2 research outputs found
Coalitions and Cliques in the School Choice Problem
The school choice mechanism design problem focuses on assignment mechanisms
matching students to public schools in a given school district. The well-known
Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most
efficient stable mechanism proposed so far as a solution to this problem.
However its inefficiency is well-documented, and recently the Efficiency
Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for
this weakness. In this note we describe two related adjustments to SOSM with
the intention to address the same inefficiency issue. In one we create possibly
artificial coalitions among students where some students modify their
preference profiles in order to improve the outcome for some other students.
Our second approach involves trading cliques among students where those
involved improve their assignments by waiving some of their priorities. The
coalition method yields the EADAM outcome among other Pareto dominations of the
SOSM outcome, while the clique method yields all possible Pareto optimal Pareto
dominations of SOSM. The clique method furthermore incorporates a natural
solution to the problem of breaking possible ties within preference and
priority profiles. We discuss the practical implications and limitations of our
approach in the final section of the article
School Choice as a One-Sided Matching Problem: Cardinal Utilities and Optimization
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. Previously considered criteria for evaluating proposed mechanisms such as stability, strategyproofness and Pareto efficiency do not always translate into desirable student assignments. In this note, we explore a class of one-sided, cardinal utility maximizing matching mechanisms focused exclusively on student preferences. We adapt a well-known combinatorial optimization technique (the Hungarian algorithm) as the kernel of this class of matching mechanisms. We find that, while such mechanisms can be adapted to meet desirable criteria not met by any previously employed mechanism in the school choice literature, they are not strategyproof. We discuss the practical implications and limitations of our approach at the end of the article