There is nothing that prevents an online voting system from having a truly secret ballot. There is a class of algorithms[0] designed to compute a verifiable result from private inputs without revealing those inputs. One of the major applications of them being researched is voting.[1][2][3]

[0] http://en.wikipedia.org/wiki/Secure_multi-party_computation

[1] https://eprint.iacr.org/2014/075

[2] http://arxiv.org/abs/1502.07469

[3] https://www.iacr.org/cryptodb/data/paper.php?pubkey=2203