Stable matchings with correlated Preferences

The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many contexts, going back to Donald Knuth in the 1970s. In this paper, we consider a family of distributions defined by the Mallows permutations and show that with high probability the number of stable matchings for these preferences is exponential in the number of people.