Group membership with unique anonymous claims
A paper was published in 2015 describing a scheme called Anonize to do just that.

It appears to be constructed around a specially designed Non-Interactive Zero-Knowledge Proof of Knowledge (NIZKPoK) protocol used by clients. 

First, a registration is made, whereby a client sends a commitment to a seed of a pseudo-random function. Sent back to it by the Server is the Server's signature on that commitment and the client's id, which becomes that client's master token. Then the client uses the seed to generate a single-use token. Finally, to submit a response the client has to prove by NIZK that it knows some master token, a survey conductor's signature authorizing some client to go through the survey, and that it indeed computed the single-use token by the seed it knows.

It's notable that the scheme actually makes it possible to conduct multiple ad-hoc surveys on a single server, without giving the server's operator an opportunity to track clients across multiple surveys. That is achieved by using a survey id, which is different for every survey, to generate single use tokens. A client can, on the other hand, only generate one single-use token for each survey id, which means it will only be able to submit one answer.

A usable online implementation can be found here and the development reference implementation is hosted over here.