[Paper Review] Decentralized Ranking Aggregation: Gossip Algorithms for Borda and Copeland Consensus

Anna Van Elst, Kerrian Le Caillec+2 more|arXiv (Cornell University)|Feb 26, 2026

Game Theory and Voting Systems0 citations

TL;DR

The paper develops and analyzes gossip-based decentralized algorithms to compute Borda and Copeland consensus rankings, with convergence guarantees and robustness considerations.

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.

Motivation & Objective

• Study how to achieve decentralized consensus on ranking aggregations when data is distributed across a network without a central server.
• Develop gossip-based algorithms to compute Borda and Copeland consensus using local interactions.
• Provide theoretical convergence guarantees and rate bounds for the proposed methods.
• Assess robustness to corrupted nodes and compare decentralized methods to centralized benchmarks.

Proposed method

• Use randomized gossip to estimate per-item scores (Borda scores and pairwise Copeland components) through local averaging.
• Decouple score estimation from final ranking by locally sorting estimated scores to obtain a consensus permutation.
• Prove convergence with exponential rates tied to the network spectral gap for Borda and Copeland aggregations.
• Extend to decentralized Footrule (median rank) and Local Kemenization as additional consensus rules.
• Provide empirical validation across network topologies and ranking datasets to demonstrate convergence and robustness.

(a) MSE of Borda/Footrule scores

Experimental results

Research questions

• RQ1 Can decentralized agents reach a correct Borda or Copeland consensus using only local communications?
• RQ2 What are the convergence rates and factors (e.g., network connectivity) that govern decentralized ranking consensus?
• RQ3 How robust are decentralized ranking methods to corrupted or adversarial inputs?
• RQ4 How do decentralized methods compare to centralized baselines in practice across different data-generating models?
• RQ5 What is the impact of incorporating local Kemenization or Footrule approaches in decentralization?

Key findings

• Gossip-based averaging yields consensus estimates that converge to the true Borda and Copeland rankings at exponential rates determined by the network’s spectral gap.
• Convergence guarantees hold under distinct score gaps and strict stochastic transitivity assumptions, with explicit rate bounds.
• Local Kemenization and decentralized Footrule methods extend the framework to robustness-focused and median-based consensus.
• Empirical experiments across network topologies and real/synthetic datasets validate fast and reliable convergence to correct rankings.
• Robustness analyses indicate varying resilience of Kemeny, Copeland, and Mallows-based scenarios to contamination.
• Theoretical and empirical results together support principled fully decentralized collective decision-making in distributed systems.

(b) MSE of pairwise scores