Generic modes of consensus formation in stochastic language dynamics
(January 2009)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.