Heterophily, Stable Matching, and Intergenerational Transmission in Cultural Evolution

We demonstrate that marital preferences, the marriage market, and intergenerational transmission mechanisms must be jointly considered to gain a more complete picture of cultural evolution. We characterize cultural processes in settings with different combinations of (i) homophilic and heterophilic marital preferences, (ii) men-optimal or women-optimal stable matching scheme, and (iii) familial, societal, and rational forces of intergenerational transmission. First, with perfect vertical transmission in homogamies and oblique transmission in heterogamies, the presence of even a small fraction of heterophilic proposers leads to complete cultural homogeneity; cultural heterogeneity arises only when proposers are all homophilic. Notably, a stable matching scheme that is optimal for a gender in the short run can lead to suboptimal outcomes for them in the long run. Second, when transmission in heterogamies incorporates Darwinian consideration, persistent or temporary cycles between cultural homogeneity and heterogeneity may arise. Third, with imperfect vertical transmission in homogamies, heterophilic preferences and heterogamies play a significant role in the determination of cultural distribution; cultural substitutability is neither sufficient nor necessary for cultural heterogeneity. Finally, we discuss our model's implications for matriarchal and patriarchal societies, the evolution of gender roles as well as cultural assimilation and identity formation of minorities and immigrants.