You don't need to trust a central authority. The vote is publicly auditable.
It is also in this case. And as I explained, I'm of the impression that you need a central authority for voting anyway (at least to specify who is allowed to vote, like a citizen registry). The only real need for the central authority in the blind signature scheme is for signing votes, which corresponds basically "only" to this function of voter registry.
If the central authority cheats, how would you know? With a blockchain, the evidence is in the inconsistency between the results the authority announces, and the results indicated by the blockchain. With a central authority that "keeps track that no-one votes twice", there's no way to know if the central authority is doing its job.
This is partially true (and may indeed be an advantage of the blockchain-based system, although I would still accept it if my government did the blind-signature thing). However, even in the system described by me (which is of course not my invention, but I don't find a good link at the moment) every participant can check that their vote was actually counted, and that not too many votes have been cast in total. It is true, though, that the authority could publish fake votes for those voters that don't exercise their right to vote (and that it could get away with forging votes if the voters don't check them). It needs active control by the voters, but the possibility is there to uncover any fraud attempts.