Convergence Bounds for Language Evolution by Iterated Learning

Similarities between human languages are often taken as evidence of constraints on language learning. However, such similarities could also be the result of descent from a common ancestor. In the framework of iterated learning, language evolution converges to an equilibrium that is independent of its starting point, with the effect of shared ancestry decaying over time. Therefore, the central question is the rate of this convergence, which we formally analyze here. We show that convergence occurs in a number of generations that is O(n logn) for Bayesian learning of the ranking of n constraints or the values of n binary parameters. We also present simulations confirming this result and indicating how convergence is affected by the entropy of the prior distribution over languages.