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This paper describes a formal model for multiple privacy notions that apply to reputation systems and shows that, for certain classes of systems, very strong privacy notions are unachievable. In particular, it is shown that, systems where a user's reputation depends exclusively on the ratings he received, necessarily leak information about the relationship between ratings and reputations. In contrast, systems where a user's reputation depends both on the received ratings, and on the ratings received by others, potentially hide all information about this relationship. The paper concludes with guidelines for the construction of reputation systems that have the potential to retain high levels of privacy.