It is possible with a group signature scheme. The idea of group signature was proposed by David Chaum and Eugene van Heyst exactly for the scenario you described.
Citing from the abstract:
In this paper we present a new type of signature for a group of persons, called a group signature, which has the following properties:
- only members of the group can sign messages;
- the receiver can verify that it is a valid group signature, but cannot discover which group member made it;
- if necessary, the signature can be “opened”, so that the person who signed the message is revealed.
In Foundations of group signatures: Formal definitions, simplified requirements, and a construction based on general assumptions (Mihir Bellare, Daniele Micciancio, Bogdan Warinschi, Eurocrypt 03), a model was proposed with formal definitions of full anonymity and full traceability. Full anonymity means that signatures should not leak the identities of their signers, whereas full traceability means that no collusion of malicious users can produce a valid signature that cannot be traced to one of them. Later a formal model for dynamic group signature was defined in Foundations of Group Signatures: The Case of Dynamic Groups (Mihir Bellare, Haixia Shi, Chong Zhang, CT-RSA 05).
There are schemes based on random oracle model (e.g. Short Group Signatures, Dan Boneh, Xavier Boyen, Hovav Shacham, Crypto 2004) and in the standard model (e.g. Fully Anonymous Group Signatures without Random Oracles, Jens Groth, Asiacrypt 2007). Another desirable property is compactness, i.e. the signature size should be small with regard to the group size (logarithm or even constant) e.g. as in Groth's scheme.