Opinion Update in a Subjective Logic Model for Social Networks
Mário S. Alvim, Sophia Knight, José C. Oliveira
TL;DR
The paper addresses modeling belief updates with uncertainty in social networks using subjective logic. It extends the Alvim–Knight–Valencia framework by incorporating multinomial opinions $\omega^{A}_{X}$ with uncertainty $u_X$ and a trust structure, and defines an update rule $\omega^{A[t+1]}_{X} = \omega^{A[t]}_{X} \oplus (\omega^{A}_{B} \otimes \omega^{B[t]}_{X})$ evaluated under cumulative, averaging, and weighted belief fusion. The key finding is that belief-fusion–based updates often fail properties like idempotence and weak convergence, though cumulative fusion can yield rich dynamics such as consensus, balanced-opposite states, or radicalization depending on initial conditions and trust; the Beta/Dirichlet mapping clarifies how evidence aggregates. This framework enables uncertainty-aware, non-binary opinion dynamics in networks and reveals interaction regimes beyond traditional polarization models, with practical relevance for understanding real-world information diffusion under uncertainty.
Abstract
Subjective Logic (SL) is a logic incorporating uncertainty and opinions for agents in dynamic systems. In this work, we investigate the use of subjective logic to model opinions and belief change in social networks. In particular, we work toward the development of a subjective logic belief/opinion update function appropriate for modeling belief change as communication occurs in social networks. We found through experiments that an update function with belief fusion from SL does not have ideal properties to represent a rational update. Even without these properties, we found that an update function with cumulative belief fusion can describe behaviors not explored by the social network model defined by Alvim, Knight, and Valencia (2019).