Analysis of a voter model with an evolving number of opinion states

TL;DR

This paper extends the classic voter model by incorporating spontaneous opinion innovation, analyzing how the interplay of innovation rate and network structure influences opinion diversity and steady-state outcomes.

Contribution

It introduces a novel innovation mechanism into the voter model, capturing the emergence of new opinions and analyzing its effects on opinion diversity.

Findings

Low innovation rates lead to consensus.

High innovation rates increase opinion diversity.

Network heterogeneity reduces the number of opinions.

Abstract

In traditional voter models, opinion dynamics are driven by interactions between individuals, where an individual adopts the opinion of a randomly chosen neighbor. However, these models often fail to capture the emergence of entirely new opinions, which can arise spontaneously in real-world scenarios. Our study introduces a novel element to the classic voter model: the concept of innovation, where individuals have a certain probability of generating new opinions independently of their neighbors' states. This innovation process allows for a more realistic representation of social dynamics, where new opinions can emerge and old ones may fade over time. Through analytical and numerical analysis, we find that the balance between innovation and extinction shapes the number of opinions in the steady state. Specifically, for low innovation rates, the system tends toward near-consensus, while higher innovation rates lead to greater opinion diversity. We also show that network structure influences opinion dynamics, with greater degree heterogeneity reducing the number of opinions in the system.