Periodic Reporting for period 1 - SchoolFlex (School choice under transferable capacities)
Periodo di rendicontazione: 2020-10-01 al 2022-09-30
In a free market economy, price is the most popular mechanism for allocating goods and services. However, many of us will find it repugnant or unethical to put for sale human organs for transplantation or public-school seats. Such resources are rather efficiently allocated by matching them to participants’ preferences via a centralized matching system. One of the challenges of the designer is to elicit the true preferences from participants and at the same time prevent participants from gaming the system. Gaming would undermine confidences of this type of market solution.
Unfortunately, in some highly publicized cases, it has proved possible to game matching systems. Usually, gaming benefit participants who have sufficient information and understanding about the allocation system to take advantage of. Despite efforts to construct ‘tamper-proof’ mechanisms to restrict opportunities for gaming and unfair advantage, it’s become clear that most mechanisms can still be manipulated under certain circumstances and to varying degrees. It has been, for example, observed in school choice design. For various reasons, admissions authorities limit the number of schools that each student may list, thus putting constraints on rankings. Ranking constraints introduces an opportunity for gaming. Over time, authorities tend to adopt more flexible rankings system in which students can rank more schools. The goal of this project was to study the relationship between gaming (manipulation) and flexible rankings as well as its fairness implication.
Unfortunately, in some highly publicized cases, it has proved possible to game matching systems. Usually, gaming benefit participants who have sufficient information and understanding about the allocation system to take advantage of. Despite efforts to construct ‘tamper-proof’ mechanisms to restrict opportunities for gaming and unfair advantage, it’s become clear that most mechanisms can still be manipulated under certain circumstances and to varying degrees. It has been, for example, observed in school choice design. For various reasons, admissions authorities limit the number of schools that each student may list, thus putting constraints on rankings. Ranking constraints introduces an opportunity for gaming. Over time, authorities tend to adopt more flexible rankings system in which students can rank more schools. The goal of this project was to study the relationship between gaming (manipulation) and flexible rankings as well as its fairness implication.
To investigate the manipulability of school choice mechanisms under flexible rankings, I trace students who have the incentive to manipulate these mechanisms. I formulate two concepts of manipulability to distinguish mechanisms by their level of manipulability in connection with the degree of flexible rankings.
In a first concept, I measure the set of schools that each student can potentially obtain by manipulation. This leads to a concept of strategic accessibility, and a mechanism is less strategically accessible than another if at the first mechanism every student can obtain a weakly less set of schools from manipulation than at the second. I applied this concept and showed that making school choice more flexible in rankings while implementing deferred acceptance instead of immediate acceptance leads to less strategically accessible mechanisms.
In a second concept, I count the number of students who have the incentive to manipulate. One mechanism is deemed less manipulable than another if it has a smaller number of manipulating students than the second. I showed that given a level of flexibility, the deferred acceptance is less manipulable than the immediate acceptance. In addition, within deferred acceptance, a greater level of flexibility is associated with less manipulability.
I further investigated the relationship between flexible rankings and fairness. I call on to two notions of fairness: fairness by the inclusion of problems without a blocking student. While more flexible rankings are associated with more problems without a blocking student, the notion is weak because the set of such problems might be very small. Then I formulated a notion of counting the number of blocking students and I showed that a greater level of flexible rankings is associated with a smaller number of blocking students under deferred acceptance. However, this result cannot be established between immediate and deferred acceptance with the same level of flexible rankings.
In a first concept, I measure the set of schools that each student can potentially obtain by manipulation. This leads to a concept of strategic accessibility, and a mechanism is less strategically accessible than another if at the first mechanism every student can obtain a weakly less set of schools from manipulation than at the second. I applied this concept and showed that making school choice more flexible in rankings while implementing deferred acceptance instead of immediate acceptance leads to less strategically accessible mechanisms.
In a second concept, I count the number of students who have the incentive to manipulate. One mechanism is deemed less manipulable than another if it has a smaller number of manipulating students than the second. I showed that given a level of flexibility, the deferred acceptance is less manipulable than the immediate acceptance. In addition, within deferred acceptance, a greater level of flexibility is associated with less manipulability.
I further investigated the relationship between flexible rankings and fairness. I call on to two notions of fairness: fairness by the inclusion of problems without a blocking student. While more flexible rankings are associated with more problems without a blocking student, the notion is weak because the set of such problems might be very small. Then I formulated a notion of counting the number of blocking students and I showed that a greater level of flexible rankings is associated with a smaller number of blocking students under deferred acceptance. However, this result cannot be established between immediate and deferred acceptance with the same level of flexible rankings.
The concept of counting the number of manipulating students that I developed proved useful for applications beyond school choice. I used it to study job matching mechanisms such as the National Resident Matching Program in the U.S. In these markets, stability is required to prevent agents from contracting outside of the clearinghouse. However, stable matching mechanisms are manipulable. I identified the least manipulable stable matching mechanism by counting the number of manipulating agents. This result sheds light on the design of many stable matching mechanisms. This mechanism is nothing but the famous student-proposing Gale and Shapley algorithm.
The results of the project widen our knowledge on market design, and I expect that some of them will be included in the teaching curricula of graduate courses in market design. I also expect some results to be one of the guiding principles for matching market design.
The results of the project widen our knowledge on market design, and I expect that some of them will be included in the teaching curricula of graduate courses in market design. I also expect some results to be one of the guiding principles for matching market design.