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We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-01 Gregor Bankhamer , Petra Berenbrink , Felix Biermeier , Robert Elsässer , Hamed Hosseinpour , Dominik Kaaser , Peter Kling

We study distributed plurality consensus among $n$ nodes, each of which initially holds one of $k$ opinions. The goal is to eventually agree on the initially dominant opinion. We consider an asynchronous communication model in which each…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-17 Gregor Bankhamer , Robert Elsässer , Dominik Kaaser , Matjaž Krnc

We consider distributed plurality consensus in a complete graph of size $n$ with $k$ initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-02-23 Robert Elsässer , Tom Friedetzky , Dominik Kaaser , Frederik Mallmann-Trenn , Horst Trinker

We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-08-28 Luca Becchetti , Andrea Clementi , Emanuele Natale , Francesco Pasquale , Luca Trevisan

We address the self-stabilizing bit-dissemination problem, designed to capture the challenges of spreading information and reaching consensus among entities with minimal cognitive and communication capacities. Specifically, a group of $n$…

Multiagent Systems · Computer Science 2024-10-10 Niccolò D'Archivio , Robin Vacus

We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-06 Antoine El-Hayek , Robert Elsässer , Stefan Schmid

We consider \emph{plurality consensus} in a network of $n$ nodes. Initially, each node has one of $k$ opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the…

Data Structures and Algorithms · Computer Science 2016-02-04 Petra Berenbrink , Tom Friedetzky , Peter Kling , Frederik Mallmann-Trenn , Chris Wastell

We analyze the convergence of the $k$-opinion Undecided State Dynamics (USD) in the population protocol model. For $k$=2 opinions it is well known that the USD reaches consensus with high probability within $O(n \log n)$ interactions.…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-02-27 Talley Amir , James Aspnes , Petra Berenbrink , Felix Biermeier , Christopher Hahn , Dominik Kaaser , John Lazarsfeld

We study the Consensus problem among $n$ agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-18 Petra Berenbrink , Amin Coja-Oghlan , Oliver Gebhard , Max Hahn-Klimroth , Dominik Kaaser , Malin Rau

Communication noise is a common feature in several real-world scenarios where systems of agents need to communicate in order to pursue some collective task. In particular, many biologically inspired systems that try to achieve agreements on…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-03 Francesco d'Amore , Isabella Ziccardi

We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is "correct" with probability $\frac{1}{2}+\delta$ for some $\delta…

Computer Science and Game Theory · Computer Science 2025-08-12 Divyarthi Mohan , Pawel Pralat

In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems - \emph{binary majority consensus}, in the presence of probabilistic message loss. Using…

Information Theory · Computer Science 2022-03-09 Ran Tamir , Ariel Livshits , Yonatan Shadmi

We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise…

Discrete Mathematics · Computer Science 2015-07-28 Luca Becchetti , Andrea Clementi , Emanuele Natale , Francesco Pasquale , Riccardo Silvestri , Luca Trevisan

In several real \emph{Multi-Agent Systems} (MAS), it has been observed that only weaker forms of\emph{metastable consensus} are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-05 Francesco d'Amore , Andrea Clementi , Emanuele Natale

We present a tight analysis for the well-studied randomized 3-majority dynamics of stabilizing consensus, hence answering the main open question of Becchetti et al. [SODA'16]. Consider a distributed system of n nodes, each initially holding…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-05-17 Mohsen Ghaffari , Johannes Lengler

The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase…

Physics and Society · Physics 2012-08-31 R. Lambiotte , M. Ausloos

The phenomenon of opinion disagreement has been empirically observed and reported in the literature, which is affected by various factors, such as the structure of social networks. An important discovery in network science is that most…

Social and Information Networks · Computer Science 2026-04-03 Wanyue Xu , Yubo Sun , Mingzhe Zhu , Zuobai Zhang , Zhongzhi Zhang

We study the Undecided-State Dynamics (USD), a fundamental consensus process in which each vertex holds one of $k$ decided opinions or the undecided state. We consider both the gossip model and the population protocol model. Prior work…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-04 Colin Cooper , Frederik Mallmann-Trenn , Tomasz Radzik , Nobutaka Shimizu , Takeharu Shiraga

The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry…

Disordered Systems and Neural Networks · Physics 2009-11-07 Serge Galam

We study Plurality Consensus in the Gossip Model over a network of $n$ anonymous agents. Each agent supports an initial opinion or color. We assume that at the onset, the number of agents supporting the plurality color exceeds that of the…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-07-11 L. Becchetti , A. Clementi , E. Natale , F. Pasquale , R. Silvestri
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