How can anonymity and uniqueness be achieved in the blockchain? How We Use Elliptic Curve Cryptography
At Follow My Vote, we use this technology to create votes. During the registration process, voters create two ECC key-pairs. The voter reveals her identity to a verifier, who certifies the first key-pair (the identity key-pair) as belonging to that voter, then the voter anonymously registers her second key-pair (the voting key-pair) as belonging to one of the identity keys, but the way this is done, no one can determine which identity key owns her voting key. She can then create transactions which state her votes on the contests in an election, and use her voting private key to sign those transactions. Once these are published, everyone participating in the Follow My Vote network can verify that the signature is valid and adjust the tally accordingly. This way the votes are public and anonymous, but each voter can verify that her vote was correctly recorded and counted. Furthermore, all participants can verify that none of the votes were tampered with by validating the signatures. In this way, Follow My Vote software performs transparent, end-to-end verifiable online elections without compromising on security or voter anonymity.

In particular, my doubt is about the selected phrase: &quot;no one can determine which identity key owns her voting key.&quot;
I think the best way to interpret the sentence is that the voter can cast her vote anonymously and she can also verify that her vote was tallied. 

This has less to do with the blockchain than just end-to-end verifiable elections. A simple example of such an election is the ThreeBallot system.