In Civ 4, as I recall, you could trade for another civilization's vote in the U.N., but I can't seem to find that option in Civ 5. Are the only votes I can earn those of the city states?
Civilization – earn AI player’s votes for a diplomatic victory in Civ 5
civilization-5
Related Solutions
Although bwarner's answer was helpful as always, no one verified beyond "I think so" that puppet cities are affected by each of the civilization wide effects, so I did some testing and:
Yes, puppet cities are affected normally by all civilization-wide effects.
I can't verify that there are no exceptions, but I verified at least one of each of the things I was concerned about...
The Testing
Civilization Special Trait
I loaded up France on easy, and went about conquering. Japan fell, giving me Kyoto to play with. As soon as I conquered the city and took it as a puppet, it was producing 2 culture. This matches perfectly with France's ability, so CHECK!
More Test Setup
Having acquired my victim, I setup the test: social policy ready, golden-age ready, and wonder ready all on the same turn! (Save file available upon request, whenever I get around to it after that.)
Before
Social Policy
I enacted Liberty->Republic, which gives +1 production/city. That matches, so CHECK!
Golden Age
I already had culture working for me, so I started the golden age by enacting the social policy Piety->Reformation. Clearly shows an increase in both gold and production, CHECK!
World Wonder
If you take a look at all of my cities from the same turn, you can see Orleans is about to finish the Sistine Chapel, which gives +33% culture/city. I went to the next turn, and without any growth or buildings completing, the after shows increased culture on Kyoto. (Lyon also started with 7 culture and ended with 9 as well, so the rounding definitely matches.) CHECK!
Everything checks out. I suppose puppets really are just normal cities that you don't control. I would still love to hear if anyone finds any exceptions!
If you kill quite a number of units of a city state and/or keep trespassing on their territory enough to get your score very very low over an extended period of time, they eventually will be convinced that you are so evil it's not worth considering peaceful coexistence, so they will be in perpetual war with you. You will not be able to buy their friendship and relations will not heal by themselves over time.
Actually that doesn't mean too much, though. If you go near them, they'll attack you, and if you leave cities undefended near them, they'll capture those. Apart from that, they won't hunt you across the map and they won't make others hate you as well. If you just leave them alone now and make their area taboo to your units you can still get along with the other city states just fine.
You might choose to have one perpetual warring city-state next to your army outfitter because city-state units train your troops longer than barbarians do.
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Best Answer
The manual explicitly states that all AI civs will vote for themselves unless they have been liberated. So the only way to get them to vote for you is to have their capital be captured by another civ, then have you conquer it and give it back to them.