Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions

Abstract

We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudospectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduce the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an order parameter.

Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases

“…The latter is only needed just ''after a collision'', as usual in Kinetic Theory. This way, (35) with the addition approximation…”

“…Moreover, the adjustment proceeds if and only if the opinion difference is below a given threshold, the so-called coefficient of bounded confidence. This abruptly removal or hard cut-off in opinion space [35] defines the similarity between individuals and, together with the social influence mechanism, determines the tendency of individuals to associate with others (homophily). Interestingly, the DM describes an evolution of the system towards consensus if the bound of confidence is bigger than a critical value, otherwise the agents split into a finite number of groups or clusters within which individuals share the same opinion [36][37][38][39].…”

Approach to consensus in models of continuous-opinion dynamics: a study inspired by the physics of granular gases

“…Moreover, the adjustment proceeds if and only if the opinion difference is below a given threshold, the so-called coefficient of bounded confidence. This abruptly removal or hard cut-off in opinion space [32] defines the similarity between individuals and, together with the social influence mechanism, determines the tendency of individuals to associate with others (homophily). Interestingly, the DM describes an evolution of the system towards consensus if the bound of confidence is bigger than a critical value, otherwise the agents split into a finite number of groups or clusters within which individuals share the same opinion [33,34,35,36].…”