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.

翻译：在经典的公平分配模型中，我们通常假设所有参与主体均为自利个体。然而，在许多实际场景中，资源分配会直接影响整个群体乃至社会的福祉。因此，本研究探讨在最大化社会效益的同时实现不可分物品的公平分配机制。在此模型中，每个主体对应两个加性函数，分别定义其对每件物品的个人价值评估与社会效益贡献。研究目标是在满足特定公平准则的前提下，通过物品分配实现社会效益最大化。我们发现问题的计算复杂度高度取决于主体是否具有社会意识——即是否将社会效益函数纳入决策考量。对于缺乏社会意识的主体，我们证明该问题在多种公平性定义下均属于NP难问题，仅在某些极端受限情况下（例如当每个主体的价值评估与社会效益函数完全一致且为二元取值时）才具有可解性。反之，具有社会意识的主体能够实现社会效益最大化的公平分配，且此类分配方案可在多项式时间内计算得出。值得注意的是，一旦放宽社会意识的定义约束，该问题将重新转化为难解问题。