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 to achieve specific distortion bounds.

中文翻译：

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窥探有序幕后：通过基数查询改善失真

将个人的偏好聚合为集体决策是社会选择理论研究的核心课题。2006 年，Procaccia 和 Rosenschein 考虑了一种功利主义的社会选择设置，其中代理有明确的替代方案数值，但他们只报告他们对它们的线性排序。为了比较不同的聚合机制，Procaccia 和 Rosenschein 引入了失真的概念，该概念量化了在尝试最大化社会福利时仅使用有序信息的低效率，即代理对所选结果的潜在价值的总和。从那时起，这个研究领域蓬勃发展，并且已经为各种基本场景获得了失真的界限。然而，绝大多数现有文献都集中在除了代理对替代方案的顺序偏好之外一无所知的情况。在本文中，我们采用更具表现力的方法，并考虑允许进一步询问一些基本查询的机制，以便部分访问代理对替代方案的潜在价值。凭借这种额外的能力，我们设计了新的确定性机制，可显着改善失真界限，并且在许多情况下，其性能优于最著名的随机有序机制。我们描绘了实现特定失真边界所需的查询数量的几乎完整图片。并考虑允许进一步询问一些基本查询的机制，以便部分访问代理对替代方案的潜在价值。凭借这种额外的能力，我们设计了新的确定性机制，可显着改善失真界限，并且在许多情况下，其性能优于最著名的随机序数机制。我们描绘了实现特定失真边界所需的查询数量的几乎完整图片。并考虑允许进一步询问一些基本查询的机制，以便部分访问代理对替代方案的潜在价值。凭借这种额外的能力，我们设计了新的确定性机制，可显着改善失真界限，并且在许多情况下，其性能优于最著名的随机序数机制。我们描绘了实现特定失真边界所需的查询数量的几乎完整图片。