论文标题
关于赋予相交小组公平份额的分配
On allocations that give intersecting groups their fair share
论文作者
论文摘要
我们考虑对具有加性估值的个体代理商的项目分配，在有保护组的设置中，分配需要给每个受保护的群体在整体福利中的“公平”份额。非正式地，在每个受保护的群体中，我们考虑分配给组成员的总福利，并将其与分配可以给小组成员提供的最大可能的福利进行比较。如果这两个值之间的比率比组的相对大小差，则分配对组是公平的。对于可划分的项目，我们对公平性的正式定义是基于比例份额的，而对于不可分割的项目，它基于Anyrice份额。 我们介绍了没有公平分配的示例，甚至不是分配近似于恒定乘法因子内的公平要求。然后，我们尝试确定足够的条件，以实现公平或近似公平的分配。例如，对于不可分割的项目，当代理具有相同的估值并且受保护群体的家族是层流时，我们表明，如果这些物品是琐事，那么满足在乘法中满足所有公平因素的分配就不得差于两个，并且可以有效地发现，而如果物品是商品，则不能保证不断的近似值。
We consider item allocation to individual agents who have additive valuations, in settings in which there are protected groups, and the allocation needs to give each protected group its "fair" share of the total welfare. Informally, within each protected group we consider the total welfare that the allocation gives the members of the group, and compare it to the maximum possible welfare that an allocation can give to the group members. An allocation is fair towards the group if the ratio between these two values is no worse then the relative size of the group. For divisible items, our formal definition of fairness is based on the proportional share, whereas for indivisible items, it is based on the anyprice share. We present examples in which there are no fair allocations, and even not allocations that approximate the fairness requirement within a constant multiplicative factor. We then attempt to identify sufficient conditions for fair or approximately fair allocations to exist. For example, for indivisible items, when agents have identical valuations and the family of protected groups is laminar, we show that if the items are chores, then an allocation that satisfies every fairness requirement within a multiplicative factor no worse than two exists and can be found efficiently, whereas if the items are goods, no constant approximation can be guaranteed.
