An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks

Abstract

Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to studying the dynamics of opinion spread on networks is by examining bounded-confidence (BC) models, in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other opinions if they lie within some confidence bound of their own opinion. We extend the Deffuant--Weisbuch (DW) model, which is a well-known BC model, by studying opinion dynamics that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinion when they interact with a neighboring node and (2) break a connection with a neighbor based on an opinion tolerance threshold and then form a new connection to a node following the principle of homophily. This opinion tolerance threshold acts as a threshold to determine if the opinions of adjacent nodes are sufficiently different to be viewed as discordant. We find that our adaptive BC model requires a larger confidence bound than the standard DW model for the nodes of a network to achieve a consensus. Interestingly, our model includes regions with `pseudo-consensus' steady states, in which there exist two subclusters within an opinion-consensus group that deviate from each other by a small amount. We conduct extensive numerical simulations of our adaptive BC model and examine the importance of early-time dynamics and nodes with initial moderate opinions for achieving consensus. We also examine the effects of coevolution on the convergence time of the dynamics.

Modeling algorithmic bias: simplicial complexes and evolving network topologies

“…The present implementation of a rewiring mechanism is just one way to incorporate the fact that users hardly know their neighbors' state before interacting with them; however, a mechanism considering only the set of agents with opinions within the confidence threshold would be a useful comparison to the present model. Moreover, to better understand the role of homophily in the sense of friendship formation and its relation to the online social network environment, the role of the recommender system-and therefore algorithmic bias-a biased mechanism simulating "link recommendations" could be implemented-as in Kan et al (2021). Finally, the importance of social interactions in opinion formation is undeniable.…”

“…Without considering the algorithmic bias in the choice of the interacting peer, our work is similar to Kozma and Barrat (2008); Kan et al (2021). In Kozma and Barrat (2008) the process of rewiring works in the same fashion as in the present work, however, every time the rewiring option is chosen over the standard DW-model update rule, the old link (i, j) is broken and a new link (i, z) is formed towards a random nonneighboring agent, even if this agent's opinion is beyond i ′ s confidence threshold.…”

“…In Kozma and Barrat (2008) the process of rewiring works in the same fashion as in the present work, however, every time the rewiring option is chosen over the standard DW-model update rule, the old link (i, j) is broken and a new link (i, z) is formed towards a random nonneighboring agent, even if this agent's opinion is beyond i ′ s confidence threshold. Even in Kan et al (2021) the rewiring process has a different formulation diverging from the proposed one due to the following specificities: (a) at iteration, a set M of discordant edges is rewired and then a set K of edges undergoes the process of opinion update (i.e., Fig. 1 A schematic illustration of the rewiring step under bounded confidence.…”

“…Not only do network topologies evolve, but often this evolution is co-dependent on the dynamic process taking place over the networks, such as opinion exchange (McPherson et al 2001). For this reason, recent efforts focus on studying opinion dynamics on dynamic/adaptive networks (Sasahara et al 2019;Kan et al 2021;Holme and Newman 2006;Iñiguez et al 2009) also in the context of the Deffuant-Weisbuch and other bounded confidence models (Kozma and Barrat 2008;Kan et al 2021;Sasahara et al 2019), describing the effects of the evolution of the underlying network structure on the final state of the population and explaining the effects of the opinion exchange on the structure topology.…”

Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise

“…Using computer simulations and computational analysis, opinion dynamics models can be used as a tool for understanding social mechanisms, uncovering social interaction patterns and exploring influences of various factors on e.g. group formation and opinion consensus [6,7,3,8]. Furthermore, mathematical description of models is a starting point that enables the use of analytical tools.…”