Anonymous ranking is a kind of privacy-preserving ranking whereby each of the involved participants can correctly and anonymously get the rankings of his data. It can be utilized to solve many practical problems, such as anonymously ranking the students' exam scores. We investigate the issue of how quantum mechanics can be of use in maintaining the anonymity of the participants in multiparty ranking and present a series of quantum anonymous multiparty, multidata ranking protocols. In each of these protocols, a participant can get the correct rankings of his data and nobody else can match the identity to his data. Furthermore, the security of these protocols with respect to different kinds of attacks is proved.