We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative for each district based on a local election with the agents therein as participants, and then chooses one of the district representatives as the winner. Previous work showed bounds on the distortion of a specific class of deterministic plurality-based mechanisms depending on the available information about the preferences of the agents in the districts. In this paper, we first consider the whole class of deterministic mechanisms and show asymptotically tight bounds on their distortion. We then initiate the study of the distortion of randomized mechanisms in distributed voting and show bounds based on several informational assumptions, which in many cases turn out to be tight. Finally, we also experimentally compare the distortion of many different mechanisms of interest using synthetic and real-world data.

我们考虑这样一种设置，其中的代理对替代方案有偏好，并且被划分为不相交的区域。其目标是通过一种机制选择一个替代方案作为获胜者，该机制首先根据地方选举确定每个区的代表性替代方案，其中代理人作为参与者，然后选择一名区代表作为获胜者。先前的工作表明，根据有关地区代理人偏好的可用信息，特定类别的基于确定性多数的机制的扭曲是有限度的。在本文中，我们首先考虑整类确定性机制，并显示其失真的渐近严格界限。然后，我们开始研究分布式投票中随机机制的扭曲，并根据几个信息假设显示界限，这些假设在许多情况下都是严格的。最后，我们还使用合成数据和真实世界数据通过实验比较了许多不同感兴趣机制的失真。