Social Network Systems (SNSs) are the predominant kind of web service around the world. They attract many users seeking popularity, entertainment and network building, along with ease of use. Most current SNSs are based on centralized designs, which are less likely to improve privacy since there is a single and central authority with exclusive administration control over user information. Many proposals have been introduced that work towards decentralizing the infrastructure support in order to enhance privacy in SNSs. However, designing decentralized social network systems (DSNS) driven by privacy is a hard task because privacy is impacted by most design choices. This paper proposes a multicriteria analysis grid designed to evaluate several properties of SNSs related to privacy trade-offs. Based on the analysis grid result, this paper also presents the application of lattice-based tools to classify and visualize social network systems in privacy-related hierarchies.