This certainly is not my bailiwick, but my first thoughts are that if the stock is vested, they won't have voting rights, nor even ownership of those shares until they vest.
What I don't know is who "owns" the shares (and that's your question too). Are they owned by the people, but the unvested shares just receive no vote?
Again, there are just thoughts and by no means purport to be an answer, right or wrong.