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

2025-11-11

AI Summary

This paper investigates the joint optimization of fairness and social welfare maximization in indivisible item allocation. To overcome limitations of traditional selfish-agent models, it introduces the “socially-aware agent” paradigm, where each agent’s utility is a weighted sum of its private valuation and a social impact function. Theoretically, under full social awareness, allocations satisfying fairness criteria such as EF1 and proportionality while maximizing social welfare are computable in polynomial time; however, even mild relaxations—e.g., when only a subset of agents are socially aware—render the problem NP-hard. The authors design efficient algorithms tailored to diverse social-awareness structures and precisely characterize the trade-off between the degree of social awareness and computational complexity. This work establishes social awareness as a key structural condition that fundamentally alleviates the tension between fairness and efficiency—a novel insight not previously identified in fair division literature.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• The paper studies fair allocation of indivisible items while maximizing social impact.
• It analyzes computational complexity differences between socially aware and unaware agents.
• The research identifies tractable and intractable cases under varying fairness constraints.

Innovation

• Social impact maximization with indivisible item allocation
• Complexity analysis based on agent social awareness
• Polynomial-time algorithm for socially aware agents