Eur. Phys. J. B 71, 557-564 (2009)
https://doi.org/10.1140/epjb/e2009-00284-2

Consensus and ordering in language dynamics

¹ IFISC, Institut de Física Interdisciplinària i Sistemes Complexos (CSIC-UIB), Campus Universitat Illes Balears E, 07122 Palma de Mallorca, Spain
² Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
³ Dipartimento di Fisica, “Sapienza” Università di Roma, P.le A. Moro 2, 00185 Roma, Italy
⁴ Fondazione ISI, Viale S. Severo 65, 10133 Torino, Italy

Corresponding author: ^a xavi@ifisc.uib-csic.es

Received: 13 January 2009
Revised: 10 July 2009
Published online: 13 August 2009

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.