Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness

TL;DR

This paper extends fair division principles to agents with matroid-rank valuations, demonstrating that weighted additive rules maintain monotonicity and strategyproofness, generalizing previous binary valuation results.

Contribution

It generalizes fairness and strategyproofness results from binary additive valuations to matroid-rank valuations under weighted additive rules.

Findings

Weighted additive rules are resource-, population-, and weight-monotone for matroid-rank valuations.

Group-strategyproofness is satisfied under these rules.

The results extend polynomial-time implementability to a broader class of valuations.

Abstract

We study the problem of fairly allocating indivisible goods to agents with weights corresponding to their entitlements. Previous work has shown that, when agents have binary additive valuations, the maximum weighted Nash welfare rule is resource-, population-, and weight-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. We generalize these results to the class of weighted additive welfarist rules with concave functions and agents with matroid-rank (also known as binary submodular) valuations.