I have not played GalCiv2 in a long time and did not play the expansions, so I apologize if this has already been improved or if I don't remember it correctly, but I remember wishing the United Planets played a bigger role in the game.  I think the biggest problem I had was that the player had no control over what votes would come up. I think another flaw was that it seemed like many of the votes would favor the race that won the vote, so every race voted for themselves.  I remember often giving my vote to another race to keep the most influential race from winning the vote, but it was disappointing that the votes were so predictable.

I think that there could be some kind of system for bringing proposals to a vote, like a race can try to bring a proposal to the United Planets, but a another race has to second it before the proposal can be voted on or maybe a majority of the races have to agree to bring it to a vote.  This would keep the most influential race from just running away with the game.  But now you are aware of what the next vote is and when it will happen (which if I remember correctly, you already did know when these votes would happen in GalCiv2).  Before the vote, you can discuss with other races (especially if you are playing multi-player) how you all should vote and even bribe for votes or offer your vote for a price. 

Since these would not be random proposals, they could be much more consequential than they have been in the past games and may give more reasons why a race would want to leave the untied planets.  For example, a race may keep getting sanctioned or all the other nations keep extending a peace resolution.  In this case, one of the races may choose that leaving is a better option at that point.

And, to take it a step further (but much more complicated), before that race just leaves the united planets, it could say "hey remove some of these restrictions or I am leaving" and the other nations might comply because it would be better to have some control over the race then no control.

To sum up though, I think 2 things

1) realistically, it just makes more sense that the proposals that we vote on are actually brought up by one of the races

2) I would like to see some of the races voting together and even surprise me (like I get three races to vote my way, but then three other nations team up and vote for my opponent and I still lose)