We present new cryptographic protocols for multi-authority secret ballot elections that guarantee privacy, robustness, and univer- sal verifiability. Application of some novel techniques, in particular the construction of witness hiding/indistinguishable protocols from Cramer, Damgård and Schoenmakers, and the verifiable secret sharing scheme of Pedersen, reduce the work required by the voter or an authority to a linear number of cryptographic operations in the population size (com- pared to quadratic in previous schemes). Thus we get significantly closer to a practical election scheme.