Aggregating the preferences of individuals into a collective decision is the core subject of study of social choice theory. In 2006, Procaccia and Rosenschein considered a utilitarian social choice setting, where the agents have explicit numerical values for the alternatives, yet they only report their linear orderings over them. To compare different aggregation mechanisms, Procaccia and Rosenschein introduced the notion of distortion, which quantifies the inefficiency of using only ordinal information when trying to maximize the social welfare, i.e., the sum of the underlying values of the agents for the chosen outcome. Since then, this research area has flourished and bounds on the distortion have been obtained for a wide variety of fundamental scenarios. However, the vast majority of the existing literature is focused on the case where nothing is known beyond the ordinal preferences of the agents over the alternatives. In this paper, we take a more expressive approach, and consider mechanisms that are allowed to further ask a few cardinal queries in order to gain partial access to the underlying values that the agents have for the alternatives. With this extra power, we design new deterministic mechanisms that achieve significantly improved distortion bounds and, in many cases, outperform the best-known randomized ordinal mechanisms. We paint an almost complete picture of the number of queries required by deterministic mechanisms to achieve specific distortion bounds.

将个人的偏好聚集到集体决策中是社会选择理论研究的核心主题。在2006年，Procaccia和Rosenschein考虑了功利主义的社会选择设置，其中代理人具有替代方案的明确数值，但他们只报告其线性顺序。为了比较不同的聚集机制，Procaccia和Rosenschein引入了失真的概念，当试图最大化社会福利时，量化仅使用序数信息的效率低下，即，对于所选结果而言，主体的基础价值之和。从那时起，这个研究领域蓬勃发展，并且在各种各样的基本情况下都获得了失真的界限。但是，现有文献中的绝大多数集中在这样的情况下，除了代理人对替代方案的优先选择之外，什么也一无所知。在本文中，我们采用一种更具表现力的方法，并考虑允许进一步询问一些基本查询的机制，以便部分访问代理所具有的替代方案的基础价值。有了这种额外的功能，我们可以设计新的确定性可以显着改善失真范围的机制，并且在许多情况下，其性能优于最著名的随机序数机制。我们对确定性机制实现特定失真范围所需的查询数量进行了几乎完整的描述。