Proportional and Pareto-Optimal Allocation of Chores with Subsidy

We consider the problem of allocating m indivisible chores among n agents with possibly different weights, aiming for a solution that is both fair and efficient. Specifically, we focus on the classic fairness notion of proportionality and efficiency notion of Pareto-optimality. Since proportional allocations may not always exist in this setting, we allow the use of subsidies (monetary compensation to agents) to ensure agents are proportionally-satisfied, and aim to minimize the total subsidy required. Wu and Zhou (WINE 2024) showed that when each chore has disutility at most 1, a total subsidy of at most n/3 - 1/6 is sufficient to guarantee proportionality. However, their approach is based on a complex technique, which does not guarantee economic efficiency -- a key desideratum in fair division.