On the evolution of individual preferences and family rules

We study how the distribution of an inherited trait evolves through marriage if couples are formed at random. If the matching occurs across the entire population, the variance of the trait tends to diminish, and the distribution converges to a common trait. If the matching is restricted to specific subpopulations, each of these converges to a different trait. This has implications for the consequences of immigration. Using a specific model where the trait is a parameter measuring a person's taste for receiving filial attention (a good without perfect market substitutes) in old age, we also show that it may be in a couple's interest to obey a rule requiring them to give specified amounts of the good to their respective parents. The matching is random in this model because preferences are private monitoring. In the long run, if the matching extends to the entire population, either everybody obeys the rule, or nobody does. In the interim, some do, and some do not. If the matching is restricted to specific ethnic or religious groups, the population will tend to break down into a number of sharply characterized subpopulations. That may undermine social cohesion and call for policy intervention.