Recent years have seen an increasing popularity of online collaborative systems like social networks and web-based collaboration platforms. Collaborative systems typically offer their users a digital environment in which they can work together and share resources and information. These resources and information might be sensitive and, thus, they should be protected from unauthorized accesses. Multi-party access control is emerging as a new paradigm for the protection of co-owned and co-managed resources, where the policies of all users involved in the management of a resource should be accounted for collaborative decision making. Existing approaches, however, only focus on the jointly protection of resources and do not address the protection of the individual user policies themselves, whose disclosure might leak sensitive information. In this work, we propose a privacy-preserving mechanism for the evaluation of multi-party access control policies, which preserves the confidentiality of user policies while remaining capable of making collaborative decisions. To this end, we design secure computation protocols for the evaluation of policies in protected form against an access query and realize such protocols using two privacy-preserving techniques, namely Homomorphic Encryption and Secure Functional Evaluation. We show the practical feasibility of our mechanism in terms of computation and communication costs through an experimental evaluation.