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While performing pure e-business transactions such as purchasing software or music, customers can act anonymously supported by, e.g., anonymous communication protocols and anonymous payment protocols. However, it is hard to establish trust relations among anonymously acting business partners. Anonymous reputation systems have been proposed to mitigate this problem. Schiffner et al. recently proved that there is a conflict between anonymity and reputation and they established the non-existence of certain privacy-preserving reputation functions. In this paper we argue that this relationship is even more intricate. First, we present a reputation function that deanonymizes the user, yet provides strong anonymity (SA) according to their definitions. However, this reputation function has no utility, i.e., the submitted ratings have no influence on the resulting reputation values. Second, we show that a reputation function having utility requires the system to choose new independently at random selected pseudonyms (for all users it has utility for) on every new rating as a necessary condition to provide strong anonymity according to the aforementioned definition. Since some persistence of pseudonyms is favorable, we present a more secure, but also more usable definition for anonymous reputation systems that allows persistency yet guaranties k-anonymity. We further present a definition for rating secrecy based on a threshold. Finally, we propose a practical reputation function, for which we prove that it satisfies these definitions.