The concept of ranking aggregation plays a central role in preference analysis, and numerous algorithms for calculating median rankings, often originating in social choice theory, have been documented in the literature, offering theoretical guarantees in a centralized setting, \textit{i.e.}, when all the ranking data to be aggregated can be brought together in a single computing unit. For many technologies (\textit{e.g.} peer-to-peer networks, IoT, multi-agent systems), extending the ability to calculate consensus rankings with guarantees of convergence and resilience to potential contamination in a decentralized setting, when preference data is initially distributed across a communicating network, remains a major methodological challenge. Indeed, in recent years, the literature on decentralized computation has mainly focused on computing or optimizing statistics such as arithmetic means using gossip algorithms. The purpose of this article is precisely to study how to achieve reliable and resilient consensus on collective rankings in a decentralized setting, thereby raising new questions, robustness to corrupted nodes, and scalability through reduced communication costs in particular. The approach proposed and analyzed here relies on the robustness guarantees offered by random gossip communication, which allows autonomous agents to compute a global ranking consensus using local interactions only, without coordination or a central authority.

翻译：排名聚合的概念在偏好分析中占据核心地位，大量源于社会选择理论的中位数排名估计算法已在文献中得到记载，这些算法在集中式环境下（即所有待聚合的排名数据可汇集至单一计算单元）提供了理论保障。然而，对于诸多技术场景（如对等网络、物联网、多智能体系统），在偏好数据初始分散于通信网络的去中心化环境中，仍面临如何实现具有收敛保证且能够抵抗潜在污染的共识排名的重大方法论挑战。事实上，近年来关于去中心化计算的研究主要集中于利用Gossip协议计算或优化算术均值等统计量。本文旨在研究如何在去中心化环境下实现可靠且鲁棒的集体排名共识，这引发了新的研究问题，特别是针对受损节点的鲁棒性，以及通过降低通信开销实现的可扩展性。本文提出并分析的方法依赖于随机Gossip通信提供的鲁棒性保证，该方法使自主智能体仅通过局部交互即可计算全局排名共识，无需协调或中央权威机构。