Network Fairness Ambivalence: When does social network capital mitigate or amplify unfairness?

Social networks inherit societal biases present across lines of gender, race, socioeconomic status, and other factors. Networks can structurally perpetuate unequal access to information and opportunities through homophilous dynamics. While there is substantial knowledge about inequity in the diffusion of opportunities in a network where nodes seek them from their immediate neighbors, much less is known when considering beyond that first hop. In this paper, we leverage recent mathematical analysis of network fairness to prove that enabling simple multi-hop dissemination can reduce inequity towards a minority group in the network as long as homophily is sufficiently weak. Otherwise, our necessary and sufficient condition proves that multi-hop dissemination strategies amplify the bias already found amongst considering direct neighbors. We empirically validate these results on four social network datasets as well as present an example of a key application of our findings with a scenario of individuals who leverage their personal network to seek job referrals. Our results suggest that online platforms designing algorithms to promote opportunities to multi-hop connections must carefully take into account network metrics measuring group size and homophily in order to avoid amplifying bias against marginalized groups on their platforms.