Opinion formation and distribution in a bounded-confidence model on various networks

Abstract

In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequential random pairwise encounters. To consider the heterogeneity of interactions in a population due to social influence, we study the Deffuant model on various network structures (deterministic synthetic networks, random synthetic networks, and social networks constructed from Facebook data) using several interaction mechanisms. We numerically simulate the Deffuant model and conduct regression analyses to investigate the dependence of the convergence time to equilibrium on parameters, including a confidence bound for opinion updates, the number of participating entities, and their willingness to compromise. We find that network structure and parameter values both have an effect on the convergence time, and for some network topologies, the convergence time undergoes a transition at a critical value of the confidence bound. We discuss the number of opinion groups that form at equilibrium in terms of a confidence-bound threshold for a transition from consensus to multiple-opinion equilibria.

Impact of temporal network structures on the speed of consensus formation in opinion dynamics

“…However, as observed in ref. [14], variations in the time for convergence to steady-state are small for ǫ > 0.5, since this typically consists of only one opinion group. We therefore expect that the conclusions of this paper apply also to models that include confidence bounds with ǫ > 0.5.…”

“…It was also modified to adaptive networks where the breaking and rewiring processes of links are introduced [11,3]. Recently, the Deffuant model was applied to empirical data sets [14]. Various generalizations include smoothing of so-called confidence bounds to avoid discontinuous jumps in opinion differences [15], as well as heterogeneous and time-dependent confidence bounds [16,17].…”

A model for the influence of media on the ideology of content in online social networks

“…, N + M }), and we take the ideology space to be continuous and bounded, such that x ∈ [−1, 1] d . We allow the ideology space to be d-dimensional, so we can be more nuanced than the typical choice in prior research of using d = 1 [44]. At time t, each account spreads content (perhaps with their own spin, as has been studied for memes using Facebook data [45]) that reflects its current ideology x t i .…”

“…In the present paper, we draw our bounded-confidence mechanism from the Hegselmann-Krause (HK) [33] and Deffuant [32,44] models of continuous opinion dynamics. Bounded-confidence updates are also related to the DeGroot-Friedkin (DF) model of social power [48].…”

Enhanced or distorted wisdom of crowds? An agent-based model of opinion formation under social influence

“…The possibility to reach consensus then depends on the value of (Lorenz 2007). To foster consensus, assumptions about the topology of social interactions (e.g., group interactions) (Meng et al 2018), hierarchical decisions (Perony et al 2013), the influence of in-groups (agents known from previous interactions) (Groeber et al 2009) can be taken into account.…”