Noisy continuous-opinion dynamics

Abstract

We study the Deffuant et al model for continuous-opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending on a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order–disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The master equation analysis is compared with direct Monte Carlo simulations. We find that the master equation and the Monte Carlo simulations do not always agree due to finite-size-induced fluctuations that we analyze in some detail.

Random Deviations Improve Micro–Macro Predictions: An Empirical Test

“…First, more theoretical and empirical work on the conditions of stochastic instability is needed in order to understand better why and when the stochastic component of individual behavior alters collective dynamics. Crucial methodological tools to analyze the stochastic stability of social systems (Foster and Young 1990;Freidlin and Wentzell 2012) have been developed, and their usefulness has been demonstrated on social processes such as the evolution of conventions and norms (Young 2015(Young , 1993, the spread of innovation (Montanari et al 2010;Young 2011), the emergence of hierarchies (Axtell et al 2000), the polarization of opinions (Mäs et al 2010;Pineda et al 2009), and residential segregation (van de Rijt et al 2009). Empirical studies are needed to test whether stochastic models outperform deterministic theories also in these contexts.…”

Towards representing human behavior and decision making in Earth system models – an overview of techniques and approaches

“…The exact type of these deviations affects model outcomes and can introduce a source of diversity into models of social influence (Mäs et al, 2010;Pineda et al, 2009;Kurahashi-Nakamura et al, 2016). For instance, some models of continuous opinion dynamics include deviations as Gaussian noise, i.e., random values drawn from a normal distribution.…”

“…In other contexts, deviations are better modeled by uniformly distributed noise, assuming that big deviations are as likely as small ones. This can help to explain, for instance, the emergence and stability of subgroups with different opinions that do not emerge in settings with Gaussian noise 5 (Pineda et al, 2009).…”

Emerging Cohesion and Individualization in Collective Action: A Co-Evolutive Approach

“…Pineda and coauthors proposed a new version of Deffuant's bounded-confidence model where noise is used to model individuals' free will [28]. Specifically, in that model agents' were given the opportunity (with a certain probability) of changing their opinions to a randomly selected position in the whole opinion space.…”

“…On one side, it is independent of the social context of the opinion holder (as in Ref. 28). On the other hand, in accordance with [22], it is defined by a normal distribution since small opinion changes are much more likely than large ones.…”