Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been significant progress towards this goal, all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a setting in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the final outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.

中文翻译：

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分布式投票的扭曲

投票可以对任何决策场景进行抽象建模，因此几十年来对其进行了广泛的研究。最近，相关文献通过限制投票规则的扭曲来量化投票过程中仅利用有限信息对结果的社会福利的影响。尽管朝着这个目标取得了重大进展，但迄今为止所有的工作都忽略了这样一个事实，即在许多情况下（如总统选举）投票实际上是一个分布式程序。在本文中，我们考虑一种设置，其中选民被划分为不相交的地区并在其中进行本地投票，以使用投票规则选出本地获胜的备选方案；然后从这些备选方案集中选择最终结果。我们证明了从最坏情况和最好情况的角度来看，这种分布式选举的众所周知的投票规则的扭曲是严格的。我们的结果表明，将选民划分为地区会导致相当大的失真，我们还使用真实世界的数据通过实验展示了这一现象。