Multiwinner voting captures a wide variety of settings, from parliamentary elections in democratic systems to product placement in online shopping platforms. There is a large body of work dealing with axiomatic characterizations, computational complexity, and algorithmic analysis of multiwinner voting rules. Although many challenges remain, significant progress has been made in showing existence of fair and representative outcomes as well as efficient algorithmic solutions for many commonly studied settings. However, much of this work focuses on single-shot elections, even though in numerous real-world settings elections are held periodically and repeatedly. Hence, it is imperative to extend the study of multiwinner voting to temporal settings. Recently, there have been several efforts to address this challenge. However, these works are difficult to compare, as they model multi-period voting in very different ways. We propose a unified framework for studying temporal fairness in this domain, drawing connections with various existing bodies of work, and consolidating them within a general framework. We also identify gaps in existing literature, outline multiple opportunities for future work, and put forward a vision for the future of multiwinner voting in temporal settings.

翻译：多赢者投票涵盖了从民主制度中的议会选举到在线购物平台的商品投放等多种场景。已有大量研究涉及多赢者投票规则的公理刻画、计算复杂性和算法分析。尽管仍面临诸多挑战，但在许多常见场景中，公平且具有代表性的结果的存在性以及高效算法解决方案已取得重要进展。然而，这些研究大多聚焦于单次选举，而现实世界中许多场景的选举是定期重复进行的。因此，将多赢者投票研究拓展到时间维度势在必行。近年来已有若干工作尝试应对这一挑战，但这些研究因对多期选举的建模方式迥异而难以比较。我们提出了一个统一框架来研究该领域的时间公平性，该框架与现有多个研究方向建立联系，并将其整合到通用体系之中。此外，我们识别了现有文献中的空白，勾勒出未来研究的多个机遇，并展望了时间场景下多赢者投票的发展前景。