Revisiting EFX and fPO Allocations for Binary Chores

RESUMO

We study fair and efficient allocations of indivisible chores under binary additive costs, with a focus on unequal entitlements and best-of-both-worlds guarantees. While binary valuations have been extensively studied for goods, their chore counterpart remains much less understood. A notable exception is due to Tao et al. (TCS 2025), who established that EFX and fPO are compatible for binary chores with equal entitlements. We revisit binary chores under unequal entitlements and establish the computation of allocations that satisfy WEFX and fPO. Our key technical contribution is a new lexicographic potential function tailored to chores: any allocation minimizing this potential ensures both WEFX and fPO. This potential further guides a polynomial-time local-search algorithm for computing allocations with such fairness and efficiency guarantees. For best-of-both-worlds guarantees, we show that unequal entitlements create a sharp obstruction: even with two agents and identical binary additive costs, no lottery can simultaneously satisfy ex-ante WEF and ex-post WEF1. In contrast, for equal entitlements, we construct in polynomial time a lottery that is ex-ante EF and fPO, while every realization is both EFX and fPO.