Votes are encrypted using the additive variant of ElGamal. I am also using ECElgamal. The idea is that to vote for a particular candidate, you set your message as one of the following $v$ calculated below.
One problem is that if the voter sends a vote not specified in the valid set of $v$'s, then the resulting sum of $v$'s would affect the tallying of votes. For example, if you vote using $2\times2^0$, you are able to vote to candidate 1 $2$ times which not ideal. Or $2\times2^m$ to vote for candidate 2 twice.
How would one verify that the vote that is recorded (which is encrypted) is in one of the valid $v_i$ without decrypting the ciphertext of the vote or showing $v_i$?