A General Framework for Fair Allocation under Matroid Rank Valuations

TL;DR

This paper introduces a versatile framework called General Yankee Swap for fair and efficient allocation of indivisible goods among agents with matroid rank valuations, optimizing various fairness criteria efficiently.

Contribution

It generalizes the Yankee Swap algorithm to efficiently compute allocations maximizing multiple fairness objectives under matroid rank valuations, including new polynomial algorithms for complex criteria.

Findings

Framework guarantees strategyproofness and social welfare maximization.

Provides the first polynomial algorithms for weighted leximin, Nash welfare, and p-mean welfare.

Efficiently computes fair allocations for five well-studied justice criteria.

Abstract

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.