We consider a distributed voting problem with a set of agents that are partitioned into disjoint groups and a set of obnoxious alternatives. Agents and alternatives are represented by points in a metric space. The goal is to compute the alternative that maximizes the total distance from all agents using a two-step mechanism which, given some information about the distances between agents and alternatives, first chooses a representative alternative for each group of agents, and then declares one of them as the overall winner. Due to the restricted nature of the mechanism and the potentially limited information it has to make its decision, it might not be always possible to choose the optimal alternative. We show tight bounds on the distortion of different mechanisms depending on the amount of the information they have access to; in particular, we study full-information and ordinal mechanisms.

翻译：我们研究一个分布式投票问题，其中智能体被划分为不相交的组，并存在一组厌恶型备选方案。智能体与备选方案均由度量空间中的点表示。目标是通过一个两步机制，在给定智能体与备选方案间距离的某些信息后，首先为每组智能体选择一个代表性备选方案，然后从中宣布一个整体获胜者，以最大化所有智能体到该方案的总距离。由于机制本身的限制性及其决策时可能仅掌握有限信息，选择最优备选方案并非总能实现。我们根据机制可获取的信息量，给出了不同机制扭曲度的紧界；特别地，我们研究了全信息机制与序数信息机制。