We study one-sided matching problems where $n$ agents have preferences over $m$ objects and each of them need to be assigned to at most one object. Most work on such problems assume that the agents only have ordinal preferences and usually the goal in them is to compute a matching that satisfies some notion of economic efficiency. However, in reality, agents may have some preference intensities or cardinal utilities that, e.g., indicate that they like an an object much more than another object, and not taking these into account can result in a loss in welfare. While one way to potentially account for these is to directly ask the agents for this information, such an elicitation process is cognitively demanding. Therefore, we focus on learning more about their cardinal preferences using simple threshold queries which ask an agent if they value an object greater than a certain value, and use this in turn to come up with algorithms that produce a matching that, for a particular economic notion $X$, satisfies $X$ and also achieves a good approximation to the optimal welfare among all matchings that satisfy $X$. We focus on several notions of economic efficiency, and look at both adaptive and non-adaptive algorithms. Overall, our results show how one can improve welfare by even non-adaptively asking the agents for just one bit of extra information per object.

翻译：我们研究的是一面匹配问题,即美元代理人的偏好大于百万美元对象,而每个代理人都需要分配到最多一个对象。关于这些问题的多数工作假设,代理人只具有正统偏好,通常目的是计算出符合某种经济效率概念的匹配。然而,实际上,代理人可能有一些偏好强度或基本公用事业,例如,表明他们喜欢一个对象比另一个对象要多得多,而没有考虑到这些好处可能会造成福利损失。尽管可能考虑这些好处的一个方法就是直接要求代理人提供这一信息,但这种启发过程在认知上要求很高。因此,我们侧重于更多地了解他们的主要偏好,使用简单的门槛查询,即询问代理人是否认为一个对象的价值大于一定价值,然后用这种方法得出一种匹配的算法,例如,他们喜欢一个对象比另一个对象更像另一个对象,即X美元,能够满足美元,并且能够使所有符合X美元的最佳福利。我们侧重于几个经济效率概念的概念,甚至看一种不适应性、不适应性、不适应性、不适应性、不适应性、不适应性、不要求一种全面、不适应性的方法。