UMUTCAN SALMAN - Recent Research

Utilitarian Object Reallocation

Best paper prize at XXXVI SIEP Conference 2024
Earlier versions of this paper circulated under the title ”The Object Allocation Problem with Maximum and Minimum Number of Changes”.

This paper studies an object allocation problem, which involves assigning objects to agents while taking into account agents’ endowments, object capacities and agents’ preferences. We focus on the Pareto efficient and individually rational allocations. The goal is to study the Pareto efficient and individually rational allocations that maximize the number of individuals improving upon their initial endowments. We present the Reallocating Cycles Algorithm for addressing this problem. Next, we discuss several extensions where our algorithm can be used with a minor modification. Extensions include an affirmative action setting where priority is given to the most disadvantaged individuals.

Complexity of the Object Allocation Problem with Minimum Number of Changes

📃 Submitted version

This paper studies the problem of reallocating objects to agents while taking into account agents' endowments, object capacities and agents’ preferences. The goal is to find a Pareto efficient and individually rational allocation that minimizes the number of individuals who need to change from their initial allocation to the final one. We call this problem as MINDIST. We establish NP-completeness result for MINDIST. We also show that MINDIST remains NP-complete when we restrict individual preferences to be binary, meaning that each individual can rank at most two objects in the preferences. Finally, we present an integer programming formulation to solve small to moderately sized instances of the NP-hard problems.

Equal opportunities in school choice settings (with Domenico Moramarco)

📃Submitted version

We introduce a novel notion of fairness, inspired by the equality of opportunity literature, into the school choice setting, endowed with a measure of the match qualities between students and schools. In this framework, fairness considerations are made by a social evaluator based on the match quality distribution. We impose the standard notion of stability as a minimal desideratum and study matchings that satisfy our notion of fairness and an eciency requirement based on aggregate match quality. To overcome some of the identied incompatibilities, we relax the fairness and eciency denitions, and embed them in a family of linear social welfare functions. We then propose an algorithm that maximize social welfare over the set of stable matchings. Finally, we illustrate our approach with an application to the allocation of Italian high school students in the 2021/2022 academic year.