arXiv subjects

Satyanand Rammohan

Publications and source records attributed to Satyanand Rammohan.

3 recordsLinked to original sources

arXiv2026

Efficient and Envy-free Random Assignment Beyond Expected Utility

We consider the random assignment problem with abstract continuous and convex preferences. In particular, we admit preference relations that are not constrained by independence or transitivity. By extending the Hylland--Zeckhauser pseudo-market mechanism, we show that weakly efficient and envy-free random assignments always exist. For preferences that can be represented via skew-symmetric bilinear (SSB) utility functions -- which generalize linear expected utility functions -- we prove the existence of efficient and approximately envy-free random assignments. Efficient and envy-free random assignments exist under a mild additional assumption on preferences. These findings have notable implications for ordinal random assignment, where ordinal preferences are extended to preferences over lotteries via the pairwise comparison (PC) extension. While the probabilistic serial rule and popular random assignments frequently and significantly violate PC-efficiency and PC-envy-freeness, respectively, random assignments that satisfy both conditions do exist.

econ.TH↗

arXiv2026

Fair Division via Resource Augmentation

We introduce and formalize the notion of resource augmentation for maximin share (MMS) fairness for the allocation of indivisible goods. Given an instance with $n$ agents and $m$ goods, we ask how many copies of the goods should be added in order to guarantee that each agent receives at least their original MMS value, or a meaningful approximation thereof. For general monotone valuations, we establish a tight bound: an exact MMS allocation can be guaranteed using at most $Θ(m/e)$ total copies, and this bound is tight even for XOS valuations. We further show that it is unavoidable to duplicate some goods $Ω(\ln m / \ln \ln m)$ times, and provide matching upper bounds. For additive valuations, we show that at most $\min\{n-2,\lfloor\frac{m}{3}\rfloor(1+o(1))\}$ distinct copies suffice. This separates additive valuations from submodular valuations, for which we show that $n-1$ copies may be necessary. We also study approximate MMS guarantees for additive valuations and establish new tradeoffs between the number of copies needed and the approximation guaratee. In particular, we prove that $\lfloor{n/2}\rfloor$ copies suffice to guarantee a $6/7$-approximation to the original MMS, and $\lfloor{n/3}\rfloor$ copies suffice for a $4/5$-approximation. Both results improve upon the best-known approximation guarantees for additive valuations in the absence of copies. Finally, we relate MMS with copies to the relaxed notion of 1-out-of-$d$ MMS, showing that improvements in either framework translate directly to the other. In particular, we establish the first impossibility results for 1-out-of-$d$ MMS. Our results highlight the power and limits of resource augmentation for achieving MMS fairness.

cs.GT↗

arXiv2025

Exact Maximin Share Fairness via Adjusted Supply

This work addresses fair allocation of indivisible items in settings wherein it is feasible to create copies of resources or dispose of tasks. We establish that exact maximin share (MMS) fairness can be achieved via limited duplication of goods even under monotone valuations. We also show that, when allocating chores under monotone costs, MMS fairness is always feasible with limited disposal of chores. Since monotone valuations do not admit any nontrivial approximation guarantees for MMS, our results highlight that such barriers can be circumvented by post facto adjustments in the supply of the items. We prove that, for division of $m$ goods among $n$ agents with monotone valuations, there always exists an assignment of subsets of goods to the agents such that they receive at least their maximin shares and no single good is allocated to more than $3 \log m$ agents. In addition, the sum of the sizes of the assigned subsets does not exceed $m$. For identically ordered valuations, we obtain an upper bound of $O(\sqrt{\log m})$ on the maximum assignment multiplicity across goods and an $m + \widetilde{O}\left(\frac{m}{\sqrt{n}} \right)$ bound for the total number of goods assigned. Further, for additive valuations, we prove that there always exists an MMS assignment in which no single good is allocated to more than $2$ agents and the total number of goods assigned is at most $2m$. For chores, we upper bound the number of chores that need to be discarded for ensuring MMS fairness. We prove that, under monotone costs, there exists an MMS assignment in which at most $\frac{m}{e}$ remain unassigned. For identically ordered costs, we establish that MMS fairness can be achieved while keeping at most $\widetilde{O} \left(\frac{m}{n^{1/4}} \right)$ chores unassigned. We also prove that the obtained bounds for monotone valuations and monotone costs are essentially tight.

cs.GT↗