges are organized. We study the potential frequency of exchanges as a function of the number of patient-donor pairs, and the size of the largest feasible exchange. Developing infrastructure to identify and perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants, and will help the most vulnerable patients. Larger than 3-way exchanges have much smaller impact. Larger populations of
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Mechanisms that rely on course bidding are widely used at Business Schools in order to allocate seats at oversubscribed courses. Bids play two key roles under these mechanisms to infer student preferences and to determine who have bigger... more
Mechanisms that rely on course bidding are widely used at Business Schools in order to allocate seats at oversubscribed courses. Bids play two key roles under these mechanisms to infer student preferences and to determine who have bigger claims on course seats. We show that these two roles may easily conflict and preferences induced from bids may significantly differ from the true preferences. Therefore these mechanisms which are promoted as market mechanisms do not necessarily yield market outcomes. We introduce a Pareto-dominant market mechanism that can be implemented by asking students for their preferences in addition to their bids over courses.
WHEN A COLLEGE GRADUATE decides to pursue a higher degree at a particular institution, one of the first challenges she faces is finding an apartment. Most institutions have on-campus housing available that is often subsidized and hence... more
WHEN A COLLEGE GRADUATE decides to pursue a higher degree at a particular institution, one of the first challenges she faces is finding an apartment. Most institutions have on-campus housing available that is often subsidized and hence more appealing than its alternatives. Usually there are several types of on-campus housing and the attractiveness of each type changes from person to person. Therefore housing offices need to find 44mechanisms" to allocate available housing among the applicants who might have various preferences. In this paper we deal with this class of problems to which we refer as house allocation problems.2 Formally, there are n agents who collectively own n indivisible objects, say houses, and each agent has preferences over objects.3 An allocation is a matching of houses to agents and a matching mechanism is a systematic procedure to select a matching for each problem. A widely studied class of matching mechanisms is the class of simple serial dictatorships:...
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COVID-19 has revealed limitations of existing mechanisms for rationing medical resources under emergency scenarios. Many argue that these mechanisms abandon various ethical values such as equity by discriminating against disadvantaged... more
COVID-19 has revealed limitations of existing mechanisms for rationing medical resources under emergency scenarios. Many argue that these mechanisms abandon various ethical values such as equity by discriminating against disadvantaged communities. Illustrating that these limitations are aggravated by a restrictive choice of mechanism, we formulate pandemic rationing of medical resources as a new application of market design and propose a reserve system as a resolution. We develop a general theory of reserve design, introduce new concepts such as cutoff equilibria and smart reserves, extend the analysis of previously-known ones such as sequential reserve matching, relate these concepts to current debates, and present preliminary policy impact.
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A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice... more
A central issue in school choice is the design of a student assignment mechanism. Education literature provides guidance for the design of such mechanisms but does not offer specific mechanisms. The flaws in the existing school choice plans result in appeals by unsatisfied parents. We formulate the school choice problem as a mechanism design problem and analyze some of the existing school choice plans including those in Boston, Columbus, Minneapolis, and Seattle. We show tha t these existing plans have serious shortcomings, and offer two alternative mechanisms each of which may provide a practical solution to some critical school choice issues. ( MHO C78, D61, D78, I20) * Abdulkadiroglu: Department of Economics, Columbia University, New York, NY 10027; Sonmez: Department of Economics, Koc University, Sariyer, 80910, Istanbul, Turkey. The previous version of this paper was entitled "School Choice: A Solution to the Student Assignment Problem." We are grateful to Michael Joh...
We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives... more
We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives the theoretical background regarding the basic models, namely “house allocation and exchange” problems. First, we investigate the allocation and exchange problems separately, and then we combine them to present a real-life application: on-campus housing at universities. As the second application domain, we extend the basic allocation and exchange models to the “kidney exchange” problem and present new theory and applications regarding this problem. We present proposed and adopted mechanisms that take very specific institutional details into account. Then, we present the school admissions problem in three subcategories: the “college admissions” model where both schools and students are strategic agents, the “school placement” model where only students ...
We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more... more
We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more "clean") remedy renders several of the results of the paper invalid in the absence of an additional irrelevance of removed contracts condition implicitly assumed throughout the paper, whereas the second remedy results in the lack of transparency in presentation of results while at the same time reducing the scope of the analysis with no clear benefit.
