The first time I tried the diplomatic path, I lost. I didn't understand the way it worked. From then on, I haven't been too fond of it. However, in one recent game I had a very good reputation, so I decided to try it out. I didn't win the first vote (no one did), but won the second time around. To win, you not only have to have the most votes, but half or more of the civs must vote for you. So, if there are 8 civs voting, 3 vote for you, 1 for another, and the rest abstain, you will not win, despite having the most votes. But, you will not lose, either...the game goes on. Work on your reputation or pull off another path to victory. I still prefer the space ship path, but a diplomatic win can be cool.
-Dearnen