We study the problem of fairly allocating a set of indivisible goods among agents with matroid rank valuations -- every good provides a marginal value of $0$ or $1$ when added to a bundle and valuations are submodular. We generalize the Yankee Swap algorithm to create a simple framework, called General Yankee Swap, that can efficiently compute allocations that maximize any justice criterion (or fairness objective) satisfying some mild assumptions. Along with maximizing a justice criterion, General Yankee Swap is guaranteed to maximize utilitarian social welfare, ensure strategyproofness and use at most a quadratic number of valuation queries. We show how General Yankee Swap can be used to compute allocations for five different well-studied justice criteria: (a) Prioritized Lorenz dominance, (b) Maximin fairness, (c) Weighted leximin, (d) Max weighted Nash welfare, and (e) Max weighted $p$-mean welfare. In particular, our framework provides the first polynomial time algorithms to compute weighted leximin, max weighted Nash welfare and max weighted $p$-mean welfare allocations for agents with matroid rank valuations.

翻译：我们研究了在具有拟阵秩估值的智能体之间公平分配一组不可分割物品的问题——每件物品在加入一个组合时提供0或1的边际价值，且估值是次模的。我们将Yankee Swap算法推广，构建了一个称为General Yankee Swap的简单框架，该框架能够高效计算满足某些温和假设的任何正义准则（或公平目标）最大化的分配。除了最大化正义准则外，General Yankee Swap还能保证最大化功利社会福利、确保策略证明性，并且最多使用二次数量的估值查询。我们展示了General Yankee Swap如何用于计算五种不同且被广泛研究的正义准则下的分配：(a) 优先洛伦兹支配、(b) 极大极小公平性、(c) 加权词典最小化、(d) 最大加权纳什福利，以及(e) 最大加权p均值福利。特别地，我们的框架首次提出了多项式时间算法，用于计算具有拟阵秩估值的智能体在加权词典最小化、最大加权纳什福利和最大加权p均值福利准则下的分配。