In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs.