We highlight that convergence in repeated averaging models commonly used to study cultural traits or opinion dynamics is not equivalent to convergence in Markov chain settings if transition matrices are time-varying. We then establish a new proof for the convergence of cultural traits in the model of Panebianco (2014) correcting the existing proof. The new proof provides novel insights on the long-run outcomes for inessential individuals. We close with a discussion of conditions for convergence in repeated averaging models with time-varying transition matrices.
