We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of $K$ items that maximize the total derived utility of all the agents (i.e., in our example we are to pick $K$ movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among available ones (in the movie example, the perceived value of a movie depends on the values of the other ones available). Extreme examples of our model include the setting where each agent derives utility from his or her most preferred item only (e.g., an agent will watch his or her favorite movie only), from his or her least preferred item only (e.g., the agent worries that he or she will be somehow forced to watch the worst available movie), or derives $1/K$ of the utility from each of the available items (e.g., the agent will pick a movie at random). Formally, to model this process of adjusting the derived utility, we use the mechanism of ordered weighted average (OWA) operators. Our contribution is twofold: First, we provide a formal specification of the model and provide concrete examples and settings where particular OWA operators are applicable. Second, we show that, in general, our problem is NP-hard but---depending on the OWA operator and the nature of agents' utilities---there exist good, efficient approximation algorithms (sometimes even polynomial time approximation schemes). Interestingly, our results generalize and build upon those for proportional represented in multiwinner voting scenarios.

本文研究一个将物品和代理人联系起来的问题，即在代理人对物品有固定的内在效用的情况下，如何以一定的规则选择物品，以便最大化所有代理人共同获得的总效用。虽然实际效用只是内在效用的一部分，但该效用率取决于代理人对选择物品的排名，我们提供了一个形式化的模型规范，并给出了具体的适用范例及其自然特例的可行性结果。

寻找一组共同的物品：从比例多重表示到团体推荐