Marital preferences and stable matching in cultural evolution

Building on previous literature that examines the influence of intergenerational transmission in cultural evolution, we highlight the importance of the marriage market in the determination of cultural homogeneity (“melting pot”) versus heterogeneity (“diversity”). To do so, we characterize cultural evolutionary processes under different distributions of marital preferences and stable matching schemes. In our setting, cultural substitutability (Bisin and Verdier, 2001) is neither sufficient nor necessary for cultural heterogeneity. We introduce a new concept, elasticity of cultural substitution, to capture the degree of increase in vertical socialization efforts in response to minority population decline. With perfect or inelastic vertical transmission in homogamous families, cultural heterogeneity is sustained only if all proposers are homophilic or all members of a cultural group are homophilic. With imperfect vertical transmission in homogamous families, the presence of heterophilic agents may destabilize cultural heterogeneity, and the proportion of heterophilic agents and elasticity of cultural substitution determine whether cultural heterogeneity can be sustained. We discuss the model's implications for the long-lasting impact of temporary gender imbalance on cultural evolution as well as the cultural assimilation and preservation of minorities and immigrants under distinct governmental and religious attitudes toward intermarriage.