Fairness and Consensus in an Asynchronous Opinion Model for Social Networks

Authors Jesús Aranda , Sebastián Betancourt , Juan Fco. Díaz , Frank Valencia



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Author Details

Jesús Aranda
  • Universidad del Valle, Colombia
Sebastián Betancourt
  • Universidad del Valle, Colombia
Juan Fco. Díaz
  • Universidad del Valle, Colombia
Frank Valencia
  • CNRS LIX, École Polytechnique de Paris, France
  • Pontificia Universidad Javeriana Cali, Colombia

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Jesús Aranda, Sebastián Betancourt, Juan Fco. Díaz, and Frank Valencia. Fairness and Consensus in an Asynchronous Opinion Model for Social Networks. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.7

Abstract

We introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled transition systems, henceforth called opinion transition systems (OTS), whose states represent the agents' opinions and whose actions are the edges of the influence graph. If a transition labeled (i,j) is performed, agent j updates their opinion taking into account the opinion of agent i and the influence i has over j. We study (convergence to) opinion consensus among the agents of strongly-connected graphs with influence values in the interval (0,1). We show that consensus cannot be guaranteed under the standard strong fairness assumption on transition systems. We derive that consensus is guaranteed under a stronger notion from the literature of concurrent systems; bounded fairness. We argue that bounded-fairness is too strong of a notion for consensus as it almost surely rules out random runs and it is not a constructive liveness property. We introduce a weaker fairness notion, called m-bounded fairness, and show that it guarantees consensus. The new notion includes almost surely all random runs and it is a constructive liveness property. Finally, we consider OTS with dynamic influence and show convergence to consensus holds under m-bounded fairness if the influence changes within a fixed interval [L,U] with 0 < L < U < 1. We illustrate OTS with examples and simulations, offering insights into opinion formation under fairness and dynamic influence.

Subject Classification

ACM Subject Classification
  • Theory of computation → Social networks
Keywords
  • Social networks
  • fairness
  • DeGroot
  • consensus
  • asynchrony

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