Fragmentation transitions in multi-state voter models

TL;DR

This paper analyzes fragmentation transitions in multi-opinion voter models, providing detailed analytical results for three opinions and showing how opinion reduction can preserve fragmentation points.

Contribution

It offers new analytical insights into opinion fragmentation in models with arbitrary opinions, extending beyond previous assumptions of equidistant opinions.

Findings

Analytical results for three-opinion fragmentation

Agent-based simulations confirm theoretical predictions

Opinion reduction can preserve fragmentation points

Abstract

Adaptive models of opinion formation among humans can display a fragmentation transition, where a social network breaks into disconnected components. Here, we investigate this transition in a class of models with arbitrary number of opinions. In contrast to previous work we do not assume that opinions are equidistant or arranged on a one-dimensional conceptual axis. Our investigation reveals detailed analytical results on fragmentations in a three-opinion model, which are confirmed by agent-based simulations. Furthermore, we show that in certain models the number of opinions can be reduced without affecting the fragmentation points.