Random Matching Markets with Correlated Preferences

TL;DR

This paper demonstrates that in large matching markets with correlated preferences, stable matchings tend to be assortative, making the average rankings of partners similar across genders with high probability.

Contribution

It introduces a correlation-based characterization that guarantees assortative matching in large markets, extending understanding of stable matchings under preference correlation.

Findings

Preferences with weak correlation lead to assortative matchings.

Men's and women's average rankings become asymptotically equivalent.

High probability of assortative matching as market size grows.

Abstract

In the Gale-Shapley model of two-sided matching, it is well known that for generic preferences, the outcomes for each side can vary dramatically in the male-optimal vs. female-optimal stable matchings. In this paper, we show that under a widely used characterization of similarity in rankings, even a weak correlation in preferences guarantees assortative matching with high probability as the market size tends to infinity. It follows that the men's average ranking of women and the women's average ranking of men are asymptotically equivalent in all stable matchings with high probability, as long as the market imbalance is not too extreme.