Günter J. Hitsch, Ali Hortaçsu, and Dan Ariely have a paper about online dating and matching forthcoming in the AER: Matching and Sorting in Online Dating.
"Using a novel data set from an online dating site, we first estimate mate preferences and then use the classic Gale-Shapley algorithm to predict matching outcomes. Online dating exists to facilitate the search for a partner. Our results suggest that the particular site that we study leads to approximately efficient matching outcomes (within the set of stable matches), and that search frictions are mostly absent. Hence, the site appears to be efficiently designed."
Their dataset allows them to look at all the clicks and messages of a subset of participants. So they can see which profiles people look at, and whom they choose to contact. This allows them to form estimates about preferences (on the assumption that if you browse two profiles and contact one of them, you prefer the one you contacted.) And they can observe when email addresses or phone numbers are mutually exchanged, which gives them their proxy for matches.
They compare the matchings they see both to marriages in the population at large (from Census data), and to stable matchings obtained by running the deferred acceptance algorithm, using the estimated preferences. They write:
"We saw that both actual marriages and the predicted matches from the Gale-Shapley model exhibit strong intra-ethnicity sorting patterns. However, even in the absence of search frictions it is not obvious whether same-race preferences alone cause sorting within ethnicity groups: because other attributes, such as income and education, are correlated with race, preferences over these other attributes could lead to intra-ethnicity sorting as well. To investigate what fraction of the predicted endogamy patterns is driven by same-race preferences, we remove these preferences from the utility specification and simulate the corresponding stable matches. Tables 10 and 11, panel (IV), show that intra-ethnicity sorting is strongly diminished, although small degrees of endogamy remain. These results suggest that racial sorting is mostly due to the same-race preferences; preferences for non-race attributes can not quantitatively account for the small fraction of marriages across different ethnic groups."