Thinned Quantile Shares are Universally Feasible

A trio of researchers – Vishesh Jain (UIUC), Clayton Mizgerd (MIT), and Shyam Ravichandran (Harvard) – have cracked a key problem in fair division theory. Quantile shares, introduced by Babichenko et al. (STOC 2024), provide an ordinal, self-maximizing benchmark for splitting indivisible goods, but their universal feasibility was only known conditionally on the rainbow Erdős matching conjecture (EMC). The new work introduces a one-parameter refinement: the c-thinned quantile share, which “thins” the inclusion probability in the random benchmark bundle by factor c ∈ (0,1]. The team proves that for some universal constant c > 0, the c-thinned e^{-c}-quantile share is unconditionally universally feasible – no conjecture required. This is the best possible, as any q > e^{-c} can be infeasible.

Beyond this unconditional result, the thinning lens also improves the conditional guarantee for the original quantile share: assuming the rainbow EMC, the (1/e)-quantile share (not (1/2e) as previously known) is universally feasible, removing a factor‑two loss. The paper thus provides the first unconditional universal feasibility result beyond Feige's residual maximin share, and tightens the conditional bound to the natural threshold. For practical fair‑division algorithms, this means stronger worst‑case guarantees without relying on unproven conjectures – a significant step for resource allocation in AI, economics, and multi‑agent systems.