Weighted Notions of Fairness with Binary Supermodular Chores
This work addresses fair allocation in multi-agent systems with specific cost structures, but it is incremental as it builds on existing techniques to generalize prior results.
The paper tackles the problem of fairly allocating indivisible chores among agents with binary supermodular cost functions, presenting a general framework that efficiently computes allocations satisfying weighted fairness notions such as weighted leximin or min weighted p-mean malfare for any p ≥ 1.
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 $p \ge 1$.