While experimental game theory has provided evidence that social norms can promote cooperation, the importance of normative conflict has received little attention so far. We present results from an experiment on the dynamics of normative conflict over the consideration of equality, equity, or efficiency for the distribution of joint earnings. Normative conflict is measured by the number of rejected offers in a dynamic bargaining game. We find that more alternative normative principles lead to more persistent normative conflict. Furthermore, we show that, in either simple or complex situations, the convergence towards a simple and widely shared norm is likely. In contrast, in moderately complex situations, convergence is unlikely and several equally reasonable norms co-exist.