"Doing what others do" does not stabilize continuous norms

Differences in social norms are a key source of behavioral variation among human populations. It is widely assumed that a vast range of behaviors, even deleterious ones, can persist as long as they are locally common because deviants suffer coordination failures and social sanctions. Previous models have confirmed this intuition, showing that different populations may exhibit different norms even if they face similar environmental pressures or are linked by migration. Crucially, these studies have modeled norms as having a few discrete variants. Many norms, however, have a continuous range of variants. Here we present a mathematical model of the evolutionary dynamics of continuously varying norms and show that when the social payoffs of the behavioral options vary continuously the pressure to do what others do does not result in multiple stable equilibria. Instead, factors such as environmental pressure, individual preferences, moral beliefs, and cognitive attractors determine the outcome even if their effects are weak, and absent such factors populations linked by migration converge to the same norm. The results suggest that the content of norms across human societies is less arbitrary or historically constrained than previously assumed. Instead, there is greater scope for norms to evolve towards optimal individual or group-level solutions. Our findings also suggest that cooperative norms such as those that increase contributions to public goods might require evolved moral preferences, and not just social sanctions on deviants, to be stable.