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:我们研究了在具有二元超模式成本功能的代理商之间分配不可分割的家务的问题,换句话说,每份杂务的边际成本为0美元或1美元,而杂务的边际成本(或边际公用事业的边际成本)增加(或下降),在本说明中,我们结合了维斯瓦纳坦和齐克(2022年)和巴曼等人(2023年)的技术,以提出与这类估值功能进行公平分配的一般框架。我们的框架使我们能够推广Barman等人(2023年)的结果,并有效地计算出拨款,这些拨款满足了加权的公平概念,如加权法理学概念或加权价为1美元或1美元以上。</s>