Fair Societies: Algorithms for House Allocations

TL;DR

This paper develops efficient algorithms to improve fairness in house allocation problems with preferences, addressing computational challenges and analyzing trade-offs between fairness and welfare.

Contribution

It introduces two tractable algorithms for reducing envy in house allocations, including cases with initial allocations and single peaked preferences, extending to Pareto efficiency.

Findings

Algorithms effectively reduce envy in allocations.

Trade-offs between fairness and overall welfare are characterized.

Extensions to Pareto efficiency are demonstrated.

Abstract

House Allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents. Every agent must receive exactly one resource. We study algorithmic approaches towards ensuring fairness in such settings. Minimizing the number of envious agents is known to be NP-complete (Kamiyama et al. 2021). We present two tractable approaches to deal with the computational hardness. When the agents are presented with an initial allocation of houses, we aim to refine this allocation by reallocating a bounded number of houses to reduce the number of envious agents. We show an efficient algorithm when the agents express preference for a bounded number of houses. Next, we consider single peaked preference domain and present a polynomial time algorithm for finding an allocation that minimize the number of envious agents. We further extend it to satisfy Pareto efficiency. Our former algorithm works for other measures of envy such as total envy, or maximum envy, with suitable modifications. Finally, we present an empirical analysis recording the fairness-welfare trade-off of our algorithms.