Conformity to continuous and discrete ordered traits

Models of conformity and anticonformity have typically focused on cultural traits with unordered variants, such as baby names, strategies (cooperate/defect), or the presence/absence of an innovation. There have been fewer studies of conformity to cultural traits with ordered variants, such as level of cooperation (low, medium, high) or proportion of time spent on a task (0% to 100%). In these studies of ordered cultural traits, conformity is defined as a preference for the mean trait value in a population even if no members of the population have variants near this mean; e.g., 50% of the population has variant 0 and 50% has variant 1, producing a mean of 0.5. Here, we introduce models of conformity to ordered traits, which can be either discrete or continuous. In these models, conformists prefer to adopt more popular cultural variants even if these variants are far from the population mean. To measure a variant's "popularity" in cases where no two individuals share precisely the same variant on a continuum, we introduce a metric called k-dispersal; this takes into account a variant's distance to its k closest neighbors, with more "popular" variants having lower distances to their neighbors. We demonstrate through simulations that conformity to ordered traits need not produce a homogeneous population, as has previously been claimed. Under some combinations of parameter values, conformity sustains substantial trait variation over many generations. Furthermore, anticonformity may produce a high level of polarization.