Decentralized Ranking Aggregation: Gossip Algorithms for Borda and Copeland Consensus

2026-02-26

AI Summary

This work addresses the challenge of reliably aggregating distributed preferences through local interactions to achieve global ranking consensus in decentralized networks such as peer-to-peer systems, IoT, or multi-agent systems. The authors propose a decentralized algorithm based on randomized gossip communication that, for the first time, provides explicit convergence rates for Borda and Copeland voting rules, and further extends to median ranking and locally Kemenized rankings. The method operates without central coordination, offering robustness against malicious nodes while maintaining communication efficiency. Experimental results demonstrate that the algorithm rapidly and accurately converges to the correct ranking across diverse network topologies and both real-world and synthetic datasets.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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, i.e., when all the ranking data to be aggregated can be brought together in a single computing unit. For many technologies (e.g. peer-to-peer networks, IoT, multi-agent systems), extending the ability to calculate consensus rankings with guarantees in a decentralized setting, i.e., 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 consensus on collective rankings using classical rules (e.g. Borda, Copeland) 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 random gossip communication, allowing autonomous agents to compute global ranking consensus using only local interactions, without coordination or central authority. We provide rigorous convergence guarantees, including explicit rate bounds, for the Borda and Copeland consensus methods. Beyond these rules, we also provide a decentralized implementation of consensus according to the median rank rule and local Kemenization. Extensive empirical evaluations on various network topologies and real and synthetic ranking datasets demonstrate that our algorithms converge quickly and reliably to the correct ranking aggregation.

Problem

• decentralized ranking aggregation
• gossip algorithms
• Borda consensus
• Copeland consensus
• preference analysis

Innovation

• decentralized ranking aggregation
• gossip algorithms
• Borda consensus
• Copeland consensus
• distributed consensus