I finally got to paying more attention to what was being voted on, but after a few failed attempts to get the last few votes to drop to me (lavishing gifts of all sorts upon two small holdouts) - and losing an unexpected space race - I backtracked and just focused on winning a space race. Wouldn't you know it, but just a few turns before that victory the UN wised up and gave me a diplomatic victory with minimal attention to the matter.
One thing I had done, along the lines of what another poster said, was to invade a neighbor (ignoring them into declaring war) who as never going to vote for me and ate half their territory.