The problem of online privacy is often reduced to individual decisions to hide or reveal personal information in online social networks (OSNs). However, with the increasing use of OSNs, it becomes more important to understand the role of the social network in disclosing personal information that a user has not revealed voluntarily: How much of our private information do our friends disclose about us, and how much of our privacy is lost simply because of online social interaction? Without strong technical effort, an OSN may be able to exploit the assortativity of human private features, this way constructing shadow profiles with information that users chose not to share. Furthermore, because many users share their phone and email contact lists, this allows an OSN to create full shadow profiles for people who do not even have an account for this OSN. We empirically test the feasibility of constructing shadow profiles of sexual orientation for users and non-users, using data from more than 3 Million accounts of a single OSN. We quantify a lower bound for the predictive power derived from the social network of a user, to demonstrate how the predictability of sexual orientation increases with the size of this network and the tendency to share personal information. This allows us to define a privacy leak factor that links individual privacy loss with the decision of other individuals to disclose information. Our statistical analysis reveals that some individuals are at a higher risk of privacy loss, as prediction accuracy increases for users with a larger and more homogeneous first- and second-order neighborhood of their social network. While we do not provide evidence that shadow profiles exist at all, our results show that disclosing of private information is not restricted to an individual choice, but becomes a collective decision that has implications for policy and privacy regulation.