I was just thinking, why can't you bribe for votes? This would have an effect on both UP votes and senate votes.
Example: United Planets
In the diplomacy screen, you can trade your vote for the next election. Once this is done, it can't be taken back until you cast your vote for the species that trade for it. However, another race could come in and pay a larger sum for it(perhaps from the race that has it). You could also buy it back.
Example: Senate
You could offer some bc to a group, and if there is enough(higher values would be needed for larger groups), then most of the group would defect to your group. If it is too low, then they will reject you and your own party would defect partially. This would be calculated with a formula perhaps like so: Roll a number between 0 and BC÷100(round down), and if it is greater than the number of votes, then you succeed, and if not, then you get screwed.