Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over outcomes that is leximin in expectation. Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces an outcome that is approximately-leximin (in expectation) - with the same approximation factor. We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.

翻译：社会选择中的两个重要目标是功利主义——最大化所有参与者效用之和，以及词典序最小公平——首先最大化最小效用参与者的效用，其次是第二小效用参与者，依此类推。功利主义目标通常在计算上更容易实现，但通常被认为公平性较低。本文提出一种通用归约方案，在给定功利主义求解器的条件下，能够生成词典序最小公平性期望下的结果分布。该方案具有鲁棒性的重要特征：给定近似功利主义求解器时，能够生成近似词典序最小公平（期望意义下）的结果——且保持相同的近似比。我们将该方案应用于多个社会选择问题：不可分物品的随机分配、赠品抽签机制以及参与式预算的公平抽签机制。