I fairly regularly run into situations where I fall a few votes short of diplomatic victory because one civ continues to abstain in their vote.
I have always figured they would be easier to turn than a civ voting for my rival, but I am not sure if there is a best way to sway them. I have tried being most generous to them in all sorts of ways - gold, trade goods, techs, and even a city once but none of them seem to work (whereas in real life they would probably be quite appreciative). One time I replayed the end of a scenario (which I won via space race) and managed to win diplomatically almost by ignoring them. One difference was that I sold them good and techs rather than giving them away.
Any tips?
The thing you need to notice is that certain things can only give you so much of a diplomatic bonus. Giving away techs/money/resources can only give you a maximum of +4 relations with that civ (Our trade relations have been fair and forthright). Sharing a religion can help a lot because you can get up to +8 for it, though from what I can tell some civs value it more than others, and the bonus will likely start smaller (+1 to +3) and then raise over time. There are a lot of long term bonuses as well that you dont get an immediate boost from, which include sharing open borders, maintaining resource trades, maintaining peace, and others. These ones take time to develop, and the bonus maxes out at +2 for most of them.
Sharing a favorite civic can be very tricky, and I usually dont worry about it unless I'm trying to get a last minute relations boost to secure someones vote (or help with a DoW). What you need to do is make sure that THEY are in that civic (or you wont get a relations boost for being in it), and make sure the civic you are switching out of isnt going to lose you a friendly relations with someone else. Again, the boost you get from this can be small for some civs (+1 even) and larger for others (max I've seen was +5, though I suspect it can go to +8 like religion), and I'm not completely sure on this last part, but I believe it raises over time. You can also consider switching into the civic and then bribing the other civ to switch into it. This requires a couple turns of planning in advance but its won me a diplo victory on more than one occasion.
"Our mutual military struggle bring us closer together" is also one you can use to secure a vote at the last minute, but of course requires very careful consideration before attempting it. You need to consider who you may take a relations hit with for declaring on that person ("You declared war on our friends"), and who you are trying to curry favor with. I haven't done any real studying of it, but it seems the warlike leaders (Shaka, Tokugawa) will give you a bigger relations boost than more peaceful leaders (Mansa Musa) for this. As above, this bonus has given me the diplo win with a last minute declaration, but in most games the diplomatic atmosphere wont allow for this kind of thing.
