Let's assume 100 true shares out and each is shorted 10 times. Everyone votes and nobody holds paper certs. 600 shares are voted yes, and 400 shares are voted no.
The clearinghouse just reports to the company that 60 voted yes and 40 voted no. Nobody is the wiser... well, except for those who read the fine print.
That wouldn't seem horrible unless someone decided to, for example, short shares to themselves multiple times. ?
Not good, but in general practice probably not too distorting?