Consensus and ordering in language dynamics

TL;DR

This paper compares two social consensus models, the AB-model and the Naming Game, analyzing their dynamics, phase transitions, and interface behaviors in different network structures, revealing both similarities and key differences.

Contribution

It demonstrates the equivalence of the models in mean field approximation and explores their distinct behaviors when considering trust, network topology, and interface dynamics.

Findings

Models are equivalent in mean field approximation.

The Naming Game exhibits a consensus-polarization phase transition, absent in the AB-model.

The AB-model slows down interface diffusion compared to the Naming Game.

Abstract

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.