论文标题
在不可分割的琐事中分配雷克西蛋白的公平性
The Fairness of Leximin in Allocation of Indivisible Chores
论文作者
论文摘要
众所周知，在分配不可分割的商品时，在某些情况下，在某些情况下，选择了最大化最小效用的分配，从而选择了最大化最小效用，然后是第二个最低效用等分配。但是，当用来分配不可分割的琐事时，词汇溶液是多么公平。在本文中，我们证明可以修改词汇溶液，还为不可分割的琐事提供了令人信服的公平保证。首先，我们概括了词汇溶液的定义。然后，我们表明，在综合分配的背景下，溶血蛋白解决方案找到了3或4个代理的Prop1（最高比例）和PO（帕累托最佳）分配，并具有添加剂不同的估值。此外，我们证明了词汇解决方案是EFX，用于具有一般但相同估值的代理商的商品和杂务的组合。
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.
