There are many advantages to voting schemes in which voters rank all candidates in order, rather than just choosing their favourite. However, these schemes inherently suffer from a coercion problem when there are many candidates, because a coercer can demand a certain permutation from a voter and then check whether that permutation appears during tallying. In this paper, we solve this problem for the popular STV system, by constructing an algorithm for the verifiable tallying of encrypted votes. Our construction improves upon existing work because it extends to multiple-seat STV and reveals less information than other schemes.