Dividing Indivisible Items for the Benefit of All: It is Hard to Be Fair Without Social Awareness

TL;DR

This paper explores fair division of indivisible items considering social impact, revealing that social awareness influences the computational complexity of achieving fair and socially beneficial allocations.

Contribution

It introduces a model incorporating social impact into fair division, analyzing how social awareness affects the complexity and tractability of finding fair, impactful allocations.

Findings

NP-hardness for socially unaware agents under various fairness notions

Polynomial-time algorithms for socially aware agents with certain restrictions

Intractability re-emerges when social awareness is relaxed

Abstract

In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items that, at the same time, maximize social impact. In this model, each agent is associated with two additive functions that define their value and social impact for each item. The goal is to allocate items so that the social impact is maximized while maintaining some fairness criterion. We reveal that the complexity of the problem heavily depends on whether the agents are socially aware, i.e., they take into consideration the social impact functions. For socially unaware agents, we prove that the problem is NP-hard for a variety of fairness notions, and that it is tractable only for very restricted cases, e.g., if, for every agent, the valuation equals social impact and it is binary. On the other hand, social awareness allows for fair allocations that maximize social impact, and such allocations can be computed in polynomial time. Interestingly, the problem becomes again intractable as soon as the definition of social awareness is relaxed.