Impact of contrarians and intransigents in a kinetic model of opinion dynamics

In this work we study opinion formation on a fully-connected population participating of a public debate with two distinct choices, where the agents may adopt three different attitudes (favorable to either one choice or to the other, or undecided). The interactions between agents occur by pairs and are competitive, with couplings that are either negative with probability $p$ or positive with probability $1-p$. This bimodal probability distribution of couplings produces a behavior similar to the one resulting from the introduction of Galam’s contrarians in the population. In addition, we consider that a fraction $d$ of the individuals are intransigent, that is, reluctant to change their opinions. The consequences of the presence of contrarians and intransigents are studied by means of computer simulations. Our results suggest that the presence of inflexible agents affects the critical behavior of the system, causing either the shift of the critical point or the suppression of the ordering phase transition, depending on the groups of opinions intransigents belong to. We also discuss the relevance of the model for real social systems.

💡 Research Summary

In this paper the authors investigate a kinetic opinion‑formation model on a fully‑connected (mean‑field) population where each agent can hold one of three possible states: +1, –1, or 0 (undecided). Interactions occur in randomly chosen pairs; the influence of agent j on agent i is mediated by a coupling µij that can be either +1 (with probability 1–p) or –1 (with probability p). A negative coupling forces two agents that share the same opinion to become undecided, reproducing the effect of Galam’s contrarians without explicitly inserting a separate contrarian class.

A second ingredient is the presence of “inflexible” or “intransigent” agents. A fraction d of the population is designated as inflexible at the beginning of the simulation and never changes its opinion, regardless of the interaction rule. The authors consider three ways of assigning inflexibles: (i) uniformly at random, independent of the initial opinion; (ii) only among agents that initially hold an extreme opinion (±1); and (iii) only among agents that initially hold a specific opinion (e.g., only +1).

The dynamics proceeds as follows: at each elementary step a pair (i, j) is selected; if i is inflexible nothing happens; otherwise i updates according to
 oi(t + 1) = sgn