Research proves EFX chore allocation impossible in key cases

Researchers from unspecified institutions (authors: Zehan Lin, Shengxin Liu, Biaoshuai Tao, Shengwei Zhou) have published a paper on arXiv proving that EFX allocations for chore division don't exist under certain conditions. The team constructed two counterexamples using an 18-agent, 53-chore gadget to demonstrate that complete EFX allocations cannot be guaranteed when agents have monotone cost functions with binary marginals.

The work addresses a fundamental question in fair division theory - how to fairly allocate indivisible resources (chores) when no perfect division exists. While similar problems for divisible goods have positive results, the researchers show that for chores with binary marginal costs (where each additional chore has either fixed or zero marginal cost), EFX allocations are impossible. Their results were formalized and verified using Lean 4, adding computational rigor to the theoretical findings.