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In a wide variety of real-life resource allocation problems such as school choice or assignment of public positions, implementation of affirmative action policies rely on choice rules that balance meritocracy with equity. We study choice... more
In a wide variety of real-life resource allocation problems such as school choice or assignment of public positions, implementation of affirmative action policies rely on choice rules that balance meritocracy with equity. We study choice rules where meritocracy is attained through reliance on a priority list, and equity is attained through reserved positions for target groups of disadvantaged individuals. Focusing on overlapping reserves, the case where an individual can belong to multiple types of reserved positions, we characterize choice rules that satisfy maximal compliance with reservations, elimination of justified envy, and non-wastefulness. When an individual accommodates only one of the reserved positions, the horizontal envelope choice rule is the only rule to satisfy these three axioms. When an individual accommodates each of the reserved positions she qualifies for, there are complementarities between individuals. Under this alternative convention, and assuming there are...
Built into the country’s constitution, one of the world’s most comprehensive affirmative action programs exists in India. Government jobs and seats at publicly funded educational institutions are allocated through a Supreme Court-mandated... more
Built into the country’s constitution, one of the world’s most comprehensive affirmative action programs exists in India. Government jobs and seats at publicly funded educational institutions are allocated through a Supreme Court-mandated procedure that integrates a meritocracy-based system with a reservation system that provides a level playing field for disadvantaged groups through two types of special provisions. The higher-level provisions, known as vertical reservations, are exclusively intended for backward classes that faced historical discrimination, and implemented on a “set aside” basis. The lower-level provisions, known as horizontal reservations, are intended for other disadvantaged groups (such as women, disabled, or the economically disadvantaged), and they are implemented on a “minimum guarantee” basis. We show that, the Supreme Court-mandated procedure suffers from at least four major deficiencies. First and foremost, it is not well-defined when candidates can qualif...
A central issue in school choice is the debate over who obtains seats at oversubscribed schools. Choice plans in many cities grant students higher priority for some seats at their neighborhood schools. This paper demonstrates how the... more
A central issue in school choice is the debate over who obtains seats at oversubscribed schools. Choice plans in many cities grant students higher priority for some seats at their neighborhood schools. This paper demonstrates how the precedence order, i.e. the order in which seats are depleted by applicants with specific claims, is a lever to achieve distributional goals that has effects comparable to priorities under the deferred acceptance algorithm. While Boston gives priority to neighborhood applicants for half of each school’s seats, the intended effect of this policy is almost entirely lost because of the seat precedence order; its outcome is nearly equivalent to that of a mechanism without any neighborhood priority. A change in precedence, holding fixed the current 50-50 school seat split, corresponds to almost three-quarters of the effect of switching from 0% to 100% neighborhood priority. We formally establish that either increasing the number of neighborhood priority seats...
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In July 2005 the Boston School Committee voted to replace the existing Boston school choice mechanism with a deferred acceptance mechanism that simplifies the strategic choices facing parents. This paper presents the empirical case... more
In July 2005 the Boston School Committee voted to replace the existing Boston school choice mechanism with a deferred acceptance mechanism that simplifies the strategic choices facing parents. This paper presents the empirical case against the previous Boston mechanism, a priority matching mechanism, and the case in favor of the change to a strategy-proof mechanism. We present evidence both of sophisticated strategic behavior among some parents, and of unsophisticated strategic behavior by others. We find evidence that some parents pay close attention to the capacity constraints of different schools, while others appear not to. In particular, we identify a certain kind of mistake that can be observed in the data without knowing the true preferences of a family. Families that make this mistake are disproportionately unassigned, and in many cases they would have been assigned but for the mistake. This interaction between sophisticated and unsophisticated players identifies a new ratio...
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Over the last 15 years, kidney exchange has become a mainstream paradigm to increase transplants. However, compatible pairs do not participate, and full benefits from exchange can be realized only if they do. We propose incentivizing... more
Over the last 15 years, kidney exchange has become a mainstream paradigm to increase transplants. However, compatible pairs do not participate, and full benefits from exchange can be realized only if they do. We propose incentivizing compatible pairs to participate in exchange by insuring their patients against future renal failure via increased priority in deceased-donor queue. We analyze equity and welfare benefits of this scheme through a new dynamic continuum model. We calibrate the model with US data and quantify substantial gains from adopting incentivized exchange, both in terms of access to living-donor transplants and reduced competition for deceased-donor transplants. (JEL D47, I11, I12, I18)
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Liver exchange has been practiced in small numbers, mainly to overcome blood‐type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former... more
Liver exchange has been practiced in small numbers, mainly to overcome blood‐type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right‐lobe transplantation is often utilized due to size‐compatibility requirement with the patient. We model liver exchange as a market‐design problem, focusing on logistically simpler two‐way exchanges, and introduce an individually rational, Pareto‐efficient, and incentive‐compatible mechanism. Construction of this mechanism requires novel technical tools regarding bilateral exchanges under partial‐order‐induced preferences. Through simulations we show that not only can liver exchange increase the number of transplants by more than 30%, it can also increase the share of the safer left‐lobe transplants.