  The question that how cultural variation emerges has drawn lots of interest
in sociological inquiry. Sociologists predominantly study such variation
through the lens of social contagion, which mostly attributes cultural
variation to the underlying structural segregation, making it epiphenomenal to
the pre-existing segregated structure. On the other hand, arguing culture
doesn't spread like a virus, an alternative called associative diffusion was
proposed, in which cultural transmission occurs not at the preference of
practices, but at the association between practices. The associative diffusion
model then successfully explains cultural variation without attributing it to a
segregated social structure. The contagion model and associative diffusion
model require different types of relationships and interactions to make
cultural transmission possible. In reality, both types of relationships exist.
In light of this concern, we proposed combining the two models with the
multilayer network framework. On one layer, agents casually observed the
behaviors of others, updating their belief about the association between
practices; on another layer, agents' preference of practices are directly
influenced by closed others. In the meantime, the constraint satisfaction
between preference and association is used to link the update of both, thereby
making each individual a coherent entity in terms of preference and
association. Using this approach, we entangle the effect of social contagion
and associative diffusion through multilayer networks. For the baseline, we
explore the model dynamics on three common network models: fully connected,
small-world, and scale-free. The results show nontrivial dynamics between the
two extremes of the contagion model and the associative diffusion model,
justifying our claim that it is necessary to consider the two models at the
same time.
