I have a Sim that's the National Leader and I can at least go by what I have experienced:
-Promoting Policies helps to increase the success rate of securing votes
-Having a relationship up to Good Friends increases the success rate even more
-Be in a very good mood, ideally Confident
-Have very high Charisma skill, if not max
What I don't do is securing bribes, making empty promises, or debating politics on whatever Left or Right side, though I'm unsure how much that affects because they're usually more or less either more leaning to your views or not. Also, if you've found a Sim who has continually agreed to give you the vote, just keep using that Sim! Never hurts to ask the same Sim time and again anyway lol. My politician always ask his fiance to secure votes, and he's never said no yet.