Opinion dynamics in two dimensions: domain coarsening leads to stable bi-polarization and anomalous scaling exponents

Abstract

We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity -moderate and extremist. When two interacting agents have the same orientation become extremists with persuasion probability p, while if they have opposite orientations become moderate with compromise probability q. These updating rules lead to the formation of same-opinion domains with a coarsening dynamics that depends on the ratio r = p/q. The population initially evolves to a centralized state for small r, where domains are composed by moderate agents and coarsening is without surface tension, and to a bi-polarized state for large r, where domains are formed by extremist agents and coarsening is driven by curvature. Consensus in an extreme opinion is finally reached in a time that scales with the population size N and r as τ ≃ r −1 ln N for small r and as τ ∼ r 2 N 1.64 for large r. Bi-polarization could be quite stable when the system falls into a striped state where agents organize into single-opinion horizontal, vertical or diagonal bands. An analysis of the stripes dynamics towards consensus allows to obtain an approximate expression for τ which shows that the exponent 1.64 is a result of the diffusion of the stripe interfaces combined with their roughness properties.

Role of voting intention in public opinion polarization

“…This would imply that polarization is quite stable in populations with narrow-minded individuals that only take into account its own opinion when interacting with others, reinforcing their previous believes and adopting more extreme viewpoints. This result is akin to that obtained in related models for opinion formation [11][12][13][14] that include a reinforcement mechanism by which pairs of individuals with the same opinion orientation (both in favor or both against a given political issue) are more likely to interact and become more extremists. Even though the propensity model studied in this article does not include this mechanism implicitly, it is able to capture the same phenomenology by implementing a simple interaction rule that consider pairwise interactions between individuals as independent of the opinion group they belong to.…”

“…(13) around the fixed point n * P by rewriting n 0 and n 2 as n 0 = n * P,0 + x 0 and n 2 = n * P,2 + x 2 , with 0 < |x 0 |, |x 2 | ≪ 1 and n * P,0 = n * P,2 = 1/(2 + ǫ) from Eq. (14). Expanding the resulting equations to first order in x 0 and x 2 we arrive to the following linear system:…”

“…This model is simple enough to be analytically tractable and is able to induce polarization without relying on the previous mentioned mechanisms, and by implementing a pairwise interaction rule that is independent on the opinion orientation, unlike the models studied in [13,14].…”

Bi-layer voter model: Modeling intolerant/tolerant positions and bots in opinion dynamics

“…Moreover, the introduction of personalized information [21], reinforcing the political orientation of an agent when its opinion changes, has shown to prevent global consensus for strong captured information change, showing the phenomena of strengthening political positions observed in many countries. This polarization behavior has also recently been explored through multistate voter models that include a mechanism of opinion reinforcement, which is a consequence of exchanging persuasive arguments [22][23][24][25]. Another implementation of the voter model has investigated the role of confidence in individuals by introducing two states per agent, its opinion, and its level of commitment to the opinion: unsure or tolerant and confident or intolerant [26].…”

Caracterización de procesos dinámicos sociales en redes bidimensionales y redes complejas multicapas

“…Durante el desarrollo de la presente Tesis Doctoral fueron publicados los resultados expuestos en el Capítulo 2 que se completa con los apéndices A y B[104], en el capítulo 3 junto a los apéndices C, D, E y F[105], y se encuentra en preparación otro trabajo relativo a los estudios detallados en el Capítulo 4.Apéndice A Análisis de la distancia media de ruptura de la interfase é∆x b ê Podemos obtener una idea del escaleo é∆x b ê Ä L 0.525 relacionando la distancia entre las interfases en el momento de ruptura con sus propiedades de rugosidad, como ilustramos en la Fig. 2.10(a).…”