  The leximin solution -- which selects an allocation that maximizes the
minimum utility, then the second minimum utility, and so forth -- is known to
provide EFX (envy-free up to any good) fairness guarantee in some contexts when
allocating indivisible goods. However, it remains unknown how fair the leximin
solution is when used to allocate indivisible chores. In this paper, we
demonstrate that the leximin solution can be modified to also provide
compelling fairness guarantees for the allocation of indivisible chores. First,
we generalize the definition of the leximin solution. Then, we show that the
leximin solution finds a PROP1 (proportional up to one good) and PO
(Pareto-optimal) allocation for 3 or 4 agents in the context of chores
allocation with additive distinct valuations. Additionally, we prove that the
leximin solution is EFX for combinations of goods and chores for agents with
general but identical valuations.
