In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons between candidates. We show that a widely-popular deterministic mechanism employed in most knockout phases yields distortion $\mathcal{O}(\log m)$ while eliciting only $m-1$ out of $Θ(m^2)$ possible pairwise comparisons, where $m$ represents the number of candidates. Our analysis for this mechanism leverages a powerful technical lemma recently developed by Kempe \cite{DBLP:conf/aaai/000120a}. We also provide a matching lower bound on its distortion. In contrast, we prove that any mechanism which performs fewer than $m-1$ pairwise comparisons is destined to have unbounded distortion. Moreover, we study the power of deterministic mechanisms under incomplete rankings. Most notably, when every agent provides her $k$-top preferences we show an upper bound of $6 m/k + 1$ on the distortion, for any $k \in \{1, 2, \dots, m\}$. Thus, we substantially improve over the previous bound of $12 m/k$ recently established by Kempe \cite{DBLP:conf/aaai/000120a,DBLP:conf/aaai/000120b}, and we come closer to matching the best-known lower bound. Finally, we are concerned with the sample complexity required to ensure near-optimal distortion with high probability. Our main contribution is to show that a random sample of $Θ(m/ε^2)$ voters suffices to guarantee distortion $3 + ε$ with high probability, for any sufficiently small $ε> 0$. This result is based on analyzing the sensitivity of the deterministic mechanism introduced by Gkatzelis, Halpern, and Shah \cite{DBLP:conf/focs/Gkatzelis0020}. Importantly, all of our sample-complexity bounds are distribution-independent.
Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）；University of British Columbia（不列颠哥伦比亚大学）；Tehran Institute for Advanced Studies (TeIAS), Khatam University（德黑兰高等研究院，哈塔姆大学）；Max Planck Institut für Informatik, Universität des Saarlandes（马克斯·普朗克计算机科学研究所，萨尔兰大学）
Georgia Institute of Technology（佐治亚理工学院）；Sharif University of Technology（谢里夫理工大学）；University of Edinburgh（爱丁堡大学）；Tehran Institute for Advanced Studies（德黑兰高等研究院）
Improved Metric Distortion Bounds for Deterministic Weighted-Tournament Voting Rules
University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Beijing Normal University-Zhuhai（北京师范大学珠海校区）；Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）
Metric Distortion of Social Choice Rules: Lower Bounds and Fairness Properties
我们在功利扭曲的框架下研究社会选择规则，并对代理人的成本进行了额外的度量假设。在这种方法中，这些成本由所有代理加上替代品的集合上的基础度量给出。社会选择规则只能获得代理人的顺序偏好，而不能获得导致它们的潜在基数成本。失真被定义为社会成本（通常是代理成本的总和）之间的比率选择的替代机制在手，并选择了最佳的替代由一个无所不知的算法。因此，社会选择规则在最坏情况下的扭曲，是衡量在不知道潜在成本的情况下，它总是接近最优选择的程度。在该模型下，已经证实，排名对，众所周知的加权锦标赛规则，达到了最多3的失真[Anshelevich et al. 2015]。我们通过构造一系列实例来证明这一猜想是错误的，这些实例表明排序对的最坏情况失真至少为5。我们对排名对的最坏情况失真的下限与Copeland规则的先前已知的上限相匹配，证明在最坏的情况下，更简单的Copeland规则至少与排名对一样好。只要我们受到（加权或未加权）锦标赛规则的限制，我们就证明随机化无法帮助实现小于3的预期最坏情况失真。在失真框架内使用近似优化的概念，我们证明了Copeland和随机独裁实现了较低的常数因子公平比（分别为5和3），这是对成本和单个最大成本目标的类似结果的相当大的推广。除了上述所有内容之外，我们还概述了该领域进一步研究的几个有趣方向。
Sensitivity and Differential Privacy in Metric Voting with Distortion below Three
CyberAgent, Tokyo, Japan（CyberAgent）；National Institute of Informatics, Tokyo, Japan（国立情报学研究所）；Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan（理化学研究所先进智能研究中心）；Kyoto University, Kyoto, Japan（京都大学）
