Fair Division with Social Impact

TL;DR

This paper studies fair division of indivisible goods considering social impact, introducing impact valuations and analyzing the trade-offs between fairness and societal welfare, with new impossibility results and fairness notions for socially aware agents.

Contribution

It introduces impact valuations for social impact in fair division, provides impossibility results for approximation, and proposes fairness notions for socially aware agents.

Findings

Achieving better than linear approximation is impossible under fairness constraints.

Agents' unawareness of social impact leads to fundamental limitations.

Socially aware fairness notions can align individual fairness with social welfare maximization.

Abstract

In this paper, we consider the problem of fair division of indivisible goods when the allocation of goods impacts society. Specifically, we introduce a second valuation function for each agent, determining the social impact of allocating a good to the agent. Such impact is considered desirable for the society -- the higher, the better. Our goal is to understand how to allocate goods fairly from the agents' perspective while maintaining society as happy as possible. To this end, we measure the impact on society using the utilitarian social welfare and provide both possibility and impossibility results. Our findings reveal that achieving good approximations, better than linear in the number of agents, is not possible while ensuring fairness to the agents. These impossibility results can be attributed to the fact that agents are completely unconscious of their social impact. Consequently, we explore scenarios where agents are socially aware, by introducing related fairness notions, and demonstrate that an appropriate definition of fairness aligns with the goal of maximizing the social objective.