Wednesday, November 12, 2008

Fair marriages are impossible

Getting the right people married to each other is a very complex undertaking. Preferences are heterogeneous and information issues are important in marriage markets. Economists have been interested in finding ways to get Pareto equilibria in such markets, algorithms that can also be applied in other matching markets, says for medical school seats, medical residents, electricity markets and so on. The standard approach is the Gale and Shapley algorithm, wherein everybody ranks his/her best mate, and successive rounds of matches from the top down allow a Pareto optimum.

This algorithm has been challenged on various grounds, in particular because it does not deal with envy. One could imagine that introducing side payments may introduce fairness: if you lucked out on a potential mate, you are compensated by the lucky one. However, Bettina Klaus offers an explanation why side payments are not sufficient to gain fairness. The big stumbling block in the indivisibility of the matched objects. In other words, one cannot randomize or diversify.

Thus, even in the best of the worlds, marriages are unfair.

1 comment:

Anonymous said...

The point of these optimal marriage matching algorithms is moot. The work only if information is perfect, that is all men know all women and are able to rank them, and vice-versa. But we know reality is very far from that. And not everyone is going at the same time to the same bar.