"To influence the vote" means to try to persuade or sway people's decisions when they are voting, in order to get a specific outcome or result that benefits one's interests or agenda. Full definition
Competition between two presidential candidates may also influence voting in the European elections. (theconversation.com)
The results will have influenced the votes of those who shoot. (politics.co.uk)
He also takes out a 10 million dollar life insurance policy for his teenage daughter's benefit with an insurance representative who is influencing his vote on some impending insurance legislation. (homepages.sover.net)