For every n≥4 there are tri-valued additive chore instances with no EFX allocation, bi-valued instances where every EFX allocation fails Pareto optimality, and EFX is guaranteed for four bi-valued agents.
The fairness of leximin in allocation of indivisible chores.arXiv preprint arXiv:2005.04864,
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EFX for Additive Chores: Nonexistence, Pareto Incompatibility, and Bi-Valued Existence
For every n≥4 there are tri-valued additive chore instances with no EFX allocation, bi-valued instances where every EFX allocation fails Pareto optimality, and EFX is guaranteed for four bi-valued agents.