Generic modes of consensus formation in stochastic language dynamics

Abstract

We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are distinguished by the way agents handle variability in the language (i.e., multiple forms for the same meaning). The class of models includes as special cases two previously-studied models of language dynamics, the Naming Game, in which agents tend to standardise on variants they have encountered most frequently, and the Utterance Selection Model, in which agents tend to preserve variability by uniform sampling of a pool of utterances. We reduce the full complexities of the dynamics to a single-coordinate stochastic model which allows the probability and time taken for speakers to reach consensus on a single variant to be calculated for large communities. This analysis suggests that in the broad class of models considered, consensus is formed in one of three generic ways, according to whether agents tend to eliminate, accentuate or sample neutrally the variability in the language. These different regimes are observed in simulations of the full dynamics, and for which the simplified model in some cases makes good quantitative predictions. We use these results, along with comparisons with related models, to conjecture the likely behaviour of more general models, and further make use of empirical data to argue that in reality, biases away from neutral sampling behaviour are likely to be small.

36 pages; 22 eps figures; embarrassing sign error in v2 corrected; to appear J Stat Mech

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Cited by in corpus (9)

• Role of feedback and broadcasting in the naming game
• Consensus and ordering in language dynamics
• A gentle introduction to the minimal Naming Game
• Solution of the multi-state voter model and application to strong neutrals in the naming game
• Hierarchy of Scales in Language Dynamics
• Universal and non-universal features of the generalized voter class for ordering dynamics
• Using Complex Networks to Quantify Consistency in the Use of Words
• The statistics of fixation times for systems with recruitment
• Language change in a multiple group society