Lexicographic choice under variable capacity constraints

Abstract

In several matching markets, 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. 1 | INTRODUCTION Many real-life resource allocation problems involve the allocation of an object that is available in a limited number of identical copies, called the capacity of the object. Choice rules, which are systematic ways of rationing available copies of an object when demand exceeds the capacity, are essential in the analysis of such problems. A well-known example is the school choice problem in which each school has a certain number of seats to be allocated among students. Although student preferences are elicited from the students, endowing each school with a choice rule is an essential part of the design process. Which choice rule to use is not always evident. The school choice literature, starting with the seminal study by Abdulkadiroğlu and Sönmez (2003), has widely focused on problems

Choice with Affirmative Action

“…12 Chambers and Yenmez (2018) particularly note that lexicographic choice rules satisfy capacity-filling and substitutability, but do not provide an axiomatic characterization. Dogan et al (2021) also consider choice rules based on lexicographic choice procedures, but the class of choice rules characterized is different than the class we study here since they include variable capacity constraints and do not include a minority group or axioms for affirmative action.…”

Assignment maximization

“…The authors show that variants of serial dictatorship and Probabilistic Serial Bogomolnaia and Moulin (2001) mechanisms assign at least as many agents as one can match under the constraints, while the violations of the constraints are relatively small. Other papers studying constraints in matching settings include Kamada and Kojima (2015), Bó (2016), Liu (2019), Aygün and Turhan (2020), and Doğan et al (2021), among others.…”

Responsiveness to priority‐based affirmative action policy in school choice

“…Doğan et al (2021) provide a characterization result for sDA under a setting in which a certain sets of seats are reserved for different student groups.…”