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We study the relationship between fair division with $\textit{subsidies}$ and $\textit{best-of-both-worlds}$ (BoBW) fairness for indivisible items. We prove a general reduction of BoBW existence to envy-freeability. Specifically, for any scale-free ex-post property $P$ (e.g., EF1, EFX, PO) and any scale-free valuation...
Maximizing Nash welfare over indivisible goods is a central problem in resource allocation. For additive valuations, the best-known approximation factor is roughly $e^{-1/e}\approx0.692$, and the problem is APX-hard. We study Nash welfare maximization under lexicographic valuations, where every good is worth more than...
In approval-based committee voting, proportional approval voting (PAV) is a well-studied rule that combines proportional representation with Pareto efficiency. However, computing a PAV committee is NP-hard, raising a natural question: Can the proportionality and efficiency properties of PAV be achieved via computationa...
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