It would be beneficial (aka fun) for the AI players allied with you to hold a council on the eve of a vote to discuss their stance on the upcoming topic. There you could sway or be swayed to a particular line of thinking to ensure your collective votes push the issue yours (and your allies) direction.

Without knowing their stand, its not only unrealistic, but really leaves a huge question mark over what direction you should vote to better your stance.

Perhaps your spies (if placed) could also report on the probable vote of your enemies or non-allies.