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：我们研究了在一组具有拟阵秩估值的智能体之间公平分配不可分割物品的问题——每个物品在加入一个束时提供边际价值为$0$或$1$，且估值是子模的。我们将Yankee Swap算法推广为一种简单框架，称为通用Yankee Swap（General Yankee Swap），该框架能够高效计算任何满足温和假设的正义准则（或公平目标）最大化的分配。除了最大化正义准则外，通用Yankee Swap还能保证最大化功利主义社会福利、确保策略证明性，并且最多使用二次数量的估值查询。我们展示了如何利用通用Yankee Swap来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) 最大最小公平、(c) 加权词典序最大最小、(d) 最大加权纳什福利，以及(e) 最大加权$p$均值福利。特别地，我们的框架首次提供了多项式时间算法，用于在具有拟阵秩估值的智能体之间计算加权词典序最大最小、最大加权纳什福利和最大加权$p$均值福利分配。