Out-of-the-box, there are few ways to influence how the other AIs vote. It's dependent almost entirely on the value in the <HowWouldAIVote></HowWouldAIVote> tag, and the arrangement of the voting options of any particular issue in the "UPIssues.xml" file, detailed below.
0 = Vote completely randomly.
1 = Vote larger numbered option if you're winning.
2 = Vote larger numbered option if you're losing.
3 = Vote larger numbered option if alignment is evil.
4 = Vote larger numbered option if alignment is good.
5 = Vote for your enemy, or randomly.
6 = Vote for player with whom you have best relations, or yourself.
7 = Vote for yourself if losing, or otherwise for player with whom you have best relations.
As you can see, proper arrangement of the voting options as well as choosing the correct AI voting scheme for each issue is essential. Even a slight mistake can cause serious problems.
That said, as one as already mentioned, leaving the UP is always an option, since out-of-the-box the UP is pretty much useless. I however, recommend testing your modding skills by trying to fix or improve the UP issues. I myself am doing this, or I will be after other efforts are completed. I'd like to make the UP something that is dangerous to abandon. But, we'll see.