Lexicographic Choice Under Variable Capacity Constraints

TL;DR

This paper characterizes lexicographic choice rules and mechanisms in matching markets with variable seat capacities, with implications for school choice systems and agent diversity.

Contribution

It provides a formal characterization of lexicographic choice rules and deferred acceptance mechanisms under variable capacity constraints, enhancing understanding of their application.

Findings

Characterization of lexicographic choice rules

Analysis of deferred acceptance mechanisms with variable capacities

Implications for Boston school choice system

Abstract

In several matching markets, in order to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a (capacity-constrained) lexicographic choice rule. We provide a characterization of lexicographic choice rules and a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure under variable capacity constraints. We discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.