We study the problem of allocating indivisible chores among agents with binary supermodular cost functions. In other words, each chore has a marginal cost of $0$ or $1$ and chores exhibit increasing marginal costs (or decreasing marginal utilities). In this note, we combine the techniques of Viswanathan and Zick (2022) and Barman et al. (2023) to present a general framework for fair allocation with this class of valuation functions. Our framework allows us to generalize the results of Barman et al. (2023) and efficiently compute allocations which satisfy weighted notions of fairness like weighted leximin or min weighted $p$-mean malfare for any $p \ge 1$.

翻译：我们研究了将不可分割家务分配给具有二元超模成本函数的智能体的问题。换言之，每项家务的边际成本为$0$或$1$，且家务呈现递增的边际成本（或递减的边际效用）。在本笔记中，我们结合Viswanathan和Zick (2022)以及Barman等人 (2023)的技术，提出了一类适用于此类估值函数的公平分配通用框架。我们的框架能够推广Barman等人 (2023)的结果，并有效计算出满足带权公平性概念（如带权leximin或任意$p \ge 1$的最小化带权$p$均值危害函数）的分配方案。