Win-stay, lose-shift in language learning from peers.

Traditional language learning theory explores an idealized interaction between a teacher and a learner. The teacher provides sentences from a language, while the learner has to infer the underlying grammar. Here, we study a new approach by considering a population of individuals that learn from each other. There is no designated teacher. We are inspired by the observation that children grow up to speak the language of their peers, not of their parents. Our goal is to characterize learning strategies that generate "linguistic coherence," which means that most individuals use the same language. We model the resulting learning dynamics as a random walk of a population on a graph. Each vertex represents a candidate language. We find that a simple strategy using a certain aspiration level with the principle of win-stay, lose-shift does extremely well: stay with your current language, if at least three others use that language; otherwise, shift to an adjacent language on the graph. This strategy guarantees linguistic coherence on all nearly regular graphs, in the relevant limit where the number of candidate languages is much greater than the population size. Moreover, for many graphs, it is sufficient to have an aspiration level demanding only two other individuals to use the same language.