Privacy of vote from tallying authority in El Gamal Voting Schemes I've been reading this paper about ElGamal encryptions and its application in electronic voting:

http://www.win.tue.nl/~berry/papers/euro97.pdf

Section 2.3 talks about using Shamir secret sharing so that t-out-of-n authorities need to combine to decrypt an ElGamal ciphertext. This makes sense so that after multiplying the voters' individual commitments, authorities can combine to reveal the sum of the votes.

My question is, if this is the case, can the authorities not take advantage of this to decrypt individual voters' commitments since the commitments still use the same $g$ and $h$ values after all? Where does the security of the vote from the authority come from.

Section 3 talks about creating commitments using random values $b \in \{-1, 1\}$ and then posting another value $e \in \{-1, 1\}$ such that vote $= b \cdot e$, which I think might be where the security comes from, but does not expand further on this.

Any help is appreciated!
The random $b,e$ values would seem to allow the uniform randomisation of the message between $G$ and $G^{-1}$.

Also, while reading a technical article at this level, one can note the citing of sources [SK94,CFSY96] where the technique seems to have been first used and follow up those.