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，具有非正估值（即杂务）的不可分割任务的公平分配问题引起了大量研究。一种流行的近似公平性概念是"至多一项物品的嫉妒无妒性"（EF1），该概念要求任何成对嫉妒可通过移除单一物品来消除。尽管存在可计算且帕累托最优的EF1物品分配方案已通过多种经典算法得到证明，但杂务情况下此类解的存在性至今仍悬而未决。我们采用认知主义方法，通过引入"可疑杂务"（即接收方无成本但被他人视为昂贵的物品）来利用信息不对称性。在技术层面，与EF1等松弛方案相比，可疑杂务实现了更精细的嫉妒无妒性近似，从而推动解决关于EF1与帕累托最优分配的存在性及计算性等开放问题。特别地，我们证明即使在高度受限的估值类别中，寻找具有最优数量可疑杂务的分配方案在计算上仍是困难的。尽管如此，我们证明了对于$n$个智能体，存在仅需$2n-2$个可疑杂务的嫉妒无妒且帕累托最优分配，并在四类特殊估值情境中进一步将其强化至$n-1$个可疑杂务。实验分析表明，基线算法在实践中仅需相对少量可疑杂务即可实现嫉妒无妒性。