Whomever is the holder record has the voting rights. If you gave your stock to someone to facilitate a short you lose your voting rights until that position is closed. You can read more about it here: https://www.investopedia.com/ask/answers/05/shortsalevotingr...
It looks like nesting got too deep, but for bkh, you are correct.
> In this case, they retain a fraction or none of their voting rights, I presume?
If you have a margin account and want to vote with your shares, you need to let your broker know prior to the vote, so they can be sure and not have your shares loaned out when they're figuring out everyone's voting shares.
Some time prior to 2010, I heard some heads rolled at my firm because such a request was screwed up for a major client, and they had fewer votes than expected for some important vote.
> If you gave your stock to someone to facilitate a short you lose your voting rights...
Individuals do not loan stock for shorting, generally. But they do sometimes have margin accounts (for unrelated reasons), and this allows the broker to loan their shares out without their knowledge. In this case, they retain a fraction or none of their voting rights, I presume?