We consider the problem of allocating divisible items among multiple agents, and consider the setting where any agent is allowed to introduce diversity constraints on the items they are allocated. We motivate this via settings where the items themselves correspond to user ad slots or task workers with attributes such as race and gender on which the principal seeks to achieve demographic parity. We consider the following question: When an agent expresses diversity constraints into an allocation rule, is the allocation of other agents hurt significantly? If this happens, the cost of introducing such constraints is disproportionately borne by agents who do not benefit from diversity. We codify this via two desiderata capturing robustness. These are no negative externality -- other agents are not hurt -- and monotonicity -- the agent enforcing the constraint does not see a large increase in value. We show in a formal sense that the Nash Welfare rule that maximizes product of agent values is uniquely positioned to be robust when diversity constraints are introduced, while almost all other natural allocation rules fail this criterion. We also show that the guarantees achieved by Nash Welfare are nearly optimal within a widely studied class of allocation rules. We finally perform an empirical simulation on real-world data that models ad allocations to show that this gap between Nash Welfare and other rules persists in the wild.
翻译:我们考虑在多个代理商之间分配可分散的物品的问题,并考虑允许任何代理商对分配的物品实行多样性限制的设置。我们通过这样的设置来推动这一点,即这些物品本身与用户广告插座或具有种族和性别等属性的工作任务工人相对应,而主要目的是实现人口均等。我们考虑以下问题:当一个代理商将多样性限制纳入分配规则时,其他代理商的分配是否严重受损?如果发生这种情况,引入这些限制的成本由不从多样性中受益的代理商不成比例地承担;我们通过两个分层捕捉稳健性来编纂。这些都不是负面的外部性 -- -- 其他代理商没有受到伤害 -- -- 和单一性 -- -- 实施限制的代理商没有看到价值的大幅增长。我们从形式上表明,当引入多样性限制时,将代理商价值产品最大化的纳什福利规则具有独特优势,而几乎所有其他自然分配规则都不符合这一标准。我们还表明,纳什福利公司获得的保障在广泛研究的分配规则中几乎是最佳的。我们最后对现实世界数据进行了实验性模拟,模型分配规则表明,在野生标准中始终存在这种差距。