Fair distribution of indivisible tasks with non-positive valuations (aka chores) has given rise to a large body of work in recent years. A popular approximate fairness notion is envy-freeness up to one item (EF1), which requires that any pairwise envy can be eliminated by the removal of a single item. While an EF1 and Pareto optimal (PO) allocation of goods always exists and can be computed via several well-known algorithms, even the existence of such solutions for chores remains open, to date. We take an epistemic approach utilizing information asymmetry by introducing dubious chores -- items that inflict no cost on receiving agents, but are perceived costly by others. On a technical level, dubious chores provide a more fine-grained approximation of envy-freeness -- compared to relaxations such as EF1 -- which enables progress towards addressing open problems on the existence and computation of EF1 and PO. In particular, we show that finding allocations with optimal number of dubious chores is computationally hard even for highly restricted classes of valuations. Nonetheless, we prove the existence of envy-free and PO allocations for $n$ agents with only $2n-2$ dubious chores and strengthen it to $n-1$ dubious chores in four special classes of valuations. Our experimental analysis demonstrate that baseline algorithms only require a relatively small number of dubious chores to achieve envy-freeness in practice.

翻译：近年来，对具有非正估值（即家务）的不可分割任务的公平分配引发了大量研究。一种流行的近似公平概念是至多一项物品的无嫉妒性（EF1），它要求任何成对嫉妒均可通过移除单个物品来消除。尽管商品领域的EF1与帕累托最优（PO）分配始终存在且可通过多种经典算法计算，但此类解在家务领域的存在性至今仍是开放问题。我们通过引入可疑家务（对接收主体无成本、但被他人视为有成本的项目）来构建一种利用信息不对称的认知方法。在技术层面，与EF1等松弛概念相比，可疑家务提供了更细粒度的无嫉妒近似，从而推动解决EF1与PO存在性及计算性的开放问题。具体而言，我们证明即使对高度受限的估值类别，寻找具有最优数量可疑家务的分配在计算上仍具有难度。尽管如此，我们证明了对于包含$n$个主体的情形，仅需$2n-2$项可疑家务即可实现无嫉妒与PO分配，并在四类特殊估值场景中将其强化至$n-1$项。实验分析表明，基线算法在实践中仅需相对少量的可疑家务即可达成无嫉妒性。