I've played Liberte a couple times, and quite enjoyed it.
But... Especially toward the end of each turn, it's tough to keep track of which faction is ahead in each province. It's all there, face up on the table, but there are enough provinces that there's no way I can tally everything up quickly, even just for provinces where there's a clear majority.
So I just don't worry about the exact counts, and try to guess (well, except for royalist control of counterrevolution provinces, which I do keep track of).
That said, though it isn't really easy to count the election standings, it's easy enough -- and important enough -- that players sometimes do so. I think this sours the game for some of the people in the group, since they might play much better if they take the time to tally the totals, but also know that will slow down the game.
What would you experienced Liberte players suggest? Tell people not to tally votes in the middle of a turn? Use some bookkeeping trick to keep track of rough vote totals? Or are there any other good tricks to speed things along?