Matching Theorem on Arranged Marriage Market
Source: Arranged Marriages under Transferable Utilities
When imagining a circumstance where the matching theorem needs to be applied, one may think about a good with several levels of quality matching to a group of consumers or matching apartments to people. A common theme in these examples is the inclusion of inanimate materialistic products however the matching theorem can also be applied to the marriage market. The concept and motivations of the matching stay consistent with these listed examples matching from one set to another while trying to maximize social welfare and minimize disparity.
In most analyses of marriage markets, only pairings where the decision was made by the individuals getting married are considered when there still exist numerous societies where this decision is solely the families of the individuals getting married. Instinctually, our minds gravitate to the developing world when hearing about arranged marriages but Pauline Morault, in her work Arranged Marriages under Transferable Utilities, does not fail to mention that even the upper classes of the Western world take part in this tradition. Morault further explains her paper includes family considerations like the number of siblings an individual has, the genders of those siblings, and the wealth of the family. It became important to include family in the factors behind a pairing as doing so changed what stable matches looked like.
In the new model considered by Morault, utility is shared with the family members of an individual. If we consider individual stability to be a maximization of utility surplus in a pairing then Morault notes individual stability must imply family stability. What she noticed about family-stable matches is that they can be inefficient and not be stable for the individuals, the cause of this being primarily coordination issues and the looser constraints present by families. It was shown that a family will accept a “poorer match for one of their children of this will benefit the whole family” (p. 22). These inefficient matches are further exacerbated by families varying in size and unequal gender distributions between families.
In class, we considered matching markets with prices and analyzed the social welfare, baseline, and disparity of each possible perfect match. However, in this paper a transferable utility framework where a certain group of people is split into families with no constraints on the number of sons and daughters each family contains. In this model, instead of maximizing welfare, families seek to maximize the utility of the family, which in Morault’s model is the summation of each family member’s utility. Here the union of the two individuals is considered to raise the value of both families, though not necessarily equally. With this, we see that matching pairs becomes much more complicated as there are now much more factors to finding the ‘best’ match. It can be assumed that the families and individuals consider some non-overlapping factors that further puts the valuations made by the individual versus the family at odds. The pairing maximizing family utility may not maximize the individuals’ utilities.
Morault concludes that the usual individual stability models used to evaluate marriage markets can’t be applied to societies where arranged marriages are still prevalent and offers this new model to understand the different outcomes of the shift in decision making